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The book is devoted to the 70thbirthday of Prof. Sergey M. Aizikovich, which will celebrated on August 2nd2021. His scientific interests are related to the following topics: Mechanics of contact interactions, Functionally graded materials, Mechanics of fracture, Integral equations of mathematical physics, Inverse problems of the theory of elasticity, and Applications of elasticity to biological and medical problems of mechanics of materials. The papers, collected in the book, are contributions of authors from 10 countries.