Our aim is to develop innovative variational methods to address the challenges today in structural mechanics in the domain of the couplings and interactions between phenomena such as the plasticity, the frictional contact, the fracture mechanics, the damage and the dynamics. Challenge 1: the consideration in the functional of the non associative constitutive laws of which the most known are the unilateral contact with Coulomb's friction and numerous laws of geomaterials. Chalenge 2: the construction of variational approaches to simulate the structure evolution when dissipation is present in ways other than using classical step-by-step or incremental approaches, to control globally the computation of the overall loading history. Our ambition is to face simultaneously these two challenges. The non associative laws cannot be represented by a convex potential. In contrast, we showed that they can be modeled thanks to a bipotential, a function of 2 dual variables, biconvex. The bipotential approach leads to an extensive generalization of the calculus of variation. The Brezis-Ekeland-Nayroles principle is a non-incremental space-time variational principle. We extended it to the dynamics by introducing the concept of symplectic subdifferential. The proposed approach consists in extending this principle to the materials with bipotential. The goal is to develop the corresponding tools of numerical simulation. The target applications are the analysis of interactions such as the cyclic plasticity of metals, the plasticity of polycrystals and geomaterials and the extension of cracks compressed of which the tips rub together. Structuration: Axis 1: Mathematical and numerical tools Axis 2: Modelling and numerical simulation in non associative plasticity Axis 3: Damage and quasi brittle fracture in dynamical condition