We present an interpolation scheme for use with material models involving history‐dependent state variables. The interpolation scheme is based on the solution of a constrained optimization problem, to identify the smoothest monotone curve which produces an admissible solution. Unlike classical schemes used for transport equations, the proposed methodology accounts for the interdependence of the history variables and produces admissible interpolations of the material's state variables. After introducing a general solution scheme for the problem, a simplified and more computationally efficient method is derived. Finally, as a validation problem for the proposed methods, we consider the advection of internal state variables belonging to material models with highly nonlinear yield surfaces.

中文翻译：

---

基于历史的材料状态变量的重新映射方案

我们提出一种插值方案，用于涉及历史依赖状态变量的材料模型。插值方案基于约束优化问题的解决方案，以识别产生允许解的最平滑单调曲线。与用于输运方程的经典方案不同，所提出的方法考虑了历史变量的相互依赖性，并产生了材料状态变量的容许插值。在介绍了该问题的通用解决方案之后，得出了一种简化且计算效率更高的方法。最后，作为所提出方法的验证问题，我们考虑了内部状态变量的平流，该内部状态变量属于具有高度非线性屈服面的材料模型。