Determination of Quasi‐Plastic Strains in a Crystalline Plate Based on a Solution of the Inverse Problem of the Theory of Elasticity (One‐Dimensional Case)

An approximate solution of the inverse problem of the theory of elasticity is considered in terms of distortions for a crystalline plate with a one‐dimensional inhomogeneous distribution of point defects. It is shown that near the plate surface the distribution function of quasi‐plastic strains can be represented as a linear combination of distortion tensor components, up to second‐order infinitesimals. The errors of determining the distribution function using various approximations to a solution of the corresponding direct boundary‐value problem are evaluated. The stability of the solution is demonstrated by reconstruction of the distribution function using a set of simulated topographic images.