Existence of the Displacements Field for an Elasto-Plastic Body Subject to Hencky's Law and von Mises Yield Condition.
Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening
For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load step is formulated according to an implicit backward difference scheme (stepwise holonomic formulation), with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonie convergence of an iterative algorithm for the solution...
Extremum theorems for finite-step back-ward-difference analysis of elastic-plastic nonlinearly hardening solids
For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of "material stability"...
Gradient theory for plasticity via homogenization of discrete dislocations
We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the -limit of this energy (suitably rescaled),...
Hencky-Prandtl nets and constant principal strain mappings with isolated singularities.
Inclusions in elasto-plastic solids under the influence of internal and external pressures.
Kinematic criteria of dynamic shakedown extended to nonassociative constitutive laws with saturation nonlinear hardening
The class of elastic-plastic material models considered allows for nonassociativity, nonlinear hardening and saturation in the sense that the static internal variables are constrained by a bounding surface described through convex bounding functions. With reference to finite element, generalized variables discretization in space, two dynamic shakedown criteria are established by a kinematic approach in Koiter's sense, based on weak constitutive restrictions and centered on two suitable definitions...
Kinetic and hydrodynamic equations for granular media
In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.
Multifonctions s.c.i. et régularisée s.c.i. essentielle
Numerical algorithm for the computation of the slip-line field
Numerical stability in dynamic elastic-plastic problems
On approximate differentiability of functions with bounded deformation.
On existence and behaviour of the solution in quasistatic processes for rate-type viscoplastic models
On Finite Element Methods for Plasticity Problems.
On implicit constitutive theories
In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are constrained....
On linear versus nonlinear flow rules in strain localization analysis
This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion...
On the accuracy of Reissner–Mindlin plate model for stress boundary conditions
For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the...
On the existence of solutions of boundary-value problems for elastic-inelastic solids
On the formulation of the traction problem for the flow theory of plasticity
On the solution of the displacement boundary-value problem for elastic-inelastic materials