Establishment of strain gradient constitutive relations by homogenization

Abstract: In this Note, we describe a homogenization methodology with the aim of establishing strain gradient constitutive relations for heterogeneous materials. The presented methodology includes two main steps. The first one is the construction of the average strain-energy density for a well-chosen Representative Volume Element (RVE) by using a homogenization technique. The second one is the transformation of the obtained average strain-energy density to that of the continuum. This transformation permits to ensure that the effective moduli do not depend on the size of an RVE, but only on the intrinsic size of the components. It also ensures that the moduli related to the strain gradient vanish as the contrast between the components disappears. These features were then illustrated by means of a simple example. [Copyright &y& Elsevier]