Logarithmic strain tensor in the positional formulation of FEM

Resumo

Besides structural engineering, rubber-like materials have been used in several fields such as bioengineering and medicine. Usually, these materials undergo, not only large displacements, but large deformations as well, and this requires a special attention to write a formulation both mathematically and physically consistent. To this end, one must choose a strain measure that, preferably, depends on the initial configuration of the body and that results in the null tensor for a given arbitrary rigid body motion. One of the most used strain measures in this context is the Green strain. However, this measure does not show a physical coherence for the one-dimensional case, as it is known. Thus, this work formulates the problem by using another strain measure, namely, lnU, where U is the right stretch tensor. The positional formulation of the finite element method together with the Newton-Raphson procedure are applied for solid analysis. The constitutive equation is supposed to be linear. At the end, a comparison between the numerical results obtained by the Green strain and by lnU is performed.