# Capturing the fractocohesive length scale through a gradient-enhanced damage model for elastomers

## TL;DR

This paper introduces a gradient-enhanced damage model for elastomers that captures the fractocohesive length scale by linking microscopic chain damage to macroscopic fracture behavior through numerical simulations.

## Contribution

It develops a thermodynamically consistent damage model incorporating polymer chain mechanics and gradient effects, providing a physically meaningful description of diffuse damage and fracture in elastomers.

## Key findings

- Identification of a fractocohesive length scale related to the damage zone width.
- Demonstration of flaw insensitivity below a critical length scale.
- Establishment of a relationship between microscopic damage and macroscopic fracture response.

## Abstract

This study aims to unravel the micro-mechanical underpinnings of the emergence of the fractocohesive length scale as a central concept in modern fracture mechanics. A thermodynamically consistent damage and fracture model for elastomers is developed, incorporating elements of polymer chain statistical mechanics. This approach enables the direct incorporation of polymer chain response into a continuum gradient enhanced damage formulation, that in turn allows a physically meaningful description of diffuse chain damage and corresponding fracture events. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation. Furthermore, we investigate flaw sensitivity and demonstrate that when flaw sizes are smaller than a critical length scale, the material response becomes largely insensitive to notch size. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage zone and representing the region where the irreversible dissipation process (i.e., bond scission) is happening. As this region is dictated in the proposed FED model through the introduction of a length scale associated with the non-local nature of the damage and fracture process, the emerging relationship of the two length scales is discussed, effectively connecting the microscopic characteristics of damage to the effective macroscopic response.