Weak forms of shakedown for elastic-plastic structures exhibiting ductile damage

A special weak-form shakedown is studied for elastic-plastic internal-variable material models with nonlinear hardening, damageable elastic moduli and damageable yield surface, in the hypothesis of ductile damage, (i.e. damage induced by plastic strains), but the precise evolutive law of damage being left unspecified. Sufficient weak-form shakedown theorems are presented, one static and another kinematic, each assessing whether eventually plastic deformations cease together with their consequences, including ductile damage. A two-sided delimitation is provided, within which the weak-form shakedown safety factor can be located. An upper bound to the post-transient damage for a particular iso…

A thermodynamically consistent gradient plasticity theory and comparisons with other formulations

An extended shakedown theory for elastic-plastic-damage material models

Internal variable elastic-plastic-damage, or elastic-damage, material models endowed with free energy are considered. Referring to a structure of such a material subjected to loads varying inside a given domain, the classical notion of (elastic) shakedown is widened to signify that the structure eventually responds to the loads in an elastic manner after certain (finite) amounts of plastic strain and/or damage have been produced. For structures fulfilling an ad-hoc D-stability requisite, an extended shakedown theorem is presented as a generalization of the classical Melan theorem to nonlinear elasticity and damage - besides nonlinear hardening. For common materials exhibiting linear elastic…