An anisotropic micro-ellipsoid constitutive model based on a microstructural description of fibrous soft tissues

The aim of this paper is to propose a multi-scale anisotropic constitutive model based on a microscopic description of a soft fibrous tissue. The proposed model is based on directional (or micro-sphere) strain energy density, linking the contribution of fibers to macroscopic elasticity. The link between the microscopic fiber and the macroscopic response is obtained by homogenization involving numerical integration on the surface of the homogenized volume. Directly from the texture analysis of microscopic observations, anisotropy is accounted for an ellipsoid, used as the basis for integration. In each spatial direction of the summation, the initial length of the fibers is penalized according to the geodesic of the anisotropic ellipsoid. Unlike conventional models, anisotropy is taken into account for strains, which allows the mechanical properties of the fibers to be maintained throughout the elementary volume. A new specific integration scheme on an ellipsoidal surface was then developed to facilitate numerical implementation. The strains penalization also ensures that the solution obtained when increasing the amplitude of anisotropy is not degraded. This model, with the new integration method, has been tested for its relevance on numerical tissues. The objectivity and invariance of rotation were then proven. Finally experimental data obtained on human abdominal wall connective tissues were used to verify the accuracy of the results and the predictive capabilities of the model.