Titlebook: Mechanics of Solid Deformable Body; Michael Zhuravkov,Yongtao Lyu,Eduard Starovoitov Textbook 2023 The Editor(s) (if applicable) and The A

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Statements of Boundary Problems of Solid Mechanics, (Deformed Solid Body Mechanics) ., like the Continuum Mechanics (.), is a phenomenological science. This means that it is based on an axiomatic approach, although not as complete as mathematics.

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Construction of Mathematical Model Problems,The mathematical condition of the physical (in-situ) existence of a solid.

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Mathematical Models of the Theory of Elasticity, is a part of the continuum mechanics and the solid mechanics. The theory of elasticity deals with the determination of a stress–strain state in elastic bodies at specified external loads.

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Mathematical Models of Solid with Rheological Properties,As mentioned repeatedly before, in order to construct a full system of equations for describing the solid behavior, it is necessary to attach the special relations describing the solid mechanical behavior (the relations between the solid stress–strain state) to the constitutive equations.

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Mathematical Models of Special Classes of Solid Mechanics Problems,One of the most important points in constructing mathematical models of a solid deformable body state and behavior is the choice of constitutive equations between components of stress–strain state (which determines the medium behavior: elasticity, viscoelasticity, plasticity, etc.).

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