On configurational forces for gradient-enhanced inelasticity

Abstract

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 microstresses is used. It is demonstrated that such a formulation produces sufficient regularity to overcome numerical difficulties 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 configurational 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 computed 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.

Application of Configuration Force to Dynamic Crack of Shale under Hydration

“…e configuration force could be also viewed as the resultant of the contact forces acting on the perturbed shape of an object of substance equivalent to the defect and evaluated in the limit of the shape being restored to the primitive configuration [39]. e configuration force could be computed efficiently and robustly when a constitutive continuum model of gradient-enhanced viscoplasticity was adopted [40]. e small strain multiphasefield model accounting for configuration forces and mechanical jump conditions was constructed [41].…”