Comparison of semi and fully-implicit time integration schemes applied to a damage and fatigue phase field model

Abstract In this work, we apply semi and fully-implicit time integration schemes to the damage and fatigue phase field presented in Boldrini et al. (2016). The damage phase field is considered a continuous dynamic variable whose evolution equation is obtained by the principle of virtual power. The fatigue phase field is a continuous internal variable whose evolution equation is considered as a constitutive relation to be determined in a thermodynamically consistent way. In the semi-implicit scheme, each equation is solved separately by suited implicit method. The Newton’s method is used to linearize the equations in the fully-implicit scheme. The time integration methods are compared and the results of damage and fracture evolution under the influence of fatigue effects are presented. The computational cost associated to the semi-implicit scheme showed be lower than the fully counterpart. (AU)