Periphractic construction of elasticity and plasticity on Gurtin's generalized stress functions and the criterion for yielding

Abstract

An alternative approach is made to Gurtin's stress functions of non-Beltrami feature to paraphrase its anholonomic periphractic standpoint and to provide a basis to reconstruct the Theory of Yielding. The stress is defined with reference to a three-dimensional version of Einstein's coordinates. The meaning and construction of elasticity is attributed to the aeolotropic periphracticies of material continua. The multidimensional picture for the yielding manifold is reached in terms of average metric involving Killing's field. Account is taken of a microphysical restriction on variational degrees of freedom to assume the form of Klein-Goldon field. The fourth order partial differential equation is so secured for the field equation of yielding. The final forms of the boundary condition equations have to be fixed by taking account of the periphracticy effects, especially of the standpoint of the plasticity tensor B klmn , two components of which are independent for isotropic materials, owing to integration constants. That these equations agree with only a slight modification with the ones that have been proposed many years since is checked with reference to the isotropic uniform material. The modification is concerned also with the microphysical and thermodynamical implications. A spontaneous unification with the postulate of the principle of relativity is included summarizing also the relation between spatially-temporally fluctuating harmonic and biharmonic fields.