Thu, 21 Aug 2008 15:04:41 BST CiteULike: Tag elasticity http://www.citeulike.org/tag/elasticity CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/weeks/article/1676566 <i>Physical Review Letters, Vol. 96, No. 18. (2006)</i><br /><br />We directly probe the microscopic structure, connectivity, and elasticity of colloidal gels using confocal microscopy. We show that the gel is a random network of one-dimensional chains of particles. By measuring thermal fluctuations, we determine the effective spring constant between pairs of particles as a function of separation; this is in agreement with the theory for fractal chains. Long-range attractions between particles lead to freely rotating bonds, and the gel is stabilized by multiple connections among the chains. By contrast, short-range attractions lead to bonds that resist bending, with dramatically suppressed formation of loops of particles. Microscopic Structure and Elasticity of Weakly Aggregated Colloidal Gels AD Dinsmore V Prasad IY Wong DA Weitz doi:10.1103/PhysRevLett.96.185502 Physical Review Letters, Vol. 96, No. 18. (2006) 2007-09-19T16:41:52-00:00 2006 Physical Review Letters 96 18 APS colloidal-gel colloids confocal depletion elasticity journal-club pmma http://www.citeulike.org/user/weeks/article/1567407 <i>Physical Review Letters, Vol. 97, No. 26. (2006)</i><br /><br />We use confocal microscopy to visualize individual particles near the colloidal glass transition. We identify the most slowly-relaxing particles and show that they form spatially correlated clusters that percolate across the sample. In supercooled fluids, the largest cluster spans the system on short time scales but breaks up on longer time scales. In contrast, in glasses, a percolating cluster exists on all accessible time scales. Using molecular dynamics simulation, we show that these clusters make the dominant contribution to the bulk elasticity of the sample. Contribution of Slow Clusters to the Bulk Elasticity Near the Colloidal Glass Transition Jacinta Conrad Param Dhillon Eric Weeks David Reichman David Weitz doi:10.1103/PhysRevLett.97.265701 Physical Review Letters, Vol. 97, No. 26. (2006) 2007-08-15T16:26:46-00:00 2006 Physical Review Letters 97 26 APS colloids confocal elasticity glass pmma slow-particles http://www.citeulike.org/user/tubart/article/1374594 <i>Tire Science and Technology, Vol. 33, No. 4. (2005), pp. 227-238.</i><br /><br />The objective of this paper is to investigate a class of general tire models that provides results suitable for usage in vehicle dynamics. Tire models currently used for vehicle dynamic analyses are overly simplistic (springs, a spring and damper combination or semi-elastic substance) or based on curve fits of experimental data. In contrast, the tire models used by major tire companies are extremely complex with solutions possible only by finite element analysis. Between these two extremes exists the potential for an elasticity based shell theory tire model. Micro-mechanics and composite laminate theories provide an integrated approach to the macroscopic behavior of the tire carcass and the tread support plies. This methodology has the capability of including centrifugal and friction forces. Finite difference methods are applied that produce reliable and accurate solutions of the tire response. An Advanced Shell Theory Based Tire Model D Bozdog WW Olson doi:10.2346/1.2174345 Tire Science and Technology, Vol. 33, No. 4. (2005), pp. 227-238. 2007-06-09T17:23:53-00:00 2005 Tire Science and Technology 33 4 227 238 TIRSOC analytical difference elasticity finite method model shell theory tire http://www.citeulike.org/user/tsjipko/article/1155256 <i>J Biomech Eng, Vol. 127, No. 2. (April 2005), pp. 229-236.</i><br /><br />Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape. Mechanics of curved plasma membrane vesicles: resting shapes, membrane curvature, and in-plane shear elasticity. T Kosawada K Inoue GW Schmid-Schönbein J Biomech Eng, Vol. 127, No. 2. (April 2005), pp. 229-236. 2007-03-12T11:47:04-00:00 2005 J Biomech Eng 0148-0731 127 2 229 236 caveolae elasticity tension theoretical http://www.citeulike.org/user/softsimu/article/2397070 <i>Physical Review E, Vol. 53, No. 3. (March 1996), 2670.</i><br /><br />Phase separation within the lipid bilayer of vesicles can lead to the formation of domains that affect the equilibrium shape of these vesicles. As a result of the competition between the bending energy of the bilayer and the line energy of the domain boundaries; the domains induce the formation of buds if their size is sufficiently large. This phenomenon of domain-induced budding is studied both for freely adapting and for fixed volume. The phase diagrams show that the constraint on the volume acts against the budding process but will in general not suppress it. In many situations; domain-induced budding leads to limit shapes for which the bud consists of a closed sphere that is connected to the ‘‘mother’’ vesicle by an infinitesimal neck. This neck is characterized by a general and simple neck condition for the mean curvature of the membrane segments adjacent to the neck. Budding also occurs if the Gaussian bending energy is taken into account. The effect of the Gaussian curvature energy is to change the structure and the stability of those shapes that exhibit small necks. © 1996 The American Physical Society. Shape transformations of vesicles with intramembrane domains Frank Jülicher Reinhard Lipowsky doi:10.1103/PhysRevE.53.2670 Physical Review E, Vol. 53, No. 3. (March 1996), 2670. 2008-02-19T03:14:44-00:00 1996 Physical Review E 53 3 2670 American Physical Society elasticity vesicles http://www.citeulike.org/user/softsimu/article/2298265 <i>Biophys. J., Vol. 79, No. 1. (1 July 2000), pp. 328-339.