An incompressible Mooney-Rivlin solid has strain energy density , with right Cauchy-Green deformation tensor , and when . It extends the neo-Hookean solid by a second invariant. A convention means , ; the minus sign must be retained when comparing material constants.
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The Mooney–Rivlin solid is a mathematical model used to describe the mechanical behavior of hyperelastic materials, which are materials that can undergo large elastic deformations. Named after the contributions of Melvin Mooney and Ronald Rivlin, this model is particularly useful in the field of rubber-like materials and soft biological tissues, which can experience significant stretching and compressibility.