Phenomenological Modeling of Deformation of Porous and Cellular Materials Taking Into Account the Increase in Stiffness Because of the Collapse of Pores

Abstract

Abstract. Mathematical model for the description of deformation of a porous material with a random distribution of pores is constructed on the basis of generalized rheological method taking into account the different resistance of a material to tension and compression. Phenomenological parameters of the model are determined by means of the approximate computations for the problem of static loading of a cubic periodicity cell with spherical cavities. Within the framework of this theory the fields of displacements and stresses around expanding cavity of spherical shape in a homogenious space are constructed. It is shown that the porosity does not change at the stage of elastic deformation. When the pressure increases, a zone of plastic compaction is formed in the vicinity of a cavity, and in a part of this zone the collapse of pores takes place. Engineering formulas for calculation of critical pressures of the elastic limit state and the limit state of a medium with open pores, and also the formulas for determining the radiuses of interfaces of zones of plasticity and compaction are obtained. A complex of parallel programs for numerical analysis of the dynamic deformation of porous materials on multiprocessor computer systems is worked out. By means of this complex a series of computations for deformation of the protection elements, made of metal foams, under the action of localized impulsive loads was performed. The random nature of distribution of the pores size is taken into account with the help of computer modeling. Computations allow one to estimate plastic dissipative part of the energy of impact.