The non-stationary micromorphic approach to gradient-damage: On time and length scales, stable time increments and micromorphic damping

Explicit finite element schemes are extensively used in industrial applications characterised by elevated strain rates and complex contact interactions. A central challenge in such simulations is the achievement of mesh-independent results while accurately capturing damage localisation and evolution. Gradient-enhanced damage models provide a robust regularisation framework. However, using a micromorphic ansatz gives rise to elliptic partial differential equations which are inherently incompatible with explicit formulations. In order to address this limitation, a non-stationary extension of the micromorphic approach is in the focus of this work: The intricate interaction of time- and length-scale effects in the extended micromorphic formulation is revealed by means of dimensional analysis, and the regularisation behaviour is evaluated numerically through mesh convergence studies and analytically by using dispersion analysis. In view of explicit solution approaches, a comprehensive study on the effect of micro inertia on stable time increments is carried out, and a thermodynamically consistent damping strategy based on dissipative microforces is proposed in order to mitigate micromorphic oscillations. The applicability of the extended micromorphic approach is exemplified by a detailed study of benchmark problems involving dynamic crack propagation.