</i><br /><br />Micropipette pressurization of giant bilayer vesicles was used to measure both elastic bending kc and area stretch KA moduli of fluid-phase phosphatidylcholine (PC) membranes. Twelve diacyl PCs were chosen: eight with two 18 carbon chains and degrees of unsaturation from one double bond (C18:1/0, C18:0/1) to six double bonds per lipid (diC18:3), two with short saturated carbon chains (diC13:0, diC14:0), and two with long unsaturated carbon chains (diC20:4, diC22:1). Bending moduli were derived from measurements of apparent expansion in vesicle surface area under very low tensions (0.001-0.5 mN/m), which is dominated by smoothing of thermal bending undulations. Area stretch moduli were obtained from measurements of vesicle surface expansion under high tensions (>0.5 mN/m), which involve an increase in area per molecule and a small[---]but important[---]contribution from smoothing of residual thermal undulations. The direct stretch moduli varied little (< +/-10%) with either chain unsaturation or length about a mean of 243 mN/m. On the other hand, the bending moduli of saturated/monounsaturated chain PCs increased progressively with chain length from 0.56 x 10[-]19 J for diC13:0 to 1.2 x 10[-]19 J for diC22:1. However, quite unexpectedly for longer chains, the bending moduli dropped precipitously to ~0.4 x 10[-]19 J when two or more cis double bonds were present in a chain (C18:0/2, diC18:2, diC18:3, diC20:4). Given nearly constant area stretch moduli, the variations in bending rigidity with chain length and polyunsaturation implied significant variations in thickness. To test this hypothesis, peak-to-peak headgroup thicknesses hpp of bilayers were obtained from x-ray diffraction of multibilayer arrays at controlled relative humidities. For saturated/monounsaturated chain bilayers, the distances hpp increased smoothly from diC13:0 to diC22:1 as expected. Moreover, the distances and elastic properties correlated well with a polymer brush model of the bilayer that specifies that the elastic ratio (kc/KA)1/2 = (hpp [-] ho)/24, where ho [approx] 1 nm accounts for separation of the headgroup peaks from the deformable hydrocarbon region. However, the elastic ratios and thicknesses for diC18:2, diC18:3, and diC20:4 fell into a distinct group below the correlation, which showed that poly-cis unsaturated chain bilayers are thinner and more flexible than saturated/monounsaturated chain bilayers. Effect of Chain Length and Unsaturation on Elasticity of Lipid Bilayers W Rawicz KC Olbrich T Mcintosh D Needham E Evans Biophys. J., Vol. 79, No. 1. (1 July 2000), pp. 328-339. 2008-01-28T16:22:05-00:00 2000 Biophys. J. 79 1 328 339 cardiolipin elasticity membranes http://www.citeulike.org/user/softsimu/article/2152932 <i>Physical Review B, Vol. 49, No. 14. (1 April 1994), 9453.</i><br /><br />A simple mechanical model of planar fibrous materials with mesoscopic disorder is introduced and analyzed. In this scalar model a shear modulus controls the stress transfer in the transverse direction. The system is studied using the effective medium approximation and computer simulations; the comparison between them is quite favorable. In the disorder-controlled regime the stress-strain relation; the number of broken cells at the onset of crack propagation; and the length of the final crack scale with the system size as L 2 ; L 1.7 ; and L ; respectively. The mechanical properties are controlled by the interplay between disorder and shear modulus; which is studied in detail. Fracture in mesoscopic disordered systems MEJ Karttunen KJ Niskanen K Kaski doi:10.1103/PhysRevB.49.9453 Physical Review B, Vol. 49, No. 14. (1 April 1994), 9453. 2007-12-20T20:17:44-00:00 1994 Physical Review B 49 14 9453 American Physical Society elasticity fibers fibrous-materials fracture paper http://www.citeulike.org/user/softsimu/article/2096718 <i>Physical Review Letters, Vol. 98, No. 25. (2007), 258103.</i><br /><br />The behavior of the bending modulus of bilayers in lamellar phases was studied by Small Angle X-ray Scattering technique for various nonionic CiEj surfactants. The bilayers are either unswollen and dispersed in water or swollen by water and dispersed in dodecane. For unswollen bilayers, the values of decrease with both an increase in the area per surfactant molecule and in the polar head length. They increase when the aliphatic chain length increases at constant area per surfactant molecule. Whereas for water-swollen membranes, the values of decrease as the content of water increases converging to the value of the single monolayer bending modulus. Such a behavior results from the decoupling of the fluctuations of the two surfactant membrane monolayers. Our results emphasize the determinant contribution of the surfactant conformation to Molecular Origin of Model Membrane Bending Rigidity Erol Kurtisovski Nicolas Taulier Raymond Ober Marcel Waks Wladimir Urbach doi:10.1103/PhysRevLett.98.258103 Physical Review Letters, Vol. 98, No. 25. (2007), 258103. 2007-12-12T03:53:19-00:00 2007 Physical Review Letters 98 25 258103 APS elasticity membranes http://www.citeulike.org/user/skoch3/article/2010110 <i>Biophys. J., Vol. 93, No. 12. (15 December 2007), 4099.</i><br /><br />10.1529/biophysj.107.117572 The Great Hunt For Extra Compliance Jan Liphardt doi:10.1529/biophysj.107.117572 Biophys. J., Vol. 93, No. 12. (15 December 2007), 4099. 2007-11-29T04:28:29-00:00 2007 Biophys. J. 93 12 4099 biophysics dna elasticity wlc http://www.citeulike.org/user/skoch3/article/1911136 <i>Biophys. J. (31 August 2007), biophysj.107.112995.</i><br /><br />The worm-like chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters, the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm-7.03 microm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length pwlc depended on L; even for moderately long DNA molecules (L = 1300 nm), the apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the "finite worm-like chain (FWLC)," to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of pwlc on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of pfwlc on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules. 10.1529/biophysj.107.112995 Elasticity of short DNA molecules: theory and experiment for contour lengths of 0.6-7 microm Yeonee Seol Jinyu Li Philip Nelson Thomas Perkins MD Betterton doi:10.1529/biophysj.107.112995 Biophys. J. (31 August 2007), biophysj.107.112995. 