Abstract
A general formulation of constitutive relations in non-smooth elastoplasticity is presented. The treatment applies to general non-smooth plasticity problems and to problems characterized by non-smooth yield criteria or dealing with non-differentiable functions. The mathematical tools and instruments of convex analysis and subdifferential calculus are suitably applied since they provide the proper mathematical instruments for dealing with non-smooth problems and non-differentiable functions. General formulations of constitutive relations and evolutive laws in non-smooth elastoplasticity are illustrated within the presented theoretical framework. Connections between the proposed mathematical treatment and the classical relations in elastoplasticity are illustrated and discussed in detail. The presented generalized treatment is equipped with considerable advantages since it shows to be ideally suited for the development of variational formulations of structural problems in non-smooth elastoplasticity.
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