Efficient integration of evolution equations for a fiber-like Maxwell body

Abstract

Fiber-like Maxwell body is frequently used to model the mechanical behaviour of advanced composite materials, which appear in engineering and bio-mechanical applications. Here we consider a material model of the fiber-like Maxwell body based on the Sidoroff decomposition of the deformation gradient. In our case this decomposition yields a multiplicative split of the fiber stretch into inelastic and elastic parts. One of the advantages of the model is that various hyperelastic potentials can be employed for a greater accuracy. Three different potentials are analyzed in this paper: the classical Holzapfel potential and its modifications. The first modification accounts for a fiber slackness and the second one is intended for applications with a local fiber buckling. In terms of these three potentials, we analyze the performance of a universal iteration-free time-stepping scheme. Robustness and accuracy of this algorithm are tested. The iteration-free method is shown to compare favourably to the classical Euler-backward which includes the Newton iteration process.