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Discontinuous velocity domain splitting method (DVDS) is a mesh free method which focuses on the strain localization and completely neglect the bulk deformations. It considers the kinematic variational principle on a special class of virtual velocity fields to get an upper-bound of the limit load. To construct this class of virtual velocity fields, the rigid-plastic body is splinted into simple connected sub-domains and on each such sub-domain a rigid motion is associated. The discontinuous collapse flow velocity field results in localized deformations only, located at the boundary of the sub-domains. In the numerical applications of the DVDS method we introduce a numerical technique based on a level set description of the partition of the rigid-plastic body and on genetic minimization algorithms. In the case of in-plane deformation of pressure insensitive materials, the internal boundaries of the sub-domains are parts of circles or straight lines, tangent to the collapse velocity jumps. In this case, DVDS reduces to the block decomposition method, which was intensively used to get analytical upper bounds of the limit loads. When applied to the two notched tensile problem of a von Mises material, DVDS gives excellent results with a low computational cost. Furthermore, DVDS was applied to model collapse in pressure sensitive plastic materials. Illustrative examples for homogenous and heterogeneous Coulomb and Cam-Clay materials shows that DVDS gives excellent prediction of limit loads and on the collapse flow.

We analyse the evolution of a system of finite faults by considering the non‐linear eigenvalue problems associated to static and dynamic solutions on unbounded domains. We restrict our investigation to the first eigenvalue (Rayleigh quotient). We point out its physical significance through a stability analysis and we give an efficient numerical algorithm able to compute it together with the corresponding eigenfunction.

This work is concerned with the flow of a viscous plastic fluid. We choose a model of Bingham type taking into account inhomogeneous yield limit of the fluid, which is well-adapted in the description of landslides. After setting the general threedimensional problem, the blocking property is introduced. We then focus on necessary and sufficient conditions such that blocking of the fluid occurs. The anti-plane flow in twodimensional and onedimensional cases is considered. A variational formulation in terms of stresses is deduced. More fine properties dealing with local stagnant regions as well as local regions where the fluid behaves like a rigid body are obtained in dimension one.

This work is concerned with the flow of a viscous plastic fluid. We choose a model of Bingham type taking into account inhomogeneous yield limit of the fluid, which is well-adapted in the description of landslides. After setting the general threedimensional problem, the blocking property is introduced. We then focus on necessary and sufficient conditions such that blocking of the fluid occurs. The anti-plane flow in twodimensional and onedimensional cases is considered. A variational formulation in terms of stresses is deduced. More fine properties dealing with local stagnant regions as well as local regions where the fluid behaves like a rigid body are obtained in dimension one.

A dynamic shearing problem for rate-and temperature-dependent media is considered using an elastic-viscoplastic constitutive law with thermal softening and without hardening. The local existence of the solution and the lower-semicontinuous dependence of the blow-up time upon the initial data are obtained. The homogeneous solution is introduced and the finite-time evolution of the perturbations of this solution is studied. A stability parameter which depends only on the homogeneous solution is introduced in order to give criteria for strain localization. Finally some numerical examples are presented.

A Cauchy problem and an initial and boundary value problem for a class of rate-type elastic–viscoplastic materials involving a hardening parameter are considered. The one-dimensional mechanical problem is reduced to a semilinear hyperbolic equation in a Hilbert space and the local existence and uniqueness of the solution is proved. If the solution is not a global one, then it will blow up at the end of its maximal interval of existence in a C°-norm. The assumptions on the material functions are weak enough to include both the strain- and the work-hardening cases.