## Compatibility Conditions of the Theory of Micromorphic Elastic Solids, Volume 1236 |

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2EKL 2J 6KLM AC,BD AD,BC BC,AD center of mass classical continuum mechanics cofactor compatibility conditions 3.26 components Deformation gradients deformation tensors deformed bodies displacement fields DKMN ds(a dx(a EKL,MN EKN,LM elements ELM,KN EMN,K Engineering Science Eringen euclidean eulerian independent equations indices indicate integrability International Journal intrinsic motion inverse jacobians Journal of Engineering KL KLM KL,M linear theory material point material strain measures Mechanics of Micromorphic metric tensor microdeformations microdisplacement micromorphic elastic solids micromorphic materials Micropolar Elasticity MN,KL KN,LM MNKL MNLK necessary and sufficient Nonlinear Theory partial derivatives partial differential equations physical phenomena position vector positive definite possesses continuous rectangular coordinates rKNM rMNK rMNL,K Sandru satisfied identically second order partial second order tensor Simple Micro-elastic simply-connected domain single-valued spatial Springer-Verlag sufficient conditions Suhubi symmetric tensor theorem of Riemann theory of micromorphic Theory of Micropolar Theory of Simple UK,L UL,K undeformed X£L XmM Xm,M