Expansion of elastic bodies with application in the bread industry

This article is concerned with modeling the expansion of an elastic body with application to the evolution of bread dough during the proofing process. The main result is a set of linear second-order partial differential equations corresponding to an Hookean elastic model for the dough together with a constraint on the volume representing expansion. These equations of motion are derived from a Lagrangian energy function and quasi-static solutions are sought numerically by minimizing, using a Rayleigh-Ritz method, a stored energy function using a quadratic B-Spline basis. To model the evolution of a tin loaf, fixed boundary conditions are imposed on three sides of a unit square. The free side is seen to evolve in a way comparable in appearance to a typical slice of bread.