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Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information
Computational Mechanics ( IF 3.7 ) Pub Date : 2021-04-24 , DOI: 10.1007/s00466-021-01998-3
Stefan Hartmann , Rose Rogin Gilbert

In this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as full-field strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen, where—in the first step—the spatial discretization yields a large system of differential-algebraic equation (DAE-system). This is solved using a time-adaptive, high-order, singly diagonally-implicit Runge–Kutta method. Second, to study the fully analytical versus fully numerical determination of the sensitivities, required in a gradient-based optimization scheme, the force determination using the Lagrange-multiplier method and the strain computation must be provided explicitly. The consideration of the strains is necessary to circumvent the influence of rigid body motions occurring in the experimental data. This is done by applying an external strain determination tool which is based on the nodal displacements of the finite element program. Third, we apply the concept of local identifiability on the entire parameter identification procedure and show its influence on the choice of the parameters of the rate-type constitutive model. As a test example, a finite strain viscoelasticity model and biaxial tensile tests applied to a rubber-like material are chosen.



中文翻译:

使用具有时间自适应的高阶时间积分和实验性全场应变信息的有限元进行材料参数识别

在本文中,我们使用最小二乘法对材料参数识别进行全面的矩阵表示,其中模型是由非线性有限元给出的,而实验数据是由力数据以及全场应变提供的基于数字图像相关性的测量数据。首先,选择针对直接问题的严格半离散化概念,其中,第一步是空间离散化产生一个大型的微分代数方程组(DAE-system)。这可以通过使用时间自适应的高阶单对角隐式Runge-Kutta方法来解决。其次,研究基于梯度的优化方案所需的灵敏度的完全解析确定或完全数值确定,必须明确提供使用拉格朗日乘数法确定的力和应变计算。为了避免实验数据中发生的刚体运动的影响,必须考虑应变。这是通过应用外部应变确定工具完成的,该工具基于有限元程序的节点位移。第三,我们将局部可识别性的概念应用于整个参数识别过程,并显示其对速率型本构模型参数选择的影响。作为测试示例,选择了应用于橡胶状材料的有限应变粘弹性模型和双轴拉伸测试。为了避免实验数据中发生的刚体运动的影响,必须考虑应变。这是通过应用外部应变确定工具完成的,该工具基于有限元程序的节点位移。第三,我们将局部可识别性的概念应用于整个参数识别过程,并显示其对速率型本构模型参数选择的影响。作为测试示例,选择了应用于橡胶状材料的有限应变粘弹性模型和双轴拉伸测试。为了避免实验数据中发生的刚体运动的影响,必须考虑应变。这是通过应用外部应变确定工具完成的,该工具基于有限元程序的节点位移。第三,我们将局部可识别性的概念应用于整个参数识别过程,并显示其对速率型本构模型参数选择的影响。作为测试示例,选择了应用于橡胶状材料的有限应变粘弹性模型和双轴拉伸测试。我们将局部可识别性的概念应用于整个参数识别过程,并显示其对速率类型本构模型参数选择的影响。作为测试示例,选择了应用于橡胶状材料的有限应变粘弹性模型和双轴拉伸测试。我们将局部可识别性的概念应用于整个参数识别过程,并显示其对速率类型本构模型参数选择的影响。作为测试示例,选择了应用于橡胶状材料的有限应变粘弹性模型和双轴拉伸测试。

更新日期:2021-04-24
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