Data-Driven Cohesive Zone Modeling within the Generalized Standard Materials Framework

Abstract

Cohesive zone models are widely used to describe fracture and interfacial failure, yet most formulations prescribe problem-specific analytical traction-separation laws together with phenomenological rules for unloading and reloading, leading to specialized models for different cohesive behaviors. This work develops a unified learnable cohesive formulation within the generalized standard materials framework, in which the response is generated from learned constitutive functions while the underlying thermodynamic structure remains fixed. The surface free energy is decomposed into active and contact contributions, and irreversible damage evolution is governed by a learned mode-dependent damage resistance. The active energy is represented by an input-convex neural network, while the inverse damage resistance is represented by a monotone neural network. Convexity, monotonicity, normalization, and damage irreversibility are incorporated directly into the constitutive representation. Direct parameterization of the inverse resistance yields an explicit damage update and avoids local nonlinear inversion during constitutive evaluation. Material-point studies show that the formulation can represent qualitatively distinct cohesive responses, including plateaus, extended softening tails, irregular softening, nonlinear unloading, distinct Mode I and Mode II behaviors, and several classical mixed-mode cohesive laws. The framework therefore replaces law-specific model construction with a single thermodynamically structured representation capable of learning cohesive responses of broad functional complexity from data.