Variational and Hemivariational Inequalities in Mechanics of Elastoplastic, Granular Media, and Quasibrittle Cracks

On proportional deformation paths in hypoplasticity

“…Let V be as in (2.4) and assume tr(V ) = 0. To simplify the formulas, we introduce the constants (see (17.1) and (17.6)) 1) and the function h(s) with h(0) = 0 and depending on the initial stress tensor σ 0 , defined by the formula (see (16.4) and (17.3)):…”

“…Other typical representatives for incrementally nonlinear constitutive equations are, for instance, the Armstrong-Frederick model [2], the endochronic model by Valanis [45], the octolinear model by Darve [14,15], the CLoE model by Chambon et al [12], and the barodesy model by Kolymbas [30]. For variational approaches to modelling granular and multiphase media, we refer to [1,27,33].…”

On feasibility of rate-independent stress paths under proportional deformations within hypoplastic constitutive model for granular materials

“…In contrast to the classical elastoplastic concept, the strain in the theory of hypoplasticity is not decomposed into the elastic and plastic parts. For modelling of soil behavior with hypoplasticity we cite [2][3][4], and refer to [5,6] for other mathematical approaches. The underlying relations lie within the general context of implicit constitutive theories, see e.g.…”

Optimal control of the radius of a rigid circular inclusion in inhomogeneous two-dimensional bodies with cracks

“…The problems related to deformation of composites containing both cracks and inclusions are subject of considerable scientific interest which is caused by growing trends in the applications of composites [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In particular, general representations of the solutions for a radial crack near a single and midway between two rigid inclusions are given in the paper [17].…”