2007-11-13T22:07:22-00:00 2007 Biophys. J. biophysj.107.112995 biophysics dna elasticity wlc http://www.citeulike.org/user/skennedy/article/2638498 <i>Power Systems, IEEE Transactions on, Vol. 18, No. 2. (2003), pp. 520-527.</i><br /><br />This tutorial paper discusses some aspects of electricity markets from the perspective of the demand-side. It argues that increasing the short-run price elasticity of the demand for electrical energy would improve the operation of these markets. It shows, however, that enhancing this elasticity is not an easy task. The tools that consumers and retailers of electrical energy need to participate more actively and effectively in electricity markets are discussed. The paper also describes how consumers of electricity can take part in the provision of power system security. Demand-side view of electricity markets DS Kirschen doi:10.1109/TPWRS.2003.810692 Power Systems, IEEE Transactions on, Vol. 18, No. 2. (2003), pp. 520-527. 2008-04-07T18:44:45-00:00 2003 Power Systems, IEEE Transactions on 18 2 520 527 demand elasticity electricity market price response http://www.citeulike.org/user/skennedy/article/2642331 <i>Power Systems, IEEE Transactions on, Vol. 15, No. 2. (2000), pp. 612-617.</i><br /><br />As electricity markets are liberalized, consumers become exposed to more volatile electricity prices and may decide to modify the profile of their demand to reduce their electricity costs. This paper analyzes the effect that the market structure can have on the elasticity of the demand for electricity. It then describes how the consumers' behavior can be modeled using a matrix of self- and cross-elasticities. It is shown how these elasticities can be taken into consideration when scheduling generation and setting the price of electricity in a pool based electricity market. These concepts are illustrated using a 26-generator system Factoring the elasticity of demand in electricity prices DS Kirschen G Strbac P Cumperayot de Paiva doi:10.1109/59.867149 Power Systems, IEEE Transactions on, Vol. 15, No. 2. (2000), pp. 612-617. 2008-04-08T17:13:47-00:00 2000 Power Systems, IEEE Transactions on 15 2 612 617 demand elasticity electricity matrix price http://www.citeulike.org/user/simone/article/440241 <i>Biophys J, Vol. 80, No. 1. (January 2001), pp. 505-515.</i><br /><br />Fluctuations about the native conformation of proteins have proven to be suitably reproduced with a simple elastic network model, which has shown excellent agreement with a number of different properties for a wide variety of proteins. This scalar model simply investigates the magnitudes of motion of individual residues in the structure. To use the elastic model approach further for developing the details of protein mechanisms, it becomes essential to expand this model to include the added details of the directions of individual residue fluctuations. In this paper a new tool is presented for this purpose and applied to the retinol-binding protein, which indicates enhanced flexibility in the region of entry to the ligand binding site and for the portion of the protein binding to its carrier protein. Anisotropy of fluctuation dynamics of proteins with an elastic network model. AR Atilgan SR Durell RL Jernigan MC Demirel O Keskin I Bahar Biophys J, Vol. 80, No. 1. (January 2001), pp. 505-515. 2005-12-17T10:31:48-00:00 2001 Biophys J 0006-3495 80 1 505 515 elasticity http://www.citeulike.org/user/rodney/article/2295784 <i>Science, Vol. 271 (March 1996), pp. 1835-1837.</i><br /><br />Single linear DNA molecules were bound at multiple sites at one extremity to a treated glass cover slip and at the other to a magnetic bead. The DNA was therefore torsionally constrained. A magnetic field was used to rotate the beads and thus to coil and pull the DNA. The stretching force was determined by analysis of the Brownian fluctuations of the bead. Here, the elastic behavior of individual lambda DNA molecules over-and underwound by up to 500 turns was studied. A sharp transition was discovered from a low to a high extension state at a force of ~0.45 piconewtons for underwound molecules and at a force of ~3 piconewtons for overwound ones. These transitions, probably reflecting the formation of alternative structure in stretched coiled DNA molecules, might be relevant for DNA transcription and replication. The Elasticity of a Single Supercoiled DNA Molecule TR Strick JF Allemand D Bensimon A Bensimon V Croquette Science, Vol. 271 (March 1996), pp. 1835-1837. 2008-01-28T02:17:45-00:00 1996 Science 271 1835 1837 dna elasticity magnetic supercoiled tweezers http://www.citeulike.org/user/rodney/article/1988270 <i>Proceedings of the National Academy of Science, Vol. 101 (May 2004), pp. 7600-7605.</i><br /><br />The shell of bacteriophages protects the viral DNA during host-to-host transfer and serves as a high-pressure container storing energy for DNA injection into a host bacterium. Here, we probe the mechanical properties of nanometer-sized bacteriophage 29 shells by applying point forces. We show that empty shells withstand nanonewton forces while being indented up to 30% of their height. The elastic response varies across the surface, reflecting the arrangement of shell proteins. The measured Young's modulus (1.8 GPa) is comparable with that of hard plastic. We also observe fatigue and breakage of capsids after probing them repetitively. These results illustrate the mechanoprotection that viral shells provide and also suggest design principles for nanotechnology. Bacteriophage capsids: Tough nanoshells with complex elastic properties IL Ivanovska PJ de Pablo B Ibarra G Sgalari FC Mackintosh JL Carrascosa CF Schmidt GJL Wuite Proceedings of the National Academy of Science, Vol. 101 (May 2004), pp. 7600-7605. 