A partition of unity finite element method for obtaining elastic properties of continua with embedded thin fibres

The numerical analysis of large numbers of arbitrarily distributed discrete thin fibres embedded in a continuum is a computationally demanding process. In this contribution, we propose an approach based on the partition of unity property of finite element shape functions that can handle discrete thin fibres in a continuum matrix without meshing them. This is made possible by a special enrichment function that represents the action of each individual fibre on the matrix. Our approach allows to model fibre‐reinforced materials considering matrix, fibres and interfaces between matrix and fibres individually, each with its own elastic constitutive law.