A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress-strain-strain rate responses in both training and testing regimes, and provide improvements in terms of prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

翻译：提出了一种新型数据驱动本构建模方法，该方法融合了基于连续介质热力学的物理信息建模与机器学习的优势，并以应变率敏感软材料为例进行验证。该模型基于粘性耗散型粘超弹性框架，将总应力分解为体积应力、等容超弹性应力和等容粘性过应力三部分。研究表明，每个应力分量均可表示为不可约完整性基分量的线性组合。通过训练三个基于高斯过程回归的代理模型（每个应力分量对应一个模型），在应变与应变率张量的主不变量与完整性基分量对应系数之间建立映射。该方法构建的模型能够对预测响应施加关键物理约束：热力学第二定律、局部作用与确定性原理、客观性原理、角动量平衡、假设参考状态、各向同性和有限记忆特性。这三个组成本构模型的代理模型通过单一变形模式下的小规模数值数据集进行训练，并在包含多种变形模式的更广泛测试范围内分析预测结果。我们将所提出的物理信息驱动数据驱动本构模型预测与经典连续介质热力学模型及纯数据驱动模型的预测进行了比较。结果表明，代理模型在训练和测试阶段均能合理捕捉应力-应变-应变率响应，并在预测精度、多变形模式泛化能力及小样本兼容性方面具有显著提升。