发表机构
Columbia University; University of Texas at Austin（哥伦比亚大学; 德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出数据驱动的多材料本构建模框架，推广Bergström-Boyce公式，用于数字材料超弹性与粘弹性建模，可捕获依赖成分与速率的力学行为且保证热力学一致性。
AI 中文摘要
通过多材料3D打印制备的数字材料被设计为刚性与柔性组分的可控混合物，其有效响应在表观刚度上跨越一个数量级以上，且呈现强非线性、依赖成分及速率的耗散行为。经典有限应变粘弹性模型通过平衡态与非平衡态应力的闭式应变能函数及内部变量演化来表征此类行为，但当期望单一本构模型能跨材料与加载率泛化时，可能限制灵活性。本文提出一种数据驱动的多材料本构建模框架，该框架推广了Bergström和Boyce的公式。所提框架保留了经典模型的结构，即乘法运动学、基于不变量的应变能函数，以及沿归一化非平衡偏应力的标量耗散演化律。对于平衡态分支，数据驱动发现框架要么直接预测闭式模型参数作为成分的函数，要么使用神经常微分方程（NODEs）自动构造多凸应变能函数。非平衡态分支动力学以类似方式学习，要么直接识别跨成分的闭式参数，要么使用经适当约束的人工神经网络。通过跨多种材料成分的多速率单轴压缩数据，表明所提公式能在跨成分保留热力学一致性的同时，捕获依赖速率的刚度与滞后特性。
英文摘要
Digital materials fabricated by multi-material 3D printing are designed as controlled mixtures of stiff and compliant constituents, yielding effective responses that span more than an order of magnitude in apparent stiffness and exhibit strongly nonlinear, composition-dependent, and rate-dependent dissipative behavior. Classical finite-strain viscoelastic models represent such behavior with closed-form strain energy functions for equilibrium and non-equilibrium stresses as well as evolution of internal variables, which may limit flexibility when a single constitutive model is expected to generalize across materials and loading rates. Here, we present a data-driven multi-material constitutive modeling framework that generalizes a formulation by Bergström and Boyce. The proposed framework retains the structure of the classical model, namely multiplicative kinematics, invariant-based strain-energy functions, and a scalar dissipative evolution law directed along the normalized nonequilibrium deviatoric stress. For the equilibrium branch, the data-driven discovery framework either directly predicts closed-form model parameters as functions of composition or automatically constructs a polyconvex strain-energy function using neural ordinary differential equations (NODEs). The nonequilibrium branch kinetics are learned similarly, either by directly identifying closed-form parameters across compositions or by using appropriately constrained artificial neural networks. Using multi-rate uniaxial compression data across multiple material compositions, we show that the proposed formulation captures rate-dependent stiffness and hysteresis across compositions while preserving thermodynamic consistency.
Comments28 pages including references, 9 figures in the main manuscript. Supplementary material is available upon request from the corresponding author
