The influence of inclusive deformation mapping on the kinematic equations of nonlinear elasticity

Abstract A model of continuum is often used in statics and dynamics modeling with material spatial description. In this paper, we describe body deformation using an innovative approach employing embedding. The mapping ϕ maps a domain from the space R n to image m , where dimensions spaces are necessarily different, usually < . Due different n, determinant not defined, nor reversible. This complicates calculation fundamental kinematic quantities, J displacement gradient F transposed inverse which occur Nanson’s equation for deformed surface. derive terms these quantities. usage Moore-Penrose generalized essential here. generalization established thus opens up new possibilities describing deformation. Displacements appear as one basic unknowns, especially when finite element method. teaching nonlinear mechanics, found that displacements adequately defined. therefore attempt rectify shortcoming.