Numerical analysis of strain gradient effects in periodic media

Standard effective properties of heterogenous materials can no longer be used when strain gradients become large with respect to the scale of heterogeneity. The effective modelling can be improved in n s such cases by including higher-order deformation gradients. For the case of a periodic, linear elastic medium effective relations are derived directly from the properties of the microstructure. The coefficients in these relations can be computed by solving a set d of boundary value problems for the periodic cell. This has been done numerically for a fibre-reinforced composite showing that higher-order terms become more important as the stiffness contrast between fibre and matrix increase