2007-11-26T20:23:02-00:00 2004 Proceedings of the National Academy of Science 101 7600 7605 bacteriophage capsids elasticity nanoshells http://www.citeulike.org/user/rodney/article/1512027 <i>Physical Review Letters, Vol. 95, No. 15. (2005)</i><br /><br />Using laser tweezers, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with tangential surface anchoring. The interactions overcome the Brownian motion when the interparticle separation rp is less than 3 particle diameters. The particles attract when the angle between rp and the uniform far-field director n^0 is between 0° and 70° and repel when 75°90°. The particles aggregate in chains directed at 30° to n^0 and, at higher concentrations, form complex kinetically trapped structures. Elasticity-Mediated Self-Organization and Colloidal Interactions of Solid Spheres with Tangential Anchoring in a Nematic Liquid Crystal II Smalyukh OD Lavrentovich AN Kuzmin AV Kachynski PN Prasad doi:10.1103/PhysRevLett.95.157801 Physical Review Letters, Vol. 95, No. 15. (2005) 2007-07-29T22:15:27-00:00 2005 Physical Review Letters 95 15 APS colloidal crystal elasticity liquid nematic self-assembly sphere tangential http://www.citeulike.org/user/paulschlesinger/article/2842680 <i>Biophys. J., Vol. 94, No. 12. (15 June 2008), pp. 4725-4736.</i><br /><br />Bilayers composed of phosphatidylcholine (PC), sphingomyelin (SM), and cholesterol (CHOL) are commonly used as systems to model the raft-lipid domain structure believed to compartmentalize particular cell membrane proteins. In this work, micropipette aspiration of giant unilamellar vesicles was used to test the elasticities, water permeabilities, and rupture tensions of single-component PC, binary 1:1 PC/CHOL, and 1:1 SM/CHOL, and ternary 1:1:1 PC/SM/CHOL bilayers, one set of measurements with dioleoyl PC (DOPC; C18:1/C18:1 PC) and the other with stearoyloleoyl PC (SOPC; C18:0/C18:1 PC). Defining the elastic moduli (KA), the initial slopes of the increase in tension (sigma) versus stretch in lipid surface area (alphae) were determined for all systems at low (15degreesC) and high (32-33degreesC) temperatures. The moduli for the single-component PC and binary phospholipid/CHOL bilayers followed a descending hierarchy of stretch resistance with SM/CHOL > SOPC/CHOL > DOPC/CHOL > PC. Although much more resistant to stretch than the single-component PC bilayers, the elastic response of vesicle bilayers made from the ternary phospholipid/CHOL mixtures showed an abrupt softening (discontinuity in slope), when immediately subjected to a steady ramp of tension at the low temperature (15degreesC). However, the discontinuities in elastic stretch resistance at low temperature vanished when the bilayers were held at [~]1 mN/m prestress for long times before a tension ramp and when tested at the higher temperature 32-33degreesC. The elastic moduli of single-component PC and DOPC/CHOL bilayers changed very little with temperature, whereas the moduli of the binary SOPC/CHOL and SM/CHOL bilayers diminished markedly with increase in temperature, as did the ternary SOPC/SM/CHOL system. For all systems, increasing temperature increased the water permeability but decreased rupture tension. Concomitantly, the measurements of permeability exhibited a prominent correlation with the rupture tension across all the systems. Together, these micromechanical tests of binary and ternary phospholipid/CHOL bilayers demonstrate that PC hydrocarbon chain unsaturation and temperature are major determinants of the mechanical and permeation properties of membranes composed of raft microdomain-forming lipids. 10.1529/biophysj.107.121731 Elasticity, Strength, and Water Permeability of Bilayers that Contain Raft Microdomain-Forming Lipids W Rawicz BA Smith TJ Mcintosh SA Simon E Evans doi:10.1529/biophysj.107.121731 Biophys. J., Vol. 94, No. 12. (15 June 2008), pp. 4725-4736. 2008-05-28T20:32:14-00:00 2008 Biophys. J. 94 12 4725 4736 aspiration elasticity permeability pipette rafts rawicz08pdf http://www.citeulike.org/user/ozzy11111/article/599345 <i>Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 25-28. (1 May 2006), pp. 3224-3246.</i><br /><br />We develop the a posteriori error estimation of mixed hp-version discontinuous Galerkin finite element methods for nearly incompressible elasticity problems in two space dimensions. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders, and are independent of the locking parameter. A series of numerical experiments are presented which demonstrate the performance of the proposed error estimator within an automatic hp-adaptive refinement procedure. An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity Paul Houston Dominik Schotzau Thomas Wihler doi:10.1016/j.cma.2005.06.012 Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 25-28. (1 May 2006), pp. 3224-3246. 2006-04-25T08:27:07-00:00 2006 Computer Methods in Applied Mechanics and Engineering 195 25-28 3224 3246 elasticity numerics http://www.citeulike.org/user/ozzy11111/article/2984742 <i>SIAM Review, Vol. 37, No. 4. (1995), pp. 491-511.</i> Korn's Inequalities and Their Applications in Continuum Mechanics CO Horgan SIAM Review, Vol. 37, No. 4. (1995), pp. 491-511. 2008-07-10T12:02:55-00:00 1995 SIAM Review 37 4 491 511 SIAM elasticity numerics http://www.citeulike.org/user/ozzy11111/article/2945108 <i>Math Med Biol, Vol. 24, No. 3. (1 September 2007), pp. 327-345.</i><br /><br />Previous approaches to modelling the large deformation of breast tissue, as occurs, e.g. in imaging using magnetic resonance imaging or mammography, include using linear elasticity and pseudo-non-linear elasticity, in which case the non-linear deformation is approximated by a series of small linear isotropic deformations, with the (constant) Young's modulus of each linear deformation an exponential function of the total non-linear strain. In this paper, these two approaches are compared to the solution of the full non-linear elastic problem for tissue with an exponential relationship between stress and strain. Having formulated each model and related the coefficients between the models, numerical simulations are performed on a block of incompressible material. These demonstrate that the simpler models may not be appropriate even in the case of modelling deformations of the human breast under gravity. 10.1093/imammb/dqm006 Non-linear modelling of breast tissue Jonathan Whiteley David Gavaghan Jonathan Chapman Michael Brady doi:10.1093/imammb/dqm006 Math Med Biol, Vol. 24, No. 3. (1 September 2007), pp. 327-345. 