So far we have discussed some general concepts of mechanics of solids under small deformation. A solid is classified as elastic, if it possesses a homogeneous stress-free natural state, and if in an appropriately defined finite neighborhood of this state there exists a one-to-one correspondence between the stress tensor σ ij and the strain tensor ε ij . This definition is based on Cauchy's approach (A. L. Cauchy, 1827). It is understood here that the natural state is a state of thermodynamic equilibrium in which all components of stress and strain are zero throughout the body. In other words, the definition incorporates the idea that the body returns to the natural state when all loads are removed.
KeywordsLinear Elasticity Solid Mechanics Elastic Solid Excess Pore Pressure Strain Energy Function
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