Autori: Constantin GHITA, Ileana Nicoleta POPESCU
Editorial: 21st International Workshop on Computational Mechanics of Materials (IWCMM 21) , 2011.
The hardening state through mechanical deformation emphasized in internal structure of materials, in according with the processes of elastic-plastic deformation enables us for particular behavior laws, introducing of a dual frame needed by the treatment of quasi-static equilibrium equations. Introduction of a Hilbert space for admissible deformations of a mechanical system, following a hardening process of a cold deformed composite, a process governed by a constitutive law of Prandtl-Reuss type, permitted us the equivalence of an original problem with defining a selection criterion for the plastic component of the strain rate and a problem of sweeping process for the elastic component of strain in the case of aluminium based composite.
The sweeping problem is formulated as a Cauchy problem associated to an accretive operator (even of subdifferential type) for which are applied results of Nonlinear Semigroup. A uniqueness result for the plastic component of strain is linked of cross to varieties, defined by the multivalued applications in a Hilbert space of strain. The dual frame of energetical spaces is extended for the phenomenon of plastic flowing of a material, presented in the Moreau’ works, to the situation of hardening deformations, connected to the dissipated power through hardening, where the power of plastic strain as a hardening factor characterizes the deformation history of the composite. Experimental research work has been performed for understanding of working behaviour of Aluminium based composites reinforced with silicon carbide particles (SiCp) under various loading state conditions using non-linear constitutive low. The technique is adequate to the experiments on anisotropic materials cold quasi-static loaded, because from the thermodynamical point of view the process of deformation is irreversible (also dissipative). The constraints are set into the geometrical configurations as statical laws and the restrictions into internal tensions as resistence laws, enabling the formulation of the thermo-plastic flowing equations into the duality of energetical spaces of mechanical element. The guided hardening, which for metals is similar with Bauschinger effect, is characterized by an anisotropic factor. The possibility of choosing the plastic components of a strain for a mechanical system with hardening needs a factorizing process for a space, with respect to the subspace of elastic processes and yielding processes, respectively, if the quasi-statical deformation is regarded as a limit case of dynamical deformation, according to the small speeds and some reduced inertial forces.
Cuvinte cheie: Hardening deformation, Aluminium based composite reinforced with SiC, Non-linear constitutive law, Sweeping process