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Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, in the region of active plastic yielding, some specific series representations. Finally, the structural rate response problem for assigned load rates is studied in relation to the solution uniqueness, and two variational principles are provided for this boundary value problem.

a b s t r a c tIn the framework of numerical analysis of joined bodies, the present paper is devoted to the constitutive modeling, via an interface kinematic formulation, of mechanical behaviour of internal adhesive layers. The proposed interface constitutive model couples a cohesive behaviour, based on the damage mechanics theory, with a frictional one, defined in a non-associative plasticity framework. Namely, the interface formulation follows the transition of the adhesive material from the sound elastic condition to the fully cracked one. This formulation is able to model, by means of a specific interpretation of the damage variable and in a relevant mathematical setting, the interface intermediate mechanical properties, during the microcracks spreading process up to the discontinuity surface formation (macrocrack). The constitutive modeling is performed in fully compliance with the thermodynamic principles, in order to ensure the thermodynamic consistency requirement. In the present work, various monotonic and cyclic loading conditions are examined in order to show the main features of the constitutive formulation as well as several significant differences with respect to other existing models. Computational efficiency of the interface constitutive model is tested in a numerical application by FEM resolution strategy approach.