Analytical and numerical investigations of two special classes of generalized continuum media

In this paper, the micromorphic theory and the second gradient theory are proposed-where the micromorphic model can be reduced to the second gradient model with the vanishing relative deformation between macrodeformation gradient and microdeformation. Analytical solutions for the simple shear problem in the case of a general small strain isotropic elasticity micromorphic model and the second gradient model are presented, respectively. Besides, uniaxial tension of a constrained layer with two different boundary conditions is also analytically solved. Finally, the micromorphic theory is implemented numerically within a two-dimensional plane strain finite element framework by developing two isoparametric elements.