A Scaled Boundary Approach for Inelasticity of Fibre‐Reinforced Composites

Abstract

AbstractAs versatile materials with elevated mechanical properties, short fibre reinforced composites (SFRCs) are currently used in many applications. To enhance the mechanical properties, e.g. the ductility, or to reduce crack propagation, short fibres are added to a matrix material, such as polymers or concrete. In the case of concrete, for example, the composite might contain additional aggregates as well. Although the addition of fibres improves the mechanical properties in general, it is well‐known that many matrix materials exhibit creep deformations under constant long‐term loads.The contribution at hand discusses a scaled boundary approach to model the inelastic behaviour of SFRCs. To allow for an efficient and automated mesh generation, the scaled boundary finite element method (SBFEM) is used in conjunction with the quadtree/octree decomposition algorithm. Within this framework, the fibres are modelled in a discrete manner, and the mesh of the matrix is generated independently of the fibres. Applying a novel embedding method, the meshes of the matrix and the fibres are combined, which results in a compatible mesh without requiring additional constraints. Furthermore, it is straightforward to combine the discussed techniques with image‐based mesh generation, e.g. based on computed tomography scans. The current contribution presents various 2D and 3D examples illustrating the efficiency and adaptability of the proposed framework.In addition, we present a methodology to incorporate non‐linear constitutive models into the SBFEM. Separate constitutive equations are formulated for the matrix, aggregates, and fibres. Whereas the mechanical behaviour of the aggregates and the fibres can be modelled within the framework of elasticity, one must make use of non‐linear approaches to account for the rate‐dependent inelastic deformation of the matrix under multiaxial stress and deformation states. Overall, this method allows for the simulation of creep in SFRCs, while considering the complex microstructure of these materials in detail. This provides the basis for a realistic estimation of the effect of long‐term loading on SFRC components.