A Differentiable Framework for Inverse Identification of Heterogeneous Cohesive Laws

S. Hao, J. Han, and B. Bahmani
Preprint, 2026
Paper

This page was written by Sida Hao with the help of AI (Claude by Anthropic).

Overview

Cohesive laws, the traction-separation relations that govern how interfaces debond, can rarely be measured directly. They must be inferred from remote measurements such as force-displacement histories and sparse strain fields. This inverse problem is often ill-posed, and spatially heterogeneous interfaces make it harder still, since quite different interface laws can produce nearly the same global response.

Building on recent work on data-driven constitutive priors, this paper regularizes the problem by searching over a low-dimensional manifold of physically admissible cohesive responses rather than an unconstrained parameter space. As in earlier work on data-driven cohesive zone modeling, the cohesive laws are formulated within the generalized standard materials framework and represented by structure-preserving neural networks, which guarantee thermodynamic consistency by construction while keeping the flexibility of neural networks. Latent coordinates let the cohesive behavior vary along the interface.

Double-Cantilever Beam

A double-cantilever beam whose interface carries a spatially varying latent coordinate serves as the first test: the cohesive laws are identified from the force-displacement response and DIC strain data.

A double-cantilever beam with a spatially varying cohesive interface: the load drops and recovers as the crack crosses tougher and weaker segments.
A double-cantilever beam with a spatially varying cohesive interface: the load drops and recovers as the crack crosses tougher and weaker segments.
Inverse identification on the double-cantilever beam: over training, the predicted force-displacement curve converges to the data and the identified traction-separation laws converge to the truth.
Inverse identification on the double-cantilever beam: over training, the predicted force-displacement curve converges to the data and the identified traction-separation laws converge to the truth.

Fiber-Matrix Composite

A three-fiber composite with heterogeneous fiber-matrix interfaces extends the test to mixed-mode debonding, where both the Mode I and Mode II traction-separation laws are identified.

Three-fiber composite with heterogeneous fiber-matrix interfaces, each carrying a spatially varying latent coordinate, debonding under applied displacement.
Three-fiber composite with heterogeneous fiber-matrix interfaces, each carrying a spatially varying latent coordinate, debonding under applied displacement.
Identification on the composite: the latent field and the Mode I and Mode II traction-separation laws converge to the truth over training.
Identification on the composite: the latent field and the Mode I and Mode II traction-separation laws converge to the truth over training.

Key Features

Local measurements matter. Reproducing the global force-displacement response does not by itself guarantee that the true cohesive laws are recovered. Adding spatially resolved strain measurements, such as digital image correlation (DIC), substantially improves identification.

Force data alone reproduce the force-displacement curve but leave large errors in the interface laws; adding DIC strain data recovers them.
Force data alone reproduce the force-displacement curve but leave large errors in the interface laws; adding DIC strain data recovers them.

Beyond classical cohesive laws. The learned constitutive prior overcomes the representational limits of conventional cohesive models, even when their parameters are allowed to vary spatially.

A spatially varying bilinear cohesive model versus the learned prior: the prior reaches a far lower loss and much smaller interface errors.
A spatially varying bilinear cohesive model versus the learned prior: the prior reaches a far lower loss and much smaller interface errors.

Efficient inverse identification. The intrinsic cohesive finite element formulation is fully differentiable, so sensitivities come from a discrete adjoint that accounts for the history-dependent evolution of interfacial damage. In high-dimensional inverse problems, this adjoint-based identification outperforms derivative-free Bayesian optimization.

Bayesian optimization versus adjoint-based identification on a fiber-matrix composite: the adjoint gradients drive the loss several orders of magnitude lower and recover the interface laws.
Bayesian optimization versus adjoint-based identification on a fiber-matrix composite: the adjoint gradients drive the loss several orders of magnitude lower and recover the interface laws.

← All publications