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In this chapter, we present the basic expressions for tensor algebra (Sect. 2.1), local body deformations and basic kinematics (Sect. 2.2), and stress tensors and their rates (Sect. 2.3) required for the exposition of the basic material of the research. In addition, Sect. 2.4 presents different forms of the elastic energy and constitutive relations for the linear isotropic material model that inspired the derivation of similar forms for the nonlinear neo-Hookean material (see Chap. 3).

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Preliminaries

  • 章节

  • 发表日期：

    2026年

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  • Sergey Korobeynikov,
  • Alexey Larichkin,
  • Patrizio Neff

摘要

In this chapter, we present the basic expressions for tensor algebra (Sect. 2.1), local body deformations and basic kinematics (Sect. 2.2), and stress tensors and their rates (Sect. 2.3) required for the exposition of the basic material of the research. In addition, Sect. 2.4 presents different forms of the elastic energy and constitutive relations for the linear isotropic material model that inspired the derivation of similar forms for the nonlinear neo-Hookean material (see Chap. 3).