A computational framework for nonlinear elasticity

Abstract

Nonlinear elasticity theory plays a fundamental role in modeling the mechanical response of many polymeric and biological materials. Such materials are capable of undergoing finite deformation, and their material response is often characterized by complex, nonlinear constitutive relationships. (See, for example, Holzapfel [2000] and Truesdell and Noll [1965] and the references within for several examples.) Because of these difficulties, predicting the response of arbitrary structures composed of such materials to arbitrary loads requires numerical computation, usually based on the finite element method. The steps involved in the construction of the required finite element algorithms are classical and straightforward in principle, but their application to non-trivial material models are typically tedious and error-prone. Our recent work on an automated computational framework for nonlinear elasticity, CBC.Twist, is an attempt to alleviate this problem.