Abstract
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.
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