Search

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. [ABSTRACT FROM AUTHOR]

The Euler–Bernoulli beam bending theory in engineering mechanics assumes that the material behavior is isotropic elastic and that plane cross sections remain plane and rigid. It is well-known that this theory suffers from inconsistencies that, e.g., the shear strain is always vanishing, whereas the shear stress does not vanish. In recent work, consistent Euler–Bernoulli beam theories in classical and explicit gradient elasticities were accomplished by assuming the constitutive response to be anisotropic elastic, subject to internal constraints. This approach is extended in the present paper to get consistent Euler–Bernoulli beam theory for gradient elasticity based on Laplacians of stress and strain. The developed beam theory is employed to discuss bending of cantilever beams. [ABSTRACT FROM AUTHOR]

The classical Euler‐Bernoulli beam theory in elastostatic is known to be inconsistent, since the equilibrium equations are not satisfied in local form. Recently, it has been shown that the theory will become consistent if one assumes elastic anisotropy subject to internal constraints. This is shown to be true even for a simple gradient elasticity law. Normally, beam bending is considered as one‐dimensional problem. We summarise in the present paper the results of a previous work concerning two well‐known one‐dimensional formulations of Euler‐Bernoulli beam and gradient elastic material behaviour. The two formulations appear to be different because the functional of internal forces includes the cross‐sectional area of the beam in one but not in the other. It is shown that the two one‐dimensional formulations can be derived as special cases of a three‐dimensional simple gradient elasticity model and that they are equivalent to each other. [ABSTRACT FROM AUTHOR]

We considermaterial bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin-Mindlin's gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler-Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin-Mindlin's type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler-Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin-Mindlin's gradient elasticity theory. [ABSTRACT FROM AUTHOR]