Convergence in non‐associated plasticity and fracture propagation for standard, rate‐dependent, and Cosserat continua

The use of pressure‐dependent plasticity models with a non‐associated flow rule causes a loss of the well‐posedness for sufficiently low hardening rates. Apart from a mesh dependence, this can result in poor convergence, or even divergence of the iterative procedure employed to find an equilibrium configuration. This can be aggravated when other nonlinear, dissipative mechanisms are introduced, for instance the propagation of cracks. This is demonstrated rigorously, as well as the regularizing effect of adding viscosity or employing a Cosserat continuum. In both cases the regularization is independent of the value of the internal length scale for a fairly wide range of parameters. The spatial discretization has been done using T‐splines, and the fracture is modeled using interface elements and propagated using mesh line insertions. The time integration has been done by an implicit Newmark scheme. The use of proper regularization techniques makes an implicit scheme feasible, resulting in a reduction in the number of time steps by an order of magnitude.