Solids with cracks and non-spherical pores: proper parameters of defect density and effective elastic properties

摘要

The work is motivated by inadequacy of theconventional defect density parameters, such as porosity (relativevolume of pores) or the usual crack density in situations that arefrequently encountered in applications: mixtures of non-sphericalpores of diverse shapes, fluid-filled cracks/pores, pores in ananisotropic matrix. We call a defect density parameter proper it ifcorrectly reflects the individual defect contributions into theeffective elastic properties. Only in terms of such parameters canthese properties the uniquely expressed. Their identification isnon-trivial even in the framework of the non-interactionapproximation; defect interactions further complicate theproblem. We show that the proper parameters are identified bythe structure of the elastic potential. Besides being necessary, theproper parameters yield the following benefits:(1) anisotropy due to non-randomly oriented defects is established;(2) expressions for the effective moduli cover, in a unified way,all mixtures of defects of diverse shapes and arbitraryorientational distributions;(3) they provide guidance for the proper interpretation ofexperimental data on elasticity of porous materials.For certain types of defects (field of pores of complex, butidentical shapes, for example), the general results in terms oftensorial parameters reduce, for each particular orientationaldistribution, to expressions in terms of the conventionalparameters. However, in other situations (non-spherical pores ofdiverse shapes, fluid-filled cracks/pores, pores in an anisotropicmatrix) such a reduction cannot, generally, be done, even for aparticular orientational distribution.