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.

翻译：本构人工神经网络（CANN）提供了可解释的材料模型发现方法，但目前仅用于基于均匀测试中表观应力-应变数据的应力监督场景。由于单次测试仅采样狭窄的加载路径，且提供的是均匀化而非局部应力信息，鲁棒的模型发现通常需要多种加载模式来约束多维响应。这对于软组织生物材料而言具有挑战性——重复测试、损伤效应及样本变异性限制了单个样本的可靠信息。本研究将CANN与应力无监督的全场发现框架EUCLID相结合，直接从单个引发异质性的加载工况中的位移场与反作用力识别稀疏超弹性本构律。CANN-EUCLID通过稀疏性促进正则化最小化平衡残差，自动选择紧凑的激活项，无需局部应力测量或预设本构律。我们在具有预设真实本构律的各向同性与各向异性基准上评估该方法。当真实本构律可由所选CANN基函数表示时，本方法能以近乎精确的准确度恢复正确项（包括含嵌入式参数的指数项）；当真实本构律未包含于基函数集合时，方法保留共有项并通过可用基函数逼近缺失贡献。泛化能力强烈依赖于采样变形状态：当指数应变硬化区域被充分探查时可精确恢复相关项，但若硬化区域超出采样域则可能产生较大外推误差。正向有限元验证仿真显示，所发现的行为能准确复现真实本构响应。这些结果确立了应力无监督CANN发现方法作为可解释全场本构模型识别的潜力框架。