Adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements
Adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements
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DOI：
10.1016/j.cma.2012.06.017
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发表时间：
2012-10
影响因子：
7.2
通讯作者：
Kai‐Uwe Widany;R. Mahnken
中科院分区：
文献类型：
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作者：
Kai‐Uwe Widany;R. Mahnken
这项工作涉及各向同性、不可压缩超弹性材料模型的材料参数识别。除了 Ogden 提出的基于拉伸的主要应变能量函数之外，还考虑了 Rivlin/Saunders 提出的基于不变的应变能量函数，并推导了参数灵敏度。该识别被公式化为基于有限元方法的最小二乘最小化问题，以考虑通过光学测量获得的实验数据中的应力和应变的不均匀状态。对于有限元方法，考虑具有稳定性的混合位移-压力公式中的低阶四面体单元。特别关注基于目标导向的后验误差指示器的自适应网格细化，以获得可靠的材料参数。为了近似误差项，引入了基于增强梯度的逐元素恢复技术。
This work is concerned with the identification of material parameters for isotropic, incompressible hyperelastic material models. Besides the principal stretch-based strain–energy function by Ogden an invariant-based strain–energy function by Rivlin/Saunders is considered for which parameter sensitivities are derived. The identification is formulated as a least-squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements. For the finite element method low-order tetrahedral elements in a mixed displacement–pressure formulation with stabilization are considered. Special attention is payed to an adaptive mesh-refinement based on a goal-oriented a posteriori error indicator to gain reliable material parameters. To approximate error terms an element-wise recovery technique based on enhanced gradients is introduced.