Numerical analysis of strain gradient effects in periodic media

Standard effective proper-ties of heterogenous materials can no longer be u sed when strain gradients become large with respect to the scale of heterog eneity. The effective modelling can be improved in such cases by including higher-order deformation gradients, For the case of a periodic, linear elas tic medium effective relations are derived directly from the proper-ties of the microstructure. The coefficients in these relations can be computed by solving a set of boundary value problems for the periodic cell. This has b een done numerically for a fibre-reinforced composite, showing that higher- order terms become more important as the stiffness contrast between fibre a nd matrix increases.