Four simplified gradient elasticity models for the simulation of dispersive wave propagation

Gradient elasticity theories can be used to simulate dispersive wave propagation as it occurs in heterogeneous materials. Compared to the second-order partial differential equations of classical elasticity, in its most general format gradient elasticity also contains fourth-order spatial, temporal as well as mixed spatial temporal derivatives. The inclusion of the various higher-order terms has been motivated through arguments of causality and asymptotic accuracy, but for numerical implementations it is also important that standard discretization tools can be used for the interpolation in space and the integration in time. In this paper, we will formulate four different simplifications of the general gradient elasticity theory. We will study the dispersive properties of the models, their causality according to Einstein and their behavior in simple initial/boundary value problems

Microstructural length scale parameters to model the high-cycle fatigue behaviour of notched plain concrete

The present paper investigates the importance and relevance of using microstructural length scale parameters in estimating the high-cycle fatigue strength of notched plain concrete. In particular, the accuracy and reliability of the Theory of Critical Distances and Gradient Elasticity are checked against a number of experimental results generated by testing, under cyclic bending, square section beams of plain concrete containing stress concentrators of different sharpness. The common feature of these two modelling approaches is that the required effective stress is calculated by using a length scale which depends on the microstructural material morphology. The performed validation exercise demonstrates that microstructural length scale parameters are successful in modelling the behaviour of notched plain concrete in the high-cycle fatigue regime

Finite element implementation of a multi-scale dynamic piezomagnetic continuum model

A gradient-enriched dynamic piezomagnetic model is presented. The gradient enrichment introduces a number of microstructural terms in the model that allow the description of dispersive wave propagation. A novel derivation based on homogenisation principles is shown to lead to a multi-scale formulation in which the micro-scale displacements and magnetic potential are included alongside the macro-scale displacements and magnetic potential. The multi-scale formulation of the model has the significant advantage that all higher-order terms are rewritten as second-order spatial derivatives. As a consequence, a standard C^0-continuous finite element discretisation can be used. Details of the finite element implementation are given. A series of one and two-dimensional examples shows the effectiveness of the model to describe dispersive wave propagation and remove singularities in a coupled elasto-magnetic context