This chapter introduces the concept of stress in soft solids, highlighting its importance in ensuring equilibrium beyond balancing external forces and moments. We show that accounting for internal forces leads to the definition of the stress tensor. We cover fundamental principles such as Cauchy stress, Euler’s axioms, and the derivation of the stress tensor through Cauchy’s Theorem. The discussion extends to the definitions of normal and shear stresses, principal stresses and principal axes of stress, and various states of stress, including hydrostatic pressure, uni-axial stress, and shear stress. Additionally, we introduce the nominal stress tensor and its relation to the Cauchy stress tensor, along with the corresponding equilibrium equations in the reference and current configurations. The chapter concludes with a treatment of boundary conditions and the computation of work done by surface tractions during deformation.

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Stress

  • Michel Destrade,
  • Giuseppe Zurlo

摘要

This chapter introduces the concept of stress in soft solids, highlighting its importance in ensuring equilibrium beyond balancing external forces and moments. We show that accounting for internal forces leads to the definition of the stress tensor. We cover fundamental principles such as Cauchy stress, Euler’s axioms, and the derivation of the stress tensor through Cauchy’s Theorem. The discussion extends to the definitions of normal and shear stresses, principal stresses and principal axes of stress, and various states of stress, including hydrostatic pressure, uni-axial stress, and shear stress. Additionally, we introduce the nominal stress tensor and its relation to the Cauchy stress tensor, along with the corresponding equilibrium equations in the reference and current configurations. The chapter concludes with a treatment of boundary conditions and the computation of work done by surface tractions during deformation.