  We are concerned with the numerical solution of a unified first order
hyperbolic formulation of continuum mechanics that originates from the work of
Godunov, Peshkov and Romenski (GPR model) and which is an extension of
nonlinear hyperelasticity that is able to describe simultaneously nonlinear
elasto-plastic solids at large strain, as well as viscous and ideal fluids. The
proposed governing PDE system also contains the effect of heat conduction and
can be shown to be symmetric and thermodynamically compatible.
  In this paper we extend the GPR model to the simulation of nonlinear dynamic
rupture processes and material fatigue effects, by adding a new scalar variable
to the governing PDE system. This extra parameter describes the material damage
and is governed by an advection-reaction equation, where the stiff and highly
nonlinear reaction mechanisms depend on the ratio of the local von Mises stress
to the yield stress of the material. The stiff reaction mechanisms are
integrated in time via an efficient exponential time integrator. Due to the
multiple space-time scales, the model is solved on space-time adaptive
Cartesian meshes using high order discontinuous Galerkin finite element schemes
with a posteriori subcell finite volume limiting.
  A key feature of our new model is the use of a twofold diffuse interface
approach that allows the cracks to form anywhere and at any time, independently
of the chosen computational grid, without requiring that the geometry of the
rupture fault be known a priori. We furthermore make use of a scalar volume
fraction function that indicates whether a given point is inside the solid or
outside, allowing the description of solids of arbitrarily complex shape.
