A fractional calculus approach to the mechanics of fractal media.
A frictional contact problem with wear and damage for electro-viscoelastic materials
We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational...
A generalization of Osgood's test and a comparison criterion for integral equations with noise.
A generalization to nonlinear hardening of the first shakedown theorem for discrete elastic-plastic structural models
In the plastic constitutive laws the yield functions are assumed to be linear in the stresses, but generally non-linear in the internal variables which are non-decreasing measures of the contribution to plastic strains by each face of the yield surface. The structural models referred to for simplicity are aggregates of constant-strain finite elements. Influence of geometry changes on equilibrium are allowed for in a linearized way (the equilibrium equation contains a bilinear term in the displacements...
A model of seismic excitation
The influence of a seismic wave on a building is customarily described as a force, a function of the time, whose explicit expression is prescribed. We here suggest a one-dimensional model able to relate this force to the sudden onset of a fault in the rock layer on which the building is built.
A new approach to fracture mechanics.
A numerical method for the solution of plane crack problems in finite media.
A Reduced Basis Enrichment for the eXtended Finite Element Method
This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal a priori error estimate and some computational tests including a comparison with some other strategies....
A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem
A system of ordinary and partial differential equations describing creep behaviour of thin-walled shells.
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian....
About a stress deformation condition of a piecewise-uniform wedge with a system of collinear cracks at an antiplane deformation.
Analysis of crack propagation path on the anisotropic bi-material rock.
Analysis of crack singularities in an aging elastic material
We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near the crack tips. We prove that, depending on the regularity of the material law and the Volterra kernel,...
Antiplane fracture analysis of a crack in a monlicnic composite.
Asymptotic methods applied to problems of diffusion, crack propagation and crack tip stress analysis