This chapter delves into a detailed analysis of deformation in soft solids, which is essential to understanding how particles are displaced when a material deforms. We begin by presenting the reference and current configurations. We then introduce the concept of the deformation gradient and highlight its significance with respect to the deformations of line, volume, and area elements. Through examples such as simple shear and other homogeneous deformations, we illustrate the practical applications and theoretical underpinnings of deformation analysis. We give special attention to the composition of deformations and the polar decomposition theorem. We conclude with a discussion on strain measurement and the divergence theorem.

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Deformations

  • Michel Destrade,
  • Giuseppe Zurlo

摘要

This chapter delves into a detailed analysis of deformation in soft solids, which is essential to understanding how particles are displaced when a material deforms. We begin by presenting the reference and current configurations. We then introduce the concept of the deformation gradient and highlight its significance with respect to the deformations of line, volume, and area elements. Through examples such as simple shear and other homogeneous deformations, we illustrate the practical applications and theoretical underpinnings of deformation analysis. We give special attention to the composition of deformations and the polar decomposition theorem. We conclude with a discussion on strain measurement and the divergence theorem.