Abstract

Many results on micromorphic media can be found in the literature, where the equations of motion and the energetic foundations of the Eringen micromorphic continuum have been well established. The present paper has been devoted to the continuum modeling of a finite number of interacting, separated continua (microdomains) at the microscale, in which the strain energy has been formulated through a generalization of the Cauchy–Green deformation tensor, resulting in a degenerate metric at the considered scale, and a $(6\times 6)$ Green–Lagrange strain tensor. The equilibrium equations have been obtained by systematically applying the method of virtual power. For one of the first time, boundary layer conditions appear in micromorphic mechanics. The paper concludes with a discussion on the number of constitutive parameters, shown to coincide, in number, with those of classical (Cauchy) elasticity, together with the recovery of micropolar continua as a special case and wide spectrum of applications of the proposed framework. Further details concerning the algebraic expressions of the tensors involved are provided in the Appendices.

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