Computational Modelling and Experimental Characterisation of Heterogeneous Materials

Heterogeneous materials can exhibit behaviour under load that cannot be described by classical continuum elasticity. Beams in bending can show a relative stiffening as the beam depth tends to zero, a size effect. Size effects are recognised in higher order continuum elastic theories such as micropolar elasticity. The drawback of higher order theories is the requirement of additional constitutive relations and associated properties that are often difficult to establish experimentally. The determination of additional constitutive properties and the computational modelling of micropolar elasticity will be discussed in the context of a model heterogeneous material loaded in simple 3 point bending. The model material was created by drilling holes in aluminium bar in a regular pattern, with the hole axis normal to the plane of bending. The bending tests show that a size effect is present. These results are compared against a model of the detailed beam geometries in the finite element package ANSYS. Both the experimental and detailed FEA results are used to extract the additional micropolar elastic material properties. A comparison is then made against analytical solutions and numerical solutions using both a beam finite element and a 2D control volume method that each incorporate micropolar behaviour.