Elastic Material Law Research Articles

Some basic solutions for wave propagation in a rod exhibiting non-local elasticity

In this work, longitudinal wave propagation in a one-dimensional rod exhibiting non-local elasticity with a strain gradient is examined under time-harmonic conditions. In particular, fundamental solutions for a point force and for boundary conditions at one end of the rod are derived using the Laplace transform. Furthermore, the differences observed in the rod's response when compared with the standard case of linear elastic material law are pointed out and discussed. Finally, these fundamental solutions can be used within the context of a boundary element formulation for examining various boundary-value problems for unidimensional wave motions.

A continuum based three-dimensional shell element for laminated structures

In this paper a continuum based three-dimensional shell element for the nonlinear analysis of laminated shell structures is derived. The basis of the present finite element formulation is the standard eight-node brick element with tri-linear shape functions. Especially for thin structures under certain loading cases, the displacement based element is too stiff and tends to lock. Therefore we use assumed natural strain and enhanced assumed strain methods to improve the relatively poor element behaviour. The anisotropic material behaviour of layered shells is modeled using a linear elastic orthotropic material law in each layer. Linear and nonlinear examples show the applicability and effectivity of the element formulation.

A fully non‐linear axisymmetrical quasi‐kirchhoff‐type shell element for rubber‐like materials

AbstractAn axisymmetrical shell element for large deformations is developed by using Ogden's non‐linear elastic material law. This constitutive equation, however, demands the neglect of transverse shear deformations in order to yield a consistent theory. Therefore, the theory can be applied to thin shells only. Eventually a ‘quasi‐Kirchhoff‐type theory’ emerges. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non‐linear bending behaviour. Furthermore, special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within Newton's method. Finally, the finite element formulation for a conical two‐node element is given. Several examples show the applicability and performance of the proposed formulation.

A fully non‐linear axisymmetrical membrane element for rubber‐like materials

An axisymmetrical membrane element for large deformations is developed which is based on Ogden's non‐linear elastic material law. Special attention is given to the linearization procedure to obtain a quadratically convergence behaviour within Newton's method. Several examples show the applicability and performance of the proposed formulation.

The Nonmonotone Skin Effects in Plane Elasticity Problems Obeying to Linear Elastic and Subdifferential Material Laws

AbstractIn the present paper two‐dimensional nonlinear elasticity problems subjected to nonmonotone skin friction effects are formulated and studied. General material laws derived from convex superpotentials are assumed. The friction forces are derived from nonconvex superpotentials through the generalised gradient of F. H. Clarke. The resulting variational‐hemivariational inequalities are studied and the existence and approximation of their solution is discussed by an appropriate combination of monotonicity with compactness arguments.