Finite strain parametric HFGMC micromechanics of soft tissues

A micromechanical analysis is offered for the prediction of the global behavior of biological tissues. The analysis is based on the isotropic-hyperelastic behavior of the individual constituents (Collagen and Elastin), their volume fractions, and takes into account their detailed interactions. The present analysis predicts the instantaneous tensors from which the effective current first tangent tensor is established, thus providing the overall anisotropic constitutive behavior of the composite and the resulting field distribution in the composite. This is in contradistinction with the macroanalysis in which the composite internal energy, which involves unknown functions that depend on several strain invariants, must be proposed. The offered micromechanical analysis forms a generalization to the finite strain high-fidelity generalized method of cells (HFGMC) based on the homogenization technique for periodic composites to the parametric finite strain. This involves an arbitrary discretization of the repeating unit-cell of the periodic composites. Results are given for the response of the human abdominal aorta, which consists of three layered tissues: intima, media, and adventitia, all of which are composed out of the Collagen and Elastin. The isotropic-hyperelastic constituents (Mooney-Rivlin and Yeoh) of the composites are calibrated by utilizing available experimental data which describe the response of the tissue. Validation of the results is performed by comparison of the predicted Cauchy stress and stretches with the experimental measurements. In addition, results are given in the form of Cauchy stress and deformation gradient field distributions in the constituents of several tissues.