arXiv:2606.14565cs.CEcs.LG2026-06被引 1

无需应力数据,仅用位移场就能自动发现材料本构模型。

CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data

论文配图:CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data
图 1 · 摘自论文原文
  • 结合无应力监督的全场框架EUCLID,从单次非均匀加载的位移场中识别材料模型。
  • 在真实本构可表示时,能精确恢复所有项,包括带参数的指数型软硬特性。
  • 适合生物组织等难重复测试的材料,可避免损伤与样本变异影响。

本构人工神经网络(CANN)提供可解释的材料模型发现能力,但以往多基于均质实验中的表观应力-应变数据进行应力监督训练。由于每次测试仅覆盖狭窄加载路径,且仅提供平均应力信息,可靠建模通常需多种加载模式约束多维响应。这对软生物组织尤其困难,因重复测试易导致损伤、样品差异大。本文将CANN与无应力监督的全场发现框架EUCLID结合,仅通过一次异质性诱导加载下的位移场与反力,直接识别稀疏超弹性定律。CANN-EUCLID通过最小化平衡残差并引入稀疏正则化,自动选择紧凑有效项,无需局部应力测量或预设模型形式。在各向同性和各向异性基准测试中,当真实本构属于所选基底时,方法能近乎精确恢复正确项,包括嵌入参数的指数项;若不在基底内,则保留共享项,并用可用基函数逼近缺失部分。泛化性能高度依赖采样变形状态:当充分覆盖软硬转变区域时,指数型应变硬化项可准确恢复,否则外推误差较大。有限元前向验证显示,所发现行为能精准复现真实响应。结果表明,无应力监督的CANN全场建模是可解释本构识别的有力框架。

原文摘要 · Abstract (English)

Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests. Because each test samples only a narrow loading path and provides homogenized rather than local stress information, robust discovery typically requires multiple loading modes to constrain the multidimensional response. This is challenging for soft biological tissues, where repeated testing, damage, and sample variability limit reliable information from a single specimen. Here, we combine CANNs with the stress-unsupervised full-field discovery framework EUCLID to identify sparse hyperelastic laws directly from displacement fields and reaction forces in one heterogeneity-inducing loading case. CANN-EUCLID minimizes equilibrium imbalance with sparsity-promoting regularization selecting compact active terms, without local stress measurements or a prescribed law. We evaluate the approach on isotropic and anisotropic benchmarks with prescribed ground-truth laws. When the ground truth is representable by the chosen CANN basis, our method recovers the correct terms with near-exact accuracy, including exponential terms with embedded parameters. When it is not contained in the basis, the method retains shared terms and approximates missing contributions using available basis functions. Generalization depends strongly on sampled deformation states: exponential strain-stiffening terms can be recovered accurately when sufficiently probed, but can produce large extrapolation errors when the stiffening regime lies outside the sampled domain. Forward FE validation simulations show that the discovered behavior accurately replicates the ground truth. These results establish stress-unsupervised CANN discovery as a promising framework for interpretable full-field constitutive model identification.

材料建模神经网络无监督学习生物组织

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