Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization

@article{citeulike:2588418, abstract = {Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second-order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second-order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second-order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them. Copyright {\copyright} 2007 John Wiley \& Sons, Ltd.}, address = {Department of Civil Engineering, University of Glasgow, Rankine Building, Glasgow G12 8LT, U.K.}, author = {Kaczmarczyk, \łukasz and Pearce, Chris J. and Bi\ćani\ć, Nenad }, citeulike-article-id = {2588418}, doi = {http://dx.doi.org/10.1002/nme.2188}, journal = {International Journal for Numerical Methods in Engineering}, keywords = {general-homogenization, woven-composites}, number = {3}, pages = {506--522}, posted-at = {2008-03-26 04:46:02}, priority = {2}, title = {Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization}, url = {http://dx.doi.org/10.1002/nme.2188}, volume = {74}, year = {2008} }

TY - JOUR ID - citeulike:2588418 L3 - citeulike-article-id:2588418 TI - Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization JF - International Journal for Numerical Methods in Engineering VL - 74 IS - 3 SP - 506 EP - 522 AD - Department of Civil Engineering, University of Glasgow, Rankine Building, Glasgow G12 8LT, U.K. N2 - Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second-order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second-order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second-order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them. Copyright © 2007 John Wiley & Sons, Ltd. KW - general-homogenization KW - woven-composites AU - Kaczmarczyk, łukasz AU - Pearce, Chris AU - Bićanić, Nenad PY - 2008/// UR - http://dx.doi.org/10.1002/nme.2188 ER -