We investigate the existence and non-existence of a function-valued strain solution in various models of elastoplasticity from the perspective of the constraint-based "dual" formulations. We describe abstract frameworks for linear elasticity, …
Disordered network materials abound in both nature and synthetic situations while rigorous analysis of their nonlinear mechanical behaviors remains challenging. The purpose of this paper is to connect the mathematical framework of the sweeping …
Plasticity with softening and fracture mechanics lead to ill-posed mathematical problems due to the loss of monotonicity. Multiple co-existing solutions are possible when softening elements are coupled together, and solutions cannot be continued …
We consider a differential inclusion known as a polyhedral sweeping process. The general sweeping process was introduced by J.-J. Moreau as a modeling framework for quasistatic deformations of elastoplastic bodies, and a polyhedral sweeping process …
We use the ideas of Adly-Attouch-Cabot [Adv. Mech. Math., 12, Springer, 2006] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint …
This paper develops an analytic framework to design both stress-controlled and displacement-controlled $T$-periodic loadings which make the quasistatic evolution of a one-dimensional network of elastoplastic springs converging to a unique periodic …
Networks of elastoplastic springs (elastoplastic systems) have been linked to differential equations with polyhedral constraints in the pioneering paper by Moreau (1974). Periodic loading of an elastoplastic system, therefore, corresponds to a …
Moreau's Sweeping Process, its stability and applications. Networks of elastoplastic springs.