Fusion-Based Constitutive Model (FuCe): Toward Model-Data Augmentation in Constitutive Modeling

IF 3.4 Q1 ENGINEERING, MECHANICAL
Tushar, Sawan Kumar, Souvik Chakraborty
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Abstract

Constitutive modeling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying stress conditions due to their fixed forms and limited parameters. While recent advances in deep learning have addressed some limitations of classical models, purely data-driven methods tend to require large data sets, lack interpretability, and struggle to generalize beyond their training data. To tackle these issues, we introduce “Fusion-based Constitutive model (FuCe): Toward model-data augmentation in constitutive modeling.” This approach combines established phenomenological models with an Input Convex Neural Network architecture, designed to train on the limited and noisy force-displacement data typically available in practical applications. The hybrid model inherently adheres to necessary constitutive conditions. During inference, Monte Carlo dropout is employed to generate Bayesian predictions, providing mean values and confidence intervals that quantify uncertainty. We demonstrate the model's effectiveness by learning two isotropic constitutive models and one anisotropic model with a single fiber direction, across six different stress states. The framework's applicability is also showcased in finite element simulations across three geometries of varying complexities. Our results highlight the framework's superior extrapolation capabilities, even when trained on limited and noisy data, delivering accurate and physically meaningful predictions across all numerical examples.

Abstract Image

构造模型对于工程设计和模拟准确描述材料行为至关重要。然而,传统的现象学模型由于形式固定、参数有限,往往难以捕捉真实材料在不同应力条件下的复杂性。虽然深度学习的最新进展解决了经典模型的一些局限性,但纯粹的数据驱动方法往往需要大量数据集,缺乏可解释性,而且很难超越训练数据进行泛化。为了解决这些问题,我们推出了 "基于融合的构造模型(FuCe)":在构造建模中实现模型-数据增强"。这种方法将成熟的现象学模型与输入凸面神经网络架构相结合,旨在对实际应用中通常存在的有限且嘈杂的力位移数据进行训练。混合模型本质上遵循必要的构成条件。在推理过程中,采用蒙特卡罗剔除法生成贝叶斯预测,提供量化不确定性的平均值和置信区间。我们通过学习两个各向同性的构成模型和一个各向异性的单一纤维方向模型,在六个不同的应力状态下证明了该模型的有效性。该框架的适用性还体现在对三种复杂程度不同的几何形状进行的有限元模拟中。我们的结果凸显了该框架卓越的外推能力,即使是在有限的噪声数据上进行训练,也能在所有数值示例中提供准确且具有物理意义的预测。
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CiteScore
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