Mathematical model for diagnosing a nonlinear elastic medium

Abstract

The article deals with the problem of mathematical modeling of physical processes when conducting diagnostic tests within the framework of non-destructive testing of materials. The consideration of elastic processes is due to the fact that elasticity is characterized by the return of the body to its original state after removal of force loads (thereby ensuring the non-destructive nature of the tests). It is assumed that the material under study has weakly expressed spatially distributed anisotropic and nonlinear properties due to the uneven accumulation of microdamage during the operation of the product. The purpose of the work is to formulate and solve the problem of diagnosing a nonlinear elastic inhomogeneous anisotropic half-space within the framework of mathematical modeling of non-destructive testing of massive bodies. In mathematical terms, the problem belongs to the class of coefficient inverse problems for dynamic elasticity equations. An approach to determining density and elastic moduli (coefficients of equations) depending on spatial variables is proposed, based on the use of the perturbation method.