Dynamics in Explicit Gradient Elasticity: Material Frame-Indifference, Boundary Conditions and Consistent Euler–Bernoulli Beam Theory

Abstract

The paper is concerned with the boundary conditions of explicit gradient elasticity of Mindlin’s type in dynamics. It has been argued in an earlier paper that acceleration terms should not be present in the boundary tractions because of objectivity arguments. This is discussed in the present paper in more detail, and it is supplemented by assuming the validity of the principle of material frame indifference. Furthermore, new examples are discussed in order to illustrate that significant differences exist in the responses predicted by boundary tractions with and without acceleration terms.

Keywords

• Mindlin’s gradient elasticity
• extensions of Hamilton’s principle
• boundary conditions
• material frame-indifference
• acceleration terms
• consistent Euler–Bernoulli beam theory