Computational analysis of the nonlinear mechanical properties of anisotropic hyperelastic materials aims at a better understanding of its physiology and pathophysiology under different loading conditions. This has an important role in biomechanics, surgical, clinical diagnostic and design of medical devices. This study investigates the modeling of arterial tissues made of a four-fiber family by using an anisotropic hyperelastic model. This model is based on the theory of polynomial invariant and was implemented in the university finite element code FER. The convex property of the strain energy function is investigated as well as the positive definite nature of the tangent stiffness matrix used within the framework of a finite element analysis. This allows us to guarantee the invertibility of the linearized problem and the uniqueness of the solution computed at each step of the Newton–Raphson scheme used to solve nonlinear problems.

各向异性超弹性材料非线性力学性能的计算分析旨在更好地了解其在不同载荷条件下的生理学和病理生理学。这在生物力学、外科手术、临床诊断和医疗器械设计中具有重要作用。本研究使用各向异性超弹性模型研究了由四纤维家族组成的动脉组织的建模。该模型基于多项式不变量理论，并在大学有限元代码FER中实现。研究了应变能函数的凸特性以及在框架内使用的切线刚度矩阵的正定性质有限元分析。这使我们能够保证线性化问题的可逆性以及在用于解决非线性问题的 Newton-Raphson 方案的每一步计算的解的唯一性。