2008-06-30T14:34:41-00:00 2007 Math Med Biol 24 3 327 345 elasticity http://www.citeulike.org/user/norris/article/1885764 <i>Mathematics and Mechanics of Solids, Vol. 9, No. 2. (1 April 2004), pp. 131-139.</i><br /><br />Conditions are obtained for the incremental shear modulus to be positive for small simple shear superposed on a pure homogeneous deformation of an elastic material, the direction and plane of shear being parallel to a principal direction and principal plane respectively Results are obtained for an isotropic elastic material and for a transversely isotropic elastic material in which the axis of rotational symmetry is in a principal direction of the pure homogeneous deformation. For an isotropic material, it is shown that the BakerEricksen condition on the strain- energy function follows from the assumption that the incremental shear modulus is positive. A number of further conditions that have been proposed are shown to be unacceptable. 10.1177/1081286504042589 Restrictions on the Strain-Energy Function for an Elastic Material Ronald Rivlin doi:10.1177/1081286504042589 Mathematics and Mechanics of Solids, Vol. 9, No. 2. (1 April 2004), pp. 131-139. 2007-11-08T19:10:05-00:00 2004 Mathematics and Mechanics of Solids 9 2 131 139 elasticity http://www.citeulike.org/user/norris/article/1137271 <i>Journal of Elasticity, Vol. V66, No. 2. (1 December 2002), pp. 159-169.</i> On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector Spaces CS Jog doi:10.1023/A:1021253906202 Journal of Elasticity, Vol. V66, No. 2. (1 December 2002), pp. 159-169. 2007-03-02T22:31:13-00:00 2002 Journal of Elasticity V66 2 159 169 anisotropy elasticity http://www.citeulike.org/user/norris/article/1885758 <i>Mathematics and Mechanics of Solids, Vol. 9, No. 2. (1 April 2004), pp. 121-129.</i><br /><br />The relation is established between the constitutive equations for the stress in an isotropic elastic material based on strain-energy functions that are functions of the right Cauchy-Green strain matrix and the right stretch matrix. It is shown that results to problems obtained on the basis of the latter can be simply obtained from those derived on the basis of the former. 10.1177/1081286504042588 A Note on the Constitutive Equation for an Isotropic Elastic Material Ronald Rivlvn doi:10.1177/1081286504042588 Mathematics and Mechanics of Solids, Vol. 9, No. 2. (1 April 2004), pp. 121-129. 2007-11-08T19:08:24-00:00 2004 Mathematics and Mechanics of Solids 9 2 121 129 elasticity http://www.citeulike.org/user/norris/article/1885697 <i>Mathematics and Mechanics of Solids, Vol. 10, No. 2. (1 April 2005), pp. 145-154.</i><br /><br />The concepts of frame indifference and relative frame indifference are discussed critically in the context of materials with memory. It is shown that frame indifference implies relative frame indifference and relative frame indifference implies frame indifference if and only if the material is isotropic. 10.1177/1081286505036314 Frame Indifference and Relative Frame Indifference RS Rivlin doi:10.1177/1081286505036314 Mathematics and Mechanics of Solids, Vol. 10, No. 2. (1 April 2005), pp. 145-154. 2007-11-08T18:46:36-00:00 2005 Mathematics and Mechanics of Solids 10 2 145 154 elasticity http://www.citeulike.org/user/norris/article/1885632 <i>Mathematics and Mechanics of Solids, Vol. 11, No. 2. (1 April 2006), pp. 113-122.</i><br /><br />Frame indifference is intimately related to the idealization, in conventional continuum mechanics, of the surface on which the surface forces act as a two-dimensional continuum devoid of mass. In the kinetic theory of gases, the surface is effectively a layer with thickness of the order of magnitude of the mean free path. The calculated pressure matrix contains a frame dependent term that represents the Coriolis forces that emerge in this layer when the applied forces are transformed from a fixed to a rotating reference frame. 10.1177/1081286506063135 Some Thoughts on Frame Indifference Ronald Rivlin doi:10.1177/1081286506063135 Mathematics and Mechanics of Solids, Vol. 11, No. 2. (1 April 2006), pp. 113-122. 2007-11-08T18:24:56-00:00 2006 Mathematics and Mechanics of Solids 11 2 113 122 elasticity http://www.citeulike.org/user/norris/article/1144230 <i>Computational Mechanics, Vol. V1, No. 1. (1 March 1986), pp. 3-9.</i> Some aspects of the variational principles problem in elasticity E Reissner doi:10.1007/BF00298634 Computational Mechanics, Vol. V1, No. 1. (1 March 1986), pp. 3-9. 2007-03-06T17:19:03-00:00 1986 Computational Mechanics V1 1 3 9 elasticity variational http://www.citeulike.org/user/norris/article/1780952 <i>Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 58, No. 2. (30 March 2007), pp. 309-317.</i><br /><br />Abstract.  In this note we assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular. The elasticity of elasticity K Rajagopal doi:10.1007/s00033-006-6084-5 Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 58, No. 2. (30 March 2007), pp. 309-317. 2007-10-17T18:40:47-00:00 2007 Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 58 2 309 317 elasticity http://www.citeulike.org/user/norris/article/2099015 <i>Journal of Elasticity, Vol. 89, No. 1. (17 December 2007), pp. 5-154.</i><br /><br />Abstract  The Stroh formalism is a powerful and elegant mathematical method developed for the analysis of the equations of anisotropic elasticity. The purpose of this exposition is to introduce the essence of this formalism and demonstrate its effectiveness in both static and dynamic elasticity. The equations of elasticity are complicated, because they constitute a system and, particularly for the anisotropic cases, inherit many parameters from the elasticity tensor. The Stroh formalism reveals simple structures hidden in the equations of anisotropic elasticity and provides a systematic approach to these equations. This exposition is divided into three chapters. Chapter 1 gives a succinct introduction to the Stroh formalism so that the reader could grasp the essentials as quickly as possible. In Chapter 2 several important topics in static elasticity, which include fundamental solutions, piezoelectricity, and inverse boundary value problems, are studied on the basis of the Stroh formalism. Chapter 3 is devoted to Rayleigh waves, for long a topic of utmost importance in nondestructive evaluation, seismology, and materials science. There we discuss existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves through the Stroh formalism. Stroh Formalism and Rayleigh Waves Kazumi Tanuma doi:10.1007/s10659-007-9117-1 Journal of Elasticity, Vol. 89, No. 1. (17 December 2007), pp. 5-154. 