Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues
Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues
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DOI：
10.1007/s10237-005-0075-x
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发表时间：
2005-11-01
影响因子：
3.5
通讯作者：
Sacks, MS
中科院分区：
文献类型：
--
作者：
Sun, W;Sacks, MS
利用精确的本构模型对软组织和组织衍生生物材料的各向异性力学性能进行数值模拟仍然是生物力学中一个重要且具有挑战性的研究领域。虽然大多数本构建模的努力都集中在实验数据的表征，只有有限的研究是利用这些模型在复杂的计算应用的可行性。一个例子是广泛使用的指数本构模型提出的冯。虽然在生物力学文献中存在了几十年，但将该模型实施到有限元（FE）模拟中受到限制。有限的数值实现的一个主要原因是与固有的数值不稳定性和收敛性相关的问题。为了解决这个问题，我们开发并应用了两个限制的广义真菌弹性本构模型必须实现数值稳定性。这是（1）应变能函数的凸性，和（2）材料刚度矩阵的条件数设置为低于预定值。这些约束条件在用于本构模型参数估计的非线性回归中实现，以实验双轴力学数据。然后，我们实现了广义真菌弹性模型到商业有限元代码（ABA-QUS，Pawtucket，RI，美国）。进行了单单元和多单元平面双轴试验仿真，以验证该实现的准确性和鲁棒性。结果表明，数值收敛性和准确的有限元实现一致。因此，本研究提出了一个完整的框架，准确和强大的实现平面软组织的伪弹性本构模型。此外，由于我们的方法是制定在一个通用的FE代码，它可以直接通过跨多个软件平台。
Numerical simulations of the anisotropic mechanical properties Of Soft tissues and tissue-derived biomaterials using accurate constitutive models remain an important and challenging research area in biomechanics. While most constitutive modeling efforts have focused on the characterization of experimental data, only limited studies are available on the feasibility of utilizing those models in complex computational applications. An example is the widely utilized exponential constitutive model proposed by Fung. Although present in the biomechanics literature for several decades, implementation of this model into finite element (FE) simulations has been limited. A major reason for limited numerical implementations are problems associated with inherent numerical instability and convergence. To address this issue, we developed and applied two restrictions for a generalized Fung-elastic constitutive model necessary to achieve numerical stability. These are (1) convexity of the strain energy function, and (2) the condition number of material stiffness matrix set lower than a prescribed value. These constraints were implemented in the nonlinear regression used for constitutive model parameter estimation to the experimental biaxial mechanical data. We then implemented the generalized Fung-elastic model into a commercial FE code (ABA-QUS, Pawtucket, RI, USA). Single element and Multi-element planar biaxial test Simulations were conducted to verify the accuracy and robustness of the implementation. Results indicated that numerical convergence and accurate FE implementation were consistently obtained. The present study thus presents an integrated framework for accurate and robust implementation of pseudo-elastic constitutive models for planar soft tissues. Moreover, since our approach is formulated within a general FE code, it can be straightforwardly adopted across multiple software platforms.