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Chapter 4 Hyperelasticity

DOI: 10.1016/s0168-2024(08)70061-4
  • Mathematics


Publisher Summary This chapter discusses the hyperelasticity. If a material is elastic, one can replace the first Piola-Kirchhoff stress tensor T (x) by in the equations of equilibrium, which then form a system of three nonlinear partial differential equations, and boundary conditions, with respect to the three unknown components of the deformation φ, viz. If this is the case, and if the applied forces are conservative, solving the above boundary value problem is formally equivalent to finding the stationary point of a functional, called the total energy. If the hyperelastic material is homogeneous and isotropic, and if the reference configuration is a natural state, the terms of lowest order in the expansion of the stored energy function for small strain tensors E are of the form.

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