An inverse method for characterisation of the static elastic Hooke's tensors of solid frame of anisotropic open-cell materials

This paper proposes an inverse estimation method for the extraction of the equivalent, static elastic, Hooke's tensor. The inversion is based on a fitting of the displacements, obtained from a combination of static compression and shear traction loads, on the faces of a sample specimen. An equivalent, homogenised material model is found by varying the elastic moduli until a defined cost function, based on the error measured as the difference between the displacement fields, has reached a minimum, at which an anisotropic constitutive solid model has been identified. The method is built on a multi-level step-wise approach, both from a computational as well as an assumed constitutive model symmetry point of view. The principle of the method is validated for a target anisotropic solid material model. The proposed multi-level approach is developed and refined for a known open-cell structure based on the Kelvin cell geometry. The accuracy of the method is verified and various strategies for increasing the rate of convergence in the inversion are discussed.
QC 20200401