论文标题
来自具有自动分化敏感性的全场数据的弹性塑料本构模型参数的校准
Calibration of Elastoplastic Constitutive Model Parameters from Full-field Data with Automatic Differentiation-based Sensitivities
论文作者
论文摘要
我们提出了一个基于自动分化（AD）的弹性塑性组成模型中参数校准的框架。模型校准问题作为部分微分方程受限的优化问题提出，其中耦合平衡方程的有限元（Fe）模型和组成型模型演化方程作为约束。目标函数量化了FE模型预测的位移与全场数字图像相关数据之间的不匹配，并使用基于梯度的优化算法解决了优化问题。向前和伴随的敏感性用于计算梯度的成本要低于其从有限差近似值计算的成本。通过使用AD，我们只需要根据AD对象编写约束，在这种情况下，通过适当的播种和评估这些数量，可以获得前向和反问题所需的所有衍生物。我们提出了三个数值示例，以验证梯度的正确性，通过应用于大规模的FE模型来证明AD方法的并行计算能力，并突出显示该配方易于对其他类别的本构模型的可扩展性。
We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.