2007-12-12T14:48:15-00:00 2007 Journal of Elasticity 89 1 5 154 elasticity http://www.citeulike.org/user/norris/article/1551703 <i>Mathematics and Mechanics of Solids, Vol. 10, No. 2. (1 April 2005), pp. 167-181.</i><br /><br />Constitutive equations for the back stress in amorphous glassy polymers based on extended forms of the non-Gaussian James--Guth 3-chain and Arruda--Boyce 8-chain models of rubber elasticity are derived from the extended Wu and van der Giessen non-Gaussian full-network model. A simple and invariant constitutive equation for the back stress tensor is then derived from the Wu and van der Giessen model by an average-stretch approximation. Although the average-stretch model of the full-network amorphous microstructure is more general than other chain cell models, the constitutive equation is the same as the 8-chain back stress relation. Back stress equations for a class of extended phenomenological models, including the Gent material model, are described. 10.1177/1081286505036316 Constitutive Equations for the Back Stress in Amorphous Glassy Polymers Millard Beatty doi:10.1177/1081286505036316 Mathematics and Mechanics of Solids, Vol. 10, No. 2. (1 April 2005), pp. 167-181. 2007-08-10T13:31:03-00:00 2005 Mathematics and Mechanics of Solids 10 2 167 181 elasticity polymers http://www.citeulike.org/user/norris/article/1598550 <i>Journal of Elasticity, Vol. 22, No. 2. (1 December 1989), pp. 185-191.</i> Derivatives of the principal invariants of a second-order tensor Guo Zhong-Heng doi:10.1007/BF00041110 Journal of Elasticity, Vol. 22, No. 2. (1 December 1989), pp. 185-191. 2007-08-28T13:01:19-00:00 1989 Journal of Elasticity 22 2 185 191 elasticity http://www.citeulike.org/user/norris/article/1598546 <i>Journal of Elasticity, Vol. 21, No. 1. (1 February 1989), pp. 117-120.</i> A note on maximum orthogonal shear stress and shear strain M Hayes doi:10.1007/BF00040937 Journal of Elasticity, Vol. 21, No. 1. (1 February 1989), pp. 117-120. 2007-08-28T12:58:51-00:00 1989 Journal of Elasticity 21 1 117 120 elasticity http://www.citeulike.org/user/norris/article/1598544 <i>Journal of Elasticity, Vol. 21, No. 3. (1 June 1989), pp. 317-320.</i><br /><br />The title's result is proved by reduction to the corresponding representation theorem for linear isotropic vector-valued mappings of a vector argument. A concise proof of the representation theorem for linear isotropic tensor-valued mappings of a skew argument Guo Zhong-Heng P Podio-Guidugli doi:10.1007/BF00045782 Journal of Elasticity, Vol. 21, No. 3. (1 June 1989), pp. 317-320. 2007-08-28T12:57:37-00:00 1989 Journal of Elasticity 21 3 317 320 elasticity http://www.citeulike.org/user/norris/article/1598539 <i>Journal of Elasticity, Vol. 17, No. 2. (1 January 1987), pp. 183-187.</i><br /><br />It is shown that, whenever the residual stress does not vanish, the response function delivering the Piola-Kirchhoff stress in terms of the deformation gradient may be genuinely linear, and yet independent of the observer; moreover, an explicit representation formula for such a function is obtained. The Piola-Kirchhoff stress may depend linearly on the deformation gradient P Podio-Guidugli doi:10.1007/BF00043023 Journal of Elasticity, Vol. 17, No. 2. (1 January 1987), pp. 183-187. 2007-08-28T12:47:29-00:00 1987 Journal of Elasticity 17 2 183 187 elasticity http://www.citeulike.org/user/norris/article/1598538 <i>Journal of Elasticity, Vol. 17, No. 1. (1 January 1987), pp. 75-83.</i><br /><br />A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the deformation is supported only by shear tractions. The second relation is established for a thin-walled cylinder under combined extension, inflation and torsion. Each material element of the cylinder undergoes the same local homogeneous deformation of shear superposed on triaxial extension. The properties of this deformation are used to establish a relation between pressure, twisting moment, angle of twist and current dimensions when no axial force is applied to the cylinder. It is shown that these relations also apply for a mixture of a nonlinear isotropic solid and a fluid. New universal relations for nonlinear isotropic elastic materials KR Rajagopal Alan Wineman doi:10.1007/BF00042450 Journal of Elasticity, Vol. 17, No. 1. (1 January 1987), pp. 75-83. 2007-08-28T12:46:10-00:00 1987 Journal of Elasticity 17 1 75 83 elasticity http://www.citeulike.org/user/norris/article/895918 <i>Journal of Elasticity, Vol. V14, No. 3. (1984), pp. 329-336.</i> On the derivative of the square root of a tensor and Guo's rate theorems Anne Hoger Donald Carlson doi:10.1007/BF00041141 Journal of Elasticity, Vol. V14, No. 3. (1984), pp. 329-336. 2006-10-13T19:30:24-00:00 1984 Journal of Elasticity V14 3 329 336 elasticity http://www.citeulike.org/user/norris/article/895917 <i>Mathematics and Mechanics of Solids, Vol. 9, No. 5. (1 October 2004), pp. 543-553.</i><br /><br />Previous work on representing the rotation and stretch tensors, their time derivatives and their gradients with respect to the deformation gradient tensor is reviewed and some new results are presented. The correspondence between rates and gradients leads to a unification and clarification of previous results and to new representations of the gradients. 10.1177/1081286504038674 Derivatives of the Rotation and Stretch Tensors MM Carroll doi:10.1177/1081286504038674 Mathematics and Mechanics of Solids, Vol. 9, No. 5. (1 October 2004), pp. 543-553. 