A computationally efficient approach for generating RVEs of various inclusion/fibre shapes

A computationally efficient method for generating virtual periodic representative volume element (RVE), capable of handling arbitrary inclusion shapes, is developed. A universal collision/overlap detection and repair method is proposed, where each inclusion shape is represented as a union of n-Spheres (UnS). A constrained optimization problem is formulated and solved to remove inclusion overlaps; a closed-form solution is derived for calculating the degree of inclusions overlap and its gradient vector with respect to inclusion position. RVE generation is illustrated with circular, spherical, four non-circular and four non-spherical inclusion shapes. Computational efficiency is demonstrated using an elaborate RVE generation time study. The generated RVEs are evaluated using various statistical metrics; results confirm the random distribution of inclusions. Effective properties of RVEs, representing unidirectional composites, are determined using homogenization with various fibre cross-section shapes; obtained mechanical properties have shown transverse isotropy.

Automated summary

A computationally efficient method for generating virtual periodic representative volume element (RVE) is developed, capable of handling arbitrary inclusion shapes. A universal collision/overlap detection and repair method is proposed to remove inclusion overlaps. The generated RVEs are evaluated using statistical metrics, confirming the random distribution of inclusions. Effective properties of RVEs are determined using homogenization with various fibre cross-section shapes.