Formulation of inelastic laws in hemivariational and thermodynamic frameworks

Modeling of inelastic phenomena is a challenge from a mechanical and engineering points of view. The reason is that dissipation makes the system to be dependent upon the history of the deformation. In the first part of the talk we will present the theoretical framework for modeling a dissipative spring from two points of view: the thermodynamic [1] and the hemivariational ones [2]. In particular, we will propose how to derive kinematic, see the Fig. 1, and isotropic hardening hysteretic behavior with and without the related flow rules assumption [5,6]. In the second part of the talk we will show how it is possible to adjust the hysteretic shape of the force-displacement diagram by changing the functional shape of the dissipation energy. Thus, we will show how the coupling, in the dissipation energy, between damage and plasticity induces fatigue and therefore the change of the hysteretic cycle along the time evolution. Thus, we will show the derivation of the SN curve (or Whöler diagram). Finally, we will show how the use of granular micromechanics (in the same form Navier [3] and Cauchy [4] used almost two hundred years ago to derive linear elasticity constitutive equations) yields an immediate generalization of the spring's behavior to that of a 3D continuum.