2006-10-13T19:27:38-00:00 2004 Mathematics and Mechanics of Solids 9 5 543 553 elasticity http://www.citeulike.org/user/norris/article/1598530 <i>Journal of Elasticity, Vol. 17, No. 2. (1 January 1987), pp. 113-121.</i><br /><br />A class of universal relations for isotropic elastic materials is described by the tensor equationTB = BT. This simple rule yields at most three component relations which are the generators of many known universal relations for isotropic elasticity theory, including the well-known universal rule for a simple shear. Universal relations for four families of nonhomogeneous deformations known to be controllable in every incompressible, homogeneous and isotropic elastic material are exhibited. These same universal relations may hold for special compressible materials. New universal relations for a homogeneous controllable shear, a nonhomogeneous shear, and a variable extension are derived. The general universal relation for an arbitrary isotropic tensor function of a symmetric tensor also is noted. A class of universal relations in isotropic elasticity theory Millard Beatty doi:10.1007/BF00043019 Journal of Elasticity, Vol. 17, No. 2. (1 January 1987), pp. 113-121. 2007-08-28T12:44:10-00:00 1987 Journal of Elasticity 17 2 113 121 elasticity http://www.citeulike.org/user/norris/article/1598525 <i>Journal of Elasticity, Vol. 16, No. 2. (1 June 1986), pp. 221-224.</i> On the derivatives of the principal invariants of a second-order tensor Donald Carlson Anne Hoger doi:10.1007/BF00043588 Journal of Elasticity, Vol. 16, No. 2. (1 June 1986), pp. 221-224. 2007-08-28T12:41:14-00:00 1986 Journal of Elasticity 16 2 221 224 elasticity http://www.citeulike.org/user/norris/article/894258 <i>International Applied Mechanics, Vol. V40, No. 1. (1 January 2004), pp. 70-76.</i> Evolution Equations for Plane Cubically Nonlinear Elastic Waves JJ Rushchitsky C Cattani doi:10.1023/B:INAM.0000023812.41455.63 International Applied Mechanics, Vol. V40, No. 1. (1 January 2004), pp. 70-76. 2006-10-12T13:46:54-00:00 2004 International Applied Mechanics V40 1 70 76 cubic elasticity nonlinear http://www.citeulike.org/user/norris/article/1604848 <i>Journal of Elasticity, Vol. 29, No. 1. (1 October 1992), pp. 1-84.</i><br /><br />The nonlinear elastic response of a class of materials for which the deformation is subject to an internal material constraint described in experiments by James F. Bell on the finite deformation of a variety of metals is investigated. The purely kinematical consequences of the Bell constraint are discussed, and restrictions on the full range of compatible deformations are presented in geometrical terms. Then various forms of the constitutive equation relating the stress and stretch tensors for an isotropic elastic Bell material are presented. Inequalities on the mechanical response functions are introduced. The importance of these in applications is demonstrated in several examples throughout the paper. Deformations of an elastic, internally constrained material. Part 1: Homogeneous deformations Millard Beatty Michael Hayes doi:10.1007/BF00043445 Journal of Elasticity, Vol. 29, No. 1. (1 October 1992), pp. 1-84. 2007-08-29T13:53:09-00:00 1992 Journal of Elasticity 29 1 1 84 elasticity http://www.citeulike.org/user/norris/article/1604845 <i>Journal of Elasticity, Vol. 28, No. 1. (1 June 1992), pp. 55-78.</i><br /><br />Behavior of crystalline solids exhibiting shape memory effects seems to be associated with special kinds of Martensitic transformations, near which some linear elastic moduli are small compared to others. This work explores the possibility of interpreting this in terms of special kinds of bifurcations. Bifurcation and Martensitic transformations in Bravais lattices JL Ericksen doi:10.1007/BF00042524 Journal of Elasticity, Vol. 28, No. 1. (1 June 1992), pp. 55-78. 2007-08-29T13:51:22-00:00 1992 Journal of Elasticity 28 1 55 78 elasticity http://www.citeulike.org/user/norris/article/1026720 <i>Journal of Elasticity, Vol. V85, No. 1. (18 October 2006), pp. 21-37.</i> Perturbation Formula for Phase Velocity of Rayleigh Waves in Prestressed Anisotropic Media Kazumi Tanuma Chi-Sing Man doi:10.1007/s10659-006-9067-z Journal of Elasticity, Vol. V85, No. 1. (18 October 2006), pp. 21-37. 2007-01-05T14:40:26-00:00 2006 Journal of Elasticity V85 1 21 37 elasticity prestress http://www.citeulike.org/user/norris/article/1604825 <i>Journal of Elasticity, Vol. 26, No. 1. (1 July 1991), pp. 65-74.</i> On kinematic conditions of compatibility JL Ericksen doi:10.1007/BF00041151 Journal of Elasticity, Vol. 26, No. 1. (1 July 1991), pp. 65-74. 2007-08-29T13:28:10-00:00 1991 Journal of Elasticity 26 1 65 74 elasticity http://www.citeulike.org/user/norris/article/1604820 <i>Journal of Elasticity, Vol. 24, No. 1. (1 November 1990), pp. 129-133.</i><br /><br />In this paper, a result involving the eigenprojections of the right stretch and its derivative with respect to the deformation gradient is derived, and a related result is found for the rotation. As an application, the form of the constitutive law for an isotropic hyperelastic material in the case when the strain energy function is expressed in terms of the right stretch, is shown to follow at once. On the derivatives of the stretch and rotation with respect to the deformation gradient Lewis Wheeler doi:10.1007/BF00115556 Journal of Elasticity, Vol. 24, No. 1. (1 November 1990), pp. 129-133. 2007-08-29T13:23:27-00:00 1990 Journal of Elasticity 24 1 129 133 elasticity tensor http://www.citeulike.org/user/norris/article/887286 <i>Geophysical Journal International, Vol. 137, No. 2. (1999), pp. 353-363.