We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation. 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 automatic differentiation (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.

中文翻译：

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基于自动微分的灵敏度从全场数据校准弹塑性本构模型参数

我们提出了一个基于使用自动微分的弹塑性本构模型参数校准框架。模型校准问题作为偏微分方程约束优化问题提出，其中耦合平衡方程和本构模型演化方程的有限元 (FE) 模型作为约束。目标函数量化有限元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优化问题。前向和伴随灵敏度用于计算梯度，其成本比从有限差分近似计算的成本低得多。通过使用自动微分（AD），我们只需要根据 AD 对象编写约束，其中通过适当地播种和评估这些量来获得正向和逆向问题所需的所有导数。我们提供了三个数值例子来验证梯度的正确性，通过应用于大规模 FE 模型展示 AD 方法的并行计算能力，并强调该公式易于扩展到其他类别的本构模型。