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2EKL 2EMN,KL 6KLM ek£m AC.BD AD.BC arbitrary assumed calculated center of mass classical continuum mechanics cofactor compatibility conditions 3.26 components Deformation gradients deformation tensors deformed bodies denote displacement fields DKMN ds(a dx(a EKL,MN elements EMN,K Eringen euclidean eulerian exist F F F independent equations indices indicate integrability intrinsic motion inverse jacobians KN,LM linear theory material point material strain measures metric tensor microdeformations microdisplacement micromorphic elastic solids micropolar elasticity MN.KL necessary and sufficient neighborhood order partial derivatives partial differential equations physical phenomena position vector positive definite possesses continuous rectangular coordinates rKLM rKNM rMNK rMNL,K rNMK,L satisfied identically second order partial second order tensor simply-connected domain single-valued singular SlNKL space spatial substituting sufficient conditions symbols symmetric tensor theorem of Riemann theory of micromorphic UK,L UL,K undeformed vanish Xm,M zero