3D computational grains with embedded fibers for the direct micromechanical modeling of fiber composites

For the integrated design of composite material and structures, it is essential to have an effective micromechanical numerical tool to link macroscopic material properties to microstructural configurations. In this paper, 3D computational grains (CGs) with embedded fibers are proposed for the first time, for the direct micromechanical modeling of fiber composites. The microstructure of a unidirectional lamina with random fibers can be assembled by many CGs, and the stiffness matrix of each CG with an embedded fiber can be directly computed by combining two new algorithms. On one hand, a new kind of Trefftz trial displacement field based on scaled cylindrical harmonics is independently assumed, in addition to inter-elemental displacement interpolations with surface nodal degrees of freedom (DoFs). On the other hand, a new kind of multi-field boundary variational principle is proposed to relate independently assumed Trefftz fields to nodal DoFs and to derive the stiffness matrix. Numerical examples demonstrate that without the traditional fine meshing, accurate distribution of micro-stresses in a representative volume element (RVE) with thousands of fibers can be directly computed, and the equivalent orthotropic properties of fiber composites can be predicted. This is also the first time that a three-dimensional finite element with an embedded fiber is developed.