Gradient elasticity and nonstandard boundary conditions (Q1434689)

This paper is devoted to gradient elasticity and has as main purpose the assessment of the thermodynamic restrictions upon the related constitutive equations with particular attention to the associated (nonstandard) boundary conditions. To this end first a suitable thermodynamic framework able to account for nonlocality is presented. The classical Clausius-Duhem inequality is modified by the addition of the nonlocality residual and it used to find the thermodynamic restrictions upon the constitutive equations: it is found that these equations include, beside the field stress-strain laws, also a set of (nonstandard) boundary conditions. Moreover, the total strain energy of a strained body is determined and found to include bulk and surface energies. A minimum total potential energy principle for the structural boundary-value problem in gradient elasticity is also formulated. A few applications to a simple bar in tension are presented.