Summary
Sometimes materials break in complicated ways that are hard to see just by looking at how they bend or stretch. This work shows how a special kind of computer model can learn the hidden rules that govern how cracks grow inside materials, even when we only have a little bit of data from those materials being tested. The authors use a smart combination of physics and neural networks to figure out exactly how the material’s internal surfaces behave as they get damaged over time. Their approach also shows that just measuring how much force is needed to bend something is not enough; using detailed strain (stretching) information helps reveal the true behavior underneath. This method can improve how we predict material failure and design stronger composites.
What this means in practice
- •For materials testing teams: Recover detailed damage rules inside composites from sparse force and strain data to improve material characterization.
- •For structural engineering teams: Enhance damage prediction in composite beams by combining global and local strain measurements with learned damage models.
Abstract
This work develops a differentiable finite element framework based on an intrinsic cohesive-zone formulation for identifying traction-separation laws from global force-displacement histories and spatially sparse strain measurements. The framework employs physics-constrained neural networks to represent flexible, thermodynamically structured cohesive laws, with sensitivities computed through automatic differentiation and a discrete adjoint that accounts for the history-dependent evolution of interfacial damage. To enable identification of spatially heterogeneous cohesive behavior, we extend learned constitutive priors to irreversible interfacial damage by constructing a shared, low-dimensional family of cohesive laws from representative traction-separation histories. This representation exploits common constitutive structure and parameter sharing to reduce the number of unknowns and regularize the inverse problem, while allowing local cohesive behavior to vary spatially through latent coordinates. Numerical investigations involving double-cantilever beams and fiber-matrix composites demonstrate that accurate reproduction of global force-displacement responses does not necessarily imply accurate recovery of the underlying cohesive laws. Incorporating spatially resolved strain measurements substantially improves constitutive identification, even when the admissible responses are constrained by a learned prior. Comparisons with conventional bilinear cohesive models and Bayesian optimization further illustrate the benefits of the learned constitutive representation and adjoint-based identification for high-dimensional inverse problems.