On configurational forces for gradient-enhanced inelasticity

Journal article, 2018

In this paper we discuss how configurational forces can be computed in an efficient and robust manner when a constitutive continuum model of gradient-enhanced viscoplasticity is adopted, whereby a suitably tailored mixed variational formulation in terms of displacements and micro-stresses is used. It is demonstrated that such a formulation produces sufficient regularity to overcome numerical diffi- culties that are notorious for a local constitutive model. In particular, no nodal smoothing of the internal variable fields is required. Moreover, the pathological mesh sensitivity that has been reported in the literature for a standard local model is no longer present. Numerical results in terms of config- urational forces are shown for (1) a smooth interface and (2) a discrete edge crack. The corresponding configurational forces are computed for different values of the intrinsic length parameter. It is concluded that the convergence of the com- puted configurational forces with mesh refinement depends strongly on this parameter value. Moreover, the convergence behavior for the limit situation of rate-independent plasticity is unaffected by the relaxation time parameter