A multiscale high-cycle fatigue-damage model for the stiffness degradation of fiber-reinforced materials based on a mixed variational framework

Under fatigue-loading, short-fiber reinforced thermoplastic materials typically show a progressive degradation of the stiffnesstensor. The stiffness degradation prior to failure is of primary interest from an engineering perspective, as it determines whenfatigue cracks nucleate. Efficient modeling of this fatigue stage allows the engineer to monitor the fatigue-process prior tofailure and design criteria which ensure a safe application of the component under investigation.We propose a multiscale model for the stiffness degradation in thermoplastic materials based on resolving the fibermicrostructure. For a start, we propose a specific fatigue-damage model for the matrix, and the degradation of the thermoplasticcomposite arises from a rigorous homogenization procedure. The fatigue-dam age model for the matrix is rather special, as itsconvex nature precludes localization, permits a well-defined upscaling, and is thus well-adapted to model the phase of stablestiffness degradation under fatigue loading. We demonstrate the capabilities of the full-field model by comparing the predictionson fully resolved fiber microstructures to experimental data.Furthermore, we introduce an associated model-order reduction strategy to enable component-scale simulations of the localstiffness degradation under fatigue loading. With model-order reduction in mind and upon implicit discretization in time,we transform the minimization of the incremental potential into an equivalent mixed formulation, which combines two ratherattractive features. More precisely, upon order reduction, this mixed formulation permits precomputing all necessary quantities inadvance, yet, retains its well-posedness in the process. We study the characteristics of the model-order reduction technique, anddemonstrate its capabilities on component scale. Compared to similar approaches, the proposed model leads to improvementsin runtime by more than an order of magnitude.