一种用于材料点模型校准的直接-伴随方法及其在塑性中的应用
A Direct-adjoint Approach for Material Point Model Calibration with Application to Plasticity
AI总结：
本文提出直接-伴随方法计算Hessian矩阵，将材料参数校准构建为约束优化问题，并证明Newton-Raphson算法优于L-BFGS-B等梯度算法。
摘要：
本文提出了一种用于局部弹塑性本构模型中材料参数校准的新方法。该校准被构建为一个约束优化问题，其中单个材料点的本构模型演化方程作为约束条件。目标函数量化了模型预测的应力与相应实验测量值之间的不匹配程度。为了提高校准效率，提出了一种新颖的直接-伴随方法来计算目标函数的Hessian矩阵，从而能够使用二阶优化算法。梯度与Hessian矩阵的计算均采用自动微分。通过两个数值算例验证了Hessian矩阵的正确性，并证明Newton-Raphson算法始终优于L-BFGS-B等基于梯度的算法。
英文摘要：
This paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton-Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.
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