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

• DOI: 10.1016/j.ijengsci.2019.103198
• Publication Date: 2019-12-19T07:20:19Z
• Authors: Huina Mao; Romain Rumpler; Peter Göransson
• Keywords: Open-cell material; Inverse estimation; Anisotropy; Porous materials; 02 engineering and technology; Computational homogenisation; 0210 nano-technology; Hooke's tensor; Kelvin cell

Abstract 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.