Finite Element Historical Deformation Analysis in Piecewise Linear Plasticity by Mathematical Programming

When loads increase proportionally beyond the elastic limit with elastic-plastic piecewise linear constitutive laws, finding the whole evolution of the plastic strain may be amenable to a parametric linear complementarity problem (PLCP), where the parameter is represented by the load factor, the matrix is symmetric positive definite (or semi-definite for perfect plasticity), and the variables with a direct mechanical meaning are the plastic multipliers. In this paper the classic PLCP solution method is revisited by interpreting mechanically some major procedure steps. This allows to simplify the general algorithm by resorting to the solution of a series of elastic structures, one for each pivotal step. The method, which makes the analysis, usually numerically cumbersome, very efficient is developed and applied to some example cases.