Localized direct boundary-domain integro-differential formulations for incremental elasto-plasticity of inhomogeneous body

A quasi-static mixed boundary value problem of incremental elasto-plasticity for a continuously inhomogeneous body is considered. Using the two-operator Green–Betti formula and the fundamental solution of a reference homogeneous linear elasticity problem, with frozen initial or tangent elastic coefficients, a boundary-domain integro-differential formulation of the elasto-plastic problem is presented, with respect to the displacement rates and their gradients. Using a cut-off function approach, the corresponding localized parametrix of the reference problem is constructed to reduce the elasto-plastic problem to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations for the displacement increments.