Computational efficiency of numerical approximations of tangent moduli for finite element implementation of a fiber-reinforced hyperelastic material model.
Computational efficiency of numerical approximations of tangent moduli for finite element implementation of a fiber-reinforced hyperelastic material model.
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DOI：
10.1080/10255842.2015.1118467
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发表时间：
2016
影响因子：
1.6
通讯作者：
Sun W
中科院分区：
文献类型：
--
作者：
Liu H;Sun W
在本研究中，我们评估了采用数值近似方法获得切模时有限元模拟的计算效率。采用近似法和封闭解析法建立了三维实体单元的纤维增强超弹性材料近不可压缩软组织模型，并通过比较两种方法的切模量张量（也称为材料雅可比矩阵）的分量来验证模型的有效性。采用不同的摄动参数和近似方案对逼近方法的计算效率进行了评价，并通过完成这些模拟所需的迭代步数和CPU时间进行了量化。从仿真结果可以看出，采用中心差分近似方案相比于正演欧拉近似方案，提高了近似方法的整体精度。对于大约10,000 dof的小规模模拟，由于每个积分点所需的计算步骤更少，与封闭形式的解决方案相比，近似方案可以大大减少CPU时间。然而，对于约30万自由度的大规模模拟，由于刚度矩阵的分解将主导求解时间，因此近似格式的优势减弱。总的来说，由于它与材料模型无关，近似方法简化了复杂本构模型的有限元实现，具有与封闭形式解相当的精度和计算效率，这使得它在复杂材料模型的有限元模拟中具有吸引力。
In this study, we evaluated computational efficiency of finite element (FE) simulations when a numerical approximation method was used to obtain the tangent moduli. A fiber-reinforced hyperelastic material model for nearly incompressible soft tissues was implemented for 3D solid elements using both the approximation method and the closed-form analytical method, and validated by comparing the components of the tangent modulus tensor (also referred to as the material Jacobian) between the two methods. The computational efficiency of the approximation method was evaluated with different perturbation parameters and approximation schemes, and quantified by the number of iteration steps and CPU time required to complete these simulations. From the simulation results, it can be seen that the overall accuracy of the approximation method is improved by adopting the central difference approximation scheme compared to the forward Euler approximation scheme. For small-scale simulations with about 10,000 DOFs, the approximation schemes could reduce the CPU time substantially compared to the closed-form solution, due to the fact that fewer calculation steps are needed at each integration point. However, for a large-scale simulation with about 300,000 DOFs, the advantages of the approximation schemes diminish because the factorization of the stiffness matrix will dominate the solution time. Overall, as it is material model independent, the approximation method simplifies the FE implementation of a complex constitutive model with comparable accuracy and computational efficiency to the closed-form solution, which makes it attractive in FE simulations with complex material models.