# A mixed-mode dependent interface and phase-field damage model for solids with inhomogeneities

**Authors:** Roman Vodička  
**arXiv:** [2308.03758](https://arxiv.org/abs/2308.03758)  
**Date:** 2023-07-12  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.03758v1/

## Key points

- The paper presents a computational approach for analyzing cracks in materials and material interfaces of multi-domain structures under quasi-static conditions.
- The focus is on solids with inhomogeneities.
- Fracture processes are described based on the theory of material damage, introducing two independent damage parameters for interface cracks and internal cracks.
- Interface cracks are defined in a thin adhesive layer using cohesive zone models, while internal cracks are defined within material domains using the theory of phase-field fracture.
- Both parameters can differentiate between different fracture modes, which is useful for structures subjected to combined loading conditions.
- The solution methodology is based on a variational approach, allowing for non-linear programming optimization in finite-element discretization and time stepping methods.
- MATLAB is used for computational implementation, providing an efficient way to solve problems related to crack initiation and propagation in complex multi-domain elements of structures.
- Numerical data obtained from simulations validate the developed formulation for analyzing fractures in materials with inhomogeneities under various loading conditions.

## Summary

The paper titled "A mixed-mode dependent interface and phase-field damage model for solids with inhomogeneities" presents a computational approach for analyzing the initiation and propagation of cracks in materials and material interfaces of multi-domain structures under quasi-static conditions. The focus is on situations involving solids with inhomogeneities. The fracture processes are described based on the theory of material damage, which introduces two independent damage parameters to distinguish between interface cracks and internal cracks. The parameter responsible for interface cracks is defined in a thin adhesive layer of the interface and establishes the relationship between stress and strain quantities using cohesive zone models. On the other hand, the second parameter is defined within material domains and is based on the theory of phase-field fracture. This parameter ensures that material damage occurs in a thin material strip, introducing a regularized model of internal cracks. One notable feature of both the interface and phase-field damage parameters is their ability to differentiate between different fracture modes. This capability becomes particularly useful when structures are subjected to combined loading conditions. The solution methodology employed in this study is based on a variational approach, which allows for the implementation of non-linear programming optimization into standard methods of finite-element discretization and time stepping methods. The computational implementation is carried out using MATLAB, providing an efficient way to solve problems related to crack initiation and propagation in complex multi-domain elements of structures. Numerical data obtained from simulations validate the developed formulation for analyzing fractures in materials with inhomogeneities under various loading conditions. In summary, this paper presents an advanced computational approach that enables accurate analysis of crack initiation and propagation in materials with inhomogeneities. The proposed model incorporates separate parameters for interface cracks and internal cracks, allowing for a comprehensive understanding of fracture behavior under various loading conditions. The use of a variational approach coupled with MATLAB implementation ensures efficient computation, while validation through numerical simulations further strengthens the reliability of this method for analyzing fractures in complex multi-domain structures.