Nonlocal Linear Elasticity

Abstract

In Chapter 3, we obtained the general constitutive equations of the memory-dependent nonlocal elastic solids. With practical applications in mind, we construct here specific constitutive equations for the nonlocal linear elastic solids. To this end, in Section 6.1, we introduce a measure for the order of magnitude evaluation. With a linear strain measure e_kl and small temperature changes T from a constant ambient temperature T₀, we write a quadratic free-energy functional in terms of e_kl and T, and a dissipation functional in terms of T,_k. The constitutive equations for the nonlocal anisotropic elastic solids are then obtained by using the equations given in Chapter 3. Afterward, we pass to the constitutive equations for the isotropic solids. Various different, but equivalent, forms of these equations are presented.