In the context of finite element analysis and computational mechanics, cohesive zones refer to regions where a specific interaction model is applied to simulate material separation or fracture processes. These zones are typically used to model the initiation and propagation of cracks and other discontinuities in materials.

Cohesive zone models (CZMs) are based on the concept of traction-separation laws, which describe the relationship between the stresses (tractions) and the relative displacements (separations) across a potential fracture surface. The cohesive zone represents the interface between two materials or within a material where the fracture may occur. As loading increases, the cohesive zone undergoes deformation until the material can no longer carry stress, leading to separation or failure.

Key features of cohesive zones:

• Crack initiation and propagation: They allow for the simulation of cracks without the need to pre-define the crack path. The crack naturally forms when the stresses in the cohesive zone exceed a critical value.
• Traction-separation law: The relationship between the normal and shear stresses and the corresponding displacements is defined through a constitutive law, which governs how the material behaves as it deforms and eventually fails.
• Energy dissipation: The cohesive zone model accounts for the energy required to create new surfaces as cracks form and propagate, which is related to the material's fracture toughness.

Cohesive zones are widely used in problems involving fracture mechanics, delamination in composites, adhesive bonding, and other scenarios where the progressive failure of material interfaces is important.

1. Textbooks

• "Cohesive Zone Models in Fracture Mechanics" by A. Carpinteri and G. Pijaudier-Cabot: This book provides in-depth information on cohesive zone models, with discussions on theory, numerical implementations, and applications.
• "Fracture Mechanics: Fundamentals and Applications" by T.L. Anderson: While focused on fracture mechanics, this textbook has sections that introduce cohesive zone models and their role in crack propagation simulations.
• "The Finite Element Method: Linear Static and Dynamic Finite Element Analysis" by Thomas J.R. Hughes: This book is a foundational text on the finite element method (FEM) and covers concepts related to cohesive zone modeling as applied in FEM simulations.

2. Online Courses & Lectures

• edX / Coursera:
  • Look for courses on Fracture Mechanics, Finite Element Methods (FEM), and Computational Mechanics. For instance:
    • "Computational Mechanics" on Coursera: It covers FEM and fracture mechanics in depth.
    • "Introduction to Fracture Mechanics" by edX: Focuses on fundamental concepts in fracture mechanics, which include cohesive zone models.
• MIT OpenCourseWare:
  • Course 3.21: Kinetic Processes in Materials has lectures and resources related to material fracture, crack propagation, and the cohesive zone theory.
  • Course 1.562: Structural Mechanics discusses fracture mechanics and material behavior, where cohesive zone models might be introduced.

3. Research Papers & Journals

• Journal of the Mechanics and Physics of Solids: This journal frequently publishes research on cohesive zone modeling and fracture mechanics.
• Engineering Fracture Mechanics: Another good resource with papers focusing on cohesive zone models, numerical methods, and simulations.
• Computer Methods in Applied Mechanics and Engineering (CMAME): You’ll find papers on numerical implementation of cohesive zone models in FEM here.

Some seminal papers to start with:

• Barenblatt, G. I. (1962): "The Mathematical Theory of Equilibrium Cracks in Brittle Fracture" – One of the early papers proposing the cohesive zone concept.