We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides information about the current material state (i.e., free energy, stress, and the evolution of internal variables) under any given loading scenario without requiring initial data. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models. Additionally, strategies are provided to reduce the required order of derivation for obtaining the tangent operator. The trained model can be directly used in any finite element package (or other numerical methods) as a user-defined material model. However, challenges remain in the proper definition of collocation points and in integrating several non-equality constraints that become active or non-active simultaneously. We tested this methodology on rate-independent processes such as the classical von Mises plasticity model with a nonlinear hardening law, as well as local damage models for interface cracking behavior with a nonlinear softening law. Finally, we discuss the potential and remaining challenges for future developments of this new approach.

翻译：我们应用物理信息神经网络求解非线性、路径依赖材料行为的本构关系。训练后的网络不仅满足所有热力学约束条件，还能在无需初始数据的情况下，针对任意加载场景即时提供当前材料状态信息（即自由能、应力及内变量的演化）。本工作的优势在于避免了求解复杂材料模型中非线性方程所需的重复牛顿迭代过程。此外，我们提出了降低获取切线算子所需求导阶数的策略。训练完成的模型可直接作为用户自定义材料模型应用于任意有限元软件包（或其他数值方法）。然而，在配点定义的规范性以及多个非等式约束的同步激活/非激活集成方面仍存在挑战。我们采用率无关过程对该方法进行了验证，包括含非线性硬化律的经典冯·米塞斯塑性模型，以及含非线性软化律的界面开裂行为局部损伤模型。最后，我们探讨了该方法的发展潜力与未来面临的挑战。