Abstract
This chapter presents constitutive equations appropriate for a broad class of engineering materials known as nonlinear elastic solids. Common examples include rubber, elastomers (rubber-like polymers), and soft biological tissues. Nonlinear elastic solids are characterized by their ability to undergo large recoverable deformations and their highly nonlinear stress-strain response. Hence, they exhibit geometric nonlinearity (i.e., strain-displacement nonlinearity) due to finite elastic deformations, and material nonlinearity (i.e., stress-strain nonlinearity) due to nonlinear constitutive response. We examine nonlinear elastic materials in the context of the mechanical (isothermal) theory as well as the thermomechanical theory. In the latter case, we explicitly illustrate how the constitutive equations must satisfy the second law of thermodynamics, invariance, conservation of angular momentum, and material symmetry (isotropy).
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