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.

应用了物理启发式神经网络来解决非线性、路径依赖性材料行为的本构关系，该模型除了满足所有热力学约束条件外，还能够在不需要初始数据的情况下即时提供有关当前材料状态的信息，并提供了降低正切算子所需导数阶数的策略。