In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient F to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.

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Soft tissues are characterized by a nonlinear mechanical response, highly affected by the multiscale structure of collagen fibers. The effectiveness and the calibration of constitutive models play a major role on the reliability and the applicability of computational models in biomechanics. This paper presents a procedure for the identification of the relationship between collagen-related structural features in soft tissues with model parameters of classical polynomial- and exponential-based constitutive models. Histological features at microscale, as well as biochemical and biophysical properties at nanoscale, are addressed by employing a multiscale structural description of soft tissue mechanics as benchmark data set. Both the direct (from structure to parameters) and the inverse (from parameters to structure) problem are addressed. Suitable optimization problems are introduced for accurate numerical and approximated analytical direct relationships. The inverse identification has been addressed by providing also a measure of the reliability of the computed estimates. Results show the effectiveness of the proposed strategies and allow to discuss the fitting capabilities of classical constitutive approaches in terms of parameters identification.

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