This paper presents an enhanced coupled approach between the finite element method (FEM) and the discrete element method (DEM) in which an adaptive remeshing technique has been implemented. The remeshing technique is based on the computation of the Hessian of a selected nodal variable, i.e. the mesh is refined where the curvature of the variable field is greater. Once the Hessian is known, a metric tensor is defined node-wise that serves as input data for the remesher (MmgTools) that creates a new mesh. After remeshing, the mapping of the internal variables and the nodal values is performed and a regeneration of the discrete elements on the crack faces of the new mesh is carried out. Several examples of fracturing problems using the enhanced FEM–DEM formulation are presented. Accurate results in comparison with analytical and experimental solutions are obtained.

The simulation of damage in composite materials is an important research area that impacts different engineering applications from aerospace structures to renewable energy systems. This review provides a comprehensive analysis of current damage modeling approaches, including intra-layer and inter-layer failures. Various numerical strategies, such as continuum damage mechanics (CDM), cohesive zone models (CZM), extended finite element methods (XFEM), phase-field models (PFM), and peridynamics (PD), are examined to assess their efficiency in predicting crack initiation, propagation, and interaction. Additionally, the role of data-assisted (driven) techniques, such as machine learning, in enhancing predictive capabilities is explored. This review highlights the strengths and limitations of each approach, underscoring the need for further advancements in computational efficiency, multiscale modeling, and integration with experimental data. The findings serve as a foundation for future research into optimizing damage prediction techniques to improve the reliability and durability of composite structures.

We present a general framework for the analysis and modelling of frictional contact involving composite materials. The study has focused on composite materials formed by a matrix of rubber and synthetic or metallic fibres, which is the case of standard tires. We detail the numerical treatment of incompressibility at large deformations that rubber can experience, as well as the stiffening effect that properly oriented fibres will induce within the rubber. To solve the frictional contact between solids, a Dual Augmented Lagrangian Multiplier Method is used together with the Mortar method. This ensures a variationally consistent estimation of the contact forces. A modified Serial-Parallel Rule of Mixtures is employed to model the behaviour of composite materials. This is a simple and novel methodology that allows the blending of constitutive behaviours as diverse as rubber (very low stiffness and incompressible behaviour) and steel (high stiffness and compressible behaviour) taking into account the orientation of the fibres within the material. The locking due to the incompressibility constraint in the rubber material has been overcome by using Total Lagrangian mixed displacement-pressure elements. A collection of numerical examples is provided to show the accuracy and consistency of the methodology presented when solving frictional contact, incompressibility and composite materials under finite strains.