The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately,...
Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying...
Nei continui bidimensionali isotropi in fase fessurata si dimostra, nella sola ipotesi che le linee di rottura rappresentino univocamente il meccanismo di collasso, la impossibilità di ottenere un moltiplicatore ottimale del carico. La configurazione reale può essere definita considerando anche la capacità deformativa del continuo in esame.
In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.
A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.
In this work, we consider the quasistatic frictionless contact problem between a
viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic
constitutive law is employed to model the piezoelectric material and the normal compliance
condition is used to model the contact. The variational formulation is derived in a form
of a coupled system for the displacement and electric potential fields. An existence and
uniqueness result is recalled. Then, a fully discrete scheme...
A new class of history-dependent quasivariational inequalities was recently studied in [M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in contact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491]. Existence, uniqueness and regularity results were proved and used in the study of several mathematical models which describe the contact between a deformable body and an obstacle. The aim of this paper is to provide numerical analysis of the quasivariational inequalities...
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by...