论文提出无需应力的本构模型发现新方法
本文提出CANN-EUCLID方法，结合可解释的本构人工神经网络（CANN）与无应力监督的全场发现框架EUCLID，从位移场和反作用力中识别稀疏超弹性定律。在各项同性和各向异性基准测试中，当真实法则可由所选CANN基表示时，方法以近乎精确的精度恢复正确项，包括带嵌入参数的指数项。当基不包含真实法则时，方法保留共享项并使用可用基函数近似缺失贡献。泛化能力强烈依赖于采样的变形状态，指数应变硬化项在充分探测时可准确恢复，但在硬化区域外插时会产生较大误差。正向FE验证仿真表明，发现的行为准确复现了真实法则。
CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data
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.