标题： 基于物理信息的数据驱动方法用于多轴循环载荷下可压缩非线性历史依赖软材料的本构建模发现 显示英文标题

标题： A Physics-Informed Data-Driven Discovery for Constitutive Modeling of Compressible, Nonlinear, History-Dependent Soft Materials under Multiaxial Cyclic Loading

摘要： 我们提出了一种通用的混合物理信息机器学习框架，用于建模多轴循环载荷下的非线性、历史依赖的粘弹性行为。 该方法基于一种基于广义内部状态变量的粘-超弹性本构公式，其中应力被分解为体积部分、等容超弹性部分和等容粘弹性部分。 高斯过程回归（GPR）对平衡响应进行建模，而具有长短期记忆（LSTM）单元的循环神经网络（RNN）捕捉时间依赖的粘弹性效应。 物理约束，包括客观性、材料对称性和热力学一致性，被施加以确保物理有效的预测。 在开发基于张量完整性基和响应函数的代理模型的一般形式后，我们采用了非线性Holzapfel微分粘弹性模型来生成训练数据。 构建了两个数据集，一个用于短期松弛，另一个用于长期松弛，以涵盖广泛的材料记忆特性。 该模型在多种多轴加载条件下进行训练和测试，包括在纵向和横向方向上独立施加的不同拉伸水平、变化的应变率以及拉伸和压缩状态，甚至超出训练域。 对两个数据集在不同应变率下的能量耗散进行了显式分析，通过第二定律验证热力学一致性。 结果表明，所提出的框架能够准确捕捉复杂的、非线性且与速率相关的材料响应。 此外，它对合成噪声表现出强大的鲁棒性，使得在现实和可变加载场景下能够进行可推广且物理一致的预测。 显示英文摘要

摘要： We propose a general hybrid physics-informed machine learning framework for modeling nonlinear, history-dependent viscoelastic behavior under multiaxial cyclic loading. The approach is built on a generalized internal state variable-based visco-hyperelastic constitutive formulation, where stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscoelastic components. Gaussian Process Regression (GPR) models the equilibrium response, while Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units capture time-dependent viscoelastic effects. Physical constraints, including objectivity, material symmetry, and thermodynamic consistency, are enforced to ensure physically valid predictions. After developing the general form of the surrogate model based on tensor integrity bases and response functions, we employed the nonlinear Holzapfel differential viscoelastic model to generate training data. Two datasets, one for short-term and another for long-term relaxation, are constructed to span a wide range of material memory characteristics. The model is trained and tested under diverse multiaxial loading conditions, including different stretch levels applied independently in the longitudinal and transverse directions, varying strain rates, and both tension and compression states, even beyond the training domain. Energy dissipation is explicitly analyzed at different strain rates for both datasets to verify thermodynamic consistency through the second law. The results show that the proposed framework accurately captures complex, nonlinear, and rate-dependent material responses. Moreover, it demonstrates strong robustness to synthetic noise, enabling generalizable and physically consistent predictions under realistic and variable loading scenarios.