Redistribution of finite elastic strains after the formation of inclusions. Approximate analytical solution

A class of two-dimensional static problems of the stress-strain state of non-linearly elastic bodies, in which domains with different elastic properties (inclusions) arise after preloading, is considered. Problems are formulated and solved using the theory of the repeated superposition of finite strains. The mechanical properties of the initial material and the material of the inclusions are described by Murnaghan-type or Mooney-type constitutive relations. Two ways of specifying the constitutive relations for the material of an inclusion are considered: when there are inherent strains in this material and when there are not. Approximate analytical methods are used for the solution.