Data-driven hyperelasticity, Part II: A canonical framework for anisotropic soft biological tissues

In this work, we present a novel anisotropic data-driven hyperelasticity framework for the constitutive modeling of soft biological tissues that allows direct incorporation of experimental data into the constitutive model, without requirement of a predetermined mathematical formula for the strain-energy density function. The data-driven framework is constructed through dispersion-type anisotropic formulation based on a generalized structure tensor in the sense of Holzapfel et al. (2015) that take into account in-and out of plane dispersion. The partial derivatives of the strain energy density functions are replaced with appropriate B-spline interpo-lations where the control points are calibrated against experimental data obtained from uniaxial tension, triaxial shear, and (equi)biaxial tension deformations. The model calibration phase incorporates the normalization condition and the polyconvexity condition is enforced through the control points of the B-splines in order to ensure a stable constitutive response that allows unique solution in finite element analysis. The predictive capabilities of the proposed model are shown against linea alba, rectus sheath, aneurysmal abdominal aorta, and myocardium tissues. On the numerical side, the stress and moduli expressions of the model are derived and implemented into the finite element method. The performance of the model is demonstrated through representative boundary value problems.