</i><br /><br />Summary There exists a strong need in seismology for fast, accurate calculation of broad-band synthetic seismograms for waves propagating in three-dimensionally heterogeneous media. We present a promising tool for such calculations in the form of a path integral solution to the acoustic wave equation. Unlike other work in this area, we consider the effects of variable density as well as variable wave velocity. An additional parameter is introduced to transform the hyperbolic wave equation into a parabolic one similar in form to the Schrodinger equation, allowing the solution by path integration. Two cases are considered. First, we develop the solution for a constant-density medium in substantial detail for the benefit of readers unfamiliar with path integrals. In the process, we indicate how geometric ray theory may be extracted from our solution in the high-frequency limit. Next, we solve the general problem which includes the effects of variable density. Here the smoothness of the paths that contribute the most to the integral is contrasted to the extreme roughness of those dominant in the quantum mechanical analogue. In both cases, the final solutions have had both frequency and the additional parameter integrated out analytically, leaving a 'configuration space' path integral. Finally, an outline for numerical implementation is presented as well as the prospects for extension to isotropic elastic wave propagation. A path integral formulation of acoustic wave propagation RB Schlottmann doi:10.1046/j.1365-246X.1999.00793.x Geophysical Journal International, Vol. 137, No. 2. (1999), pp. 353-363. 2006-10-06T12:44:21-00:00 1999 Geophysical Journal International 137 2 353 363 elasticity random http://www.citeulike.org/user/norris/article/887280 <i>International Journal of Solids and Structures, Vol. 37, No. 42. (18 October 2000), pp. 6085-6105.</i><br /><br />A probabilistic method is proposed and implemented to solve linear elasticity problems. The method, called walk on the boundary method (WBM), uses the same governing equations as the boundary element method. Unlike in finite element and boundary element methods, WBM does not require any meshing. Also, error estimates for WBM are easier to obtain than in finite element and boundary element methods. Furthermore, WBM obtains a point solution at a specific point of interest instead of a full field solution as in finite element and boundary element methods. WBM is developed for general traction boundary value problems in antiplane shear, plane strain, and 3D elasticity. Numerical implementations are performed for three example problems: (1) antiplane shear problem with a centrally located circular hole being loaded by uniformly applied traction, (2) plane strain problem with centrally located circular hole being loaded by uniform tension, and (3) 3D elasticity problem with a centrally located spherical cavity being loaded by uniform tension. Results from the three example problems compared favorably with results from the analytical and finite element solution. Three critical issues associated with the WBM for linear elasticity are pointed out for its further improvement. A Monte Carlo solution method for linear elasticity D Shia CY Hui doi:10.1016/S0020-7683(99)00263-2 International Journal of Solids and Structures, Vol. 37, No. 42. (18 October 2000), pp. 6085-6105. 2006-10-06T12:22:47-00:00 2000 International Journal of Solids and Structures 37 42 6085 6105 elasticity random http://www.citeulike.org/user/norris/article/1094959 <i>Physical Review Letters, Vol. 96, No. 13. (2006)</i><br /><br />We measure the linear viscoelasticity of sterically entangled and chemically cross-linked networks of actin filaments over more than five decades of frequency. The high-frequency response reveals rich dynamics unique to semiflexible polymers, including a previously unobserved relaxation due to rapid axial tension propagation. For high molecular weight, and for cross-linked gels, we obtain quantitative agreement with predicted shear moduli in both amplitude and frequency dependence. High-Frequency Stress Relaxation in Semiflexible Polymer Solutions and Networks GH Koenderink M Atakhorrami FC Mackintosh CF Schmidt doi:10.1103/PhysRevLett.96.138307 Physical Review Letters, Vol. 96, No. 13. (2006) 2007-02-08T15:47:03-00:00 2006 Physical Review Letters 96 13 APS bio elasticity nonlinear http://www.citeulike.org/user/norris/article/986226 <i>JMPS, Vol. 49 (November 2001), pp. 2471-2492.</i><br /><br />It is shown here that there are exactly eight different sets of symmetry planes that are admissible for an elasticity tensor. Each set can be seen as the generator of an associated group characterizing one of the traditional symmetry classes. A new proof that the number of linear elastic symmetries is eight P Chadwick SC Cowin M Vianello JMPS, Vol. 49 (November 2001), pp. 2471-2492. 2006-12-09T17:40:20-00:00 2001 JMPS 49 2471 2492 anisotropy elasticity http://www.citeulike.org/user/norris/article/1219483 <i>International Journal of Solids and Structures, Vol. 38, No. 50-51. (December 2001), pp. 9221-9232.</i> On the dual variable of the logarithmic strain tensor, the dual variable of the Cauchy stress tensor, and related issues Carlo Sansour doi:10.1016/S0020-7683(01)00073-7 International Journal of Solids and Structures, Vol. 38, No. 50-51. (December 2001), pp. 9221-9232. 2007-04-10T20:38:49-00:00 2001 International Journal of Solids and Structures 38 50-51 9221 9232 elasticity nonlinear tensor http://www.citeulike.org/user/norris/article/1080239 <i>International Journal of Engineering Science, Vol. 35, No. 14. (November 1997), pp. 1317-1326.</i><br /><br />Two different definitions of symmetries for photoelasticity tensors are compared. A count of such symmetries based on an equivalence relation induced on the set of subgroups of SO(3) was presented by Huo and Del Piero, who proved the existence of exactly 12 classes. Here, another viewpoint is chosen, and photoelasticity tensors themselves are divided into symmetry classes, according to a different definition. By use of group theoretical techniques, such as harmonic and Cartan decomposition, it is shown that this approach again leads to 12 classes. Symmetry classes and harmonic decomposition for photoelasticity tensors Sandra Forte Maurizio Vianello doi:10.1016/S0020-7225(97)00036-0 International Journal of Engineering Science, Vol. 35, No. 14. (November 1997), pp. 1317-1326. 2007-01-31T15:12:15-00:00 1997 International Journal of Engineering Science 35 14 1317 1326 anisotropy elasticity