Modeling of material damage using finite elements and time homogenization in case of finite strain

This work is aimed at numerical simulations of high-cycle fatigue behavior of elastomeric materials. The main concern, however, is not the fatigue life itself, but the changes of mechanical properties prior to failure. This is of special interest in the case of elastomers. In such a case, large strains must be considered and so does, consequently, nonlinearity of constitutive equations as well. The usual approach to fatigue analysis consists of modal analysis and application of linear cumulation rule for damage. This is not generally applicable to large-strain regime nor to nonlinear material models. The most general approach to such problem is a full simulation of damage cumulation in time domain. Such a simulation, however, would be prohibitively expensive for a large number of loading cycles. As a remedy, the method of homogenization in time domain may be applied to the problem. The method has been applied to various material models already (viscoelasticity, viscoplasticity, damage). This article shows its applicability to the problem of damage cumulation under large strains and a significant improvement in computational times over full simulation.