Abstract
The deformations that satisfy the equilibrium equations for an arbitrary material from a certain class in the absence of mass loadings are called the universal deformations (universal solutions) for this class of materials in continuum mechanics. The significance of universal solutions consists in the fact that they can be used efficiently for the experimental determination of equations of state of a material. In the nonlinear theory of elasticity of simple (nonpolar) materials [1– 5], five families of inhomogeneous deformations, which are the universal solutions of equilibrium equa� tions for homogeneous incompressible isotropic sol� ids, are known. In this work, we found the universal finite deforma� tions for incompressible isotropic micropolar materi� als, i.e., solids with moment stresses and rotation interaction of particles. The model of the micropolar medium (the Cosserat continuum) is applied to the description of composites, polymers, and also nano�
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