A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes

TLDR: In this paper, general piecewise linear constitutive laws with associated flow rules are formulated in matrix notation and some properties and specializations (in particular to kinematic and isotropic hardening) are discussed.

Abstract: General piecewise linear constitutive laws with associated flow rules are formulated in matrix notation; some properties and specializations (in particular to kinematic and isotropic hardening) are discussed. With reference to finite element models of structures and, hence, in matrix-vector description, the following results are achieved: a) the holonomic solutions to the analysis problem for given loads and dislocations are shown to be characterized by means of six “quadratic-linear” minimum principles, two of general, four of conditioned validity;b) the incremental counterparts of the above theorems are indicated by analogy; some comparison properties concerning holonomic and nonholonomic solutions, are pointed out;c) a shakedown theorem is established for variable repeated loads and dislocations, with allowance for inertia forces and viscous damping, i. e. a generalization to workhardening structures of Ceradini's and (in quasi-static situations) Melan's theorems;d) a method is proposed for evaluating under holonomy hypothesis, or bounding from above, the safety factor with respect to local failure due to limited plastic strain capacity.