Higher-order finite element modeling of biological tissues under large strain conditions

In this work, a unified numerical framework for the large strain and vibration analysis of biological tissues using high-order finite element (FE) models is presented. In this investigation, biological-like structural modeling is performed using refined FE based on the Carrera Unified Formulation (CUF) including anisotropy effects. The vibration behavior of soft tissues is analyzed including material anisotropy and large strains, examining the influence of pre-stress conditions on the modal response of such materials and structures. The governing equations in matrix form are derived using the Principle of Virtual Displacements (PVD) under a total Lagrangian formulation and solved via a Newton-Raphson linearization scheme. The energetic terms are rewritten in terms of Fundamental Nuclei (FN), which are independent of the theory of structural approximation, discretization models, and anisotropic hyperelastic constitutive potentials. Through several numerical examples, including the large strain and linearized vibration analyses of multilayered aortic materials, the accuracy and efficiency of the model are assessed by comparing the results against 3D elasticity solutions. The results highlight the potential and robustness of the CUF approach for examining equilibrium paths and the strongly nonlinear phenomena of cross-section deformation and modal interaction at large strains due to pre-stress effects, such as crossing and veering.