用新势能函数让神经网络模型更真实模拟材料大变形行为
A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains
- 基于应力不变量设计热力学一致的广义对偶势能
- 可捕捉压力敏感性等复杂材料行为，且自动揭示塑性程度
- 基于JAX实现，适合研究非线性力学与智能材料建模者
我们提出一种用于非弹性本构人工神经网络（iCANN）的广义对偶势能（伪势能）方法。该势能以应力不变量表达，在大变形条件下天然满足热力学一致性。相比前期工作，新势能可刻画更广泛的材料行为，包括压力敏感型非弹性。为此，我们重新审视了iCANN在有限应变下的热力学框架，并推导出构造凸性、零值性及非负性的对偶势能所需条件。为将这些原则嵌入神经网络，我们详细设计了网络架构，确保其预先满足热力学约束。通过评估该架构性能与局限，发现其能有效模拟黏弹性行为，但不局限于此类。在此基础上，我们探讨了发现非弹性材料的不同策略。结果表明，新架构能稳健学习可解释的模型与参数，同时自主揭示材料的非弹性程度。iCANN框架已通过JAX实现，公开于https://doi.org/10.5281/zenodo.14894687。
原文摘要 · Abstract (English)
We present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies thermodynamic consistency for large deformations. In comparison to our previous work, the new potential captures a broader spectrum of material behaviors, including pressure-sensitive inelasticity. To this end, we revisit the underlying thermodynamic framework of iCANNs for finite strain inelasticity and derive conditions for constructing a convex, zero-valued, and non-negative dual potential. To embed these principles in a neural network, we detail the architecture's design, ensuring a priori compliance with thermodynamics. To evaluate the proposed architecture, we study its performance and limitations discovering visco-elastic material behavior, though the method is not limited to visco-elasticity. In this context, we investigate different aspects in the strategy of discovering inelastic materials. Our results indicate that the novel architecture robustly discovers interpretable models and parameters, while autonomously revealing the degree of inelasticity. The iCANN framework, implemented in JAX, is publicly accessible at https://doi.org/10.5281/zenodo.14894687.
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