Special n-sided Voronoi fiber/matrix elements for clustering thermal effect in natural-hemp-fiber-filled cement composites

• Develop a general formulation of n-sided Voronoi fiber/matrix polygonal element.
• The n-sided Voronoi fiber/matrix element is to enclose each centered natural fiber in matrix.
• Provides a simple way to calculate fields everywhere in the matrix and the fibers.
• The element model is also applicable for other clustered fiber composites.

The thermal effects of clustering in natural-hemp-fiber-filled cement composites are investigated and the effective thermal conductivity of the composites is numerically evaluated using the fundamental-solution-based finite element method in conjunction with special n-sided Voronoi fiber/matrix elements. In the numerical modeling, the special n-sided fiber/matrix elements are developed by a two-variable integral functional involving an independent non-conforming element interior temperature field and an auxiliary conforming element frame temperature field. The element interior temperature field is approximated by a combination of special fundamental solutions