A new computational framework for materials with different mechanical responses in tension and compression and its applications

Materials possessing tension-compression asymmetric behavior can be simulated by a bi-modulus constitutive relation, which assumes the materials have different moduli in tension and compression. Traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model. In this paper, a new computational framework is established. Solution procedures under both small and finite deformations, which have asymptotically quadratic rate of convergence, have also been proposed and implemented in ABAQUS with UMAT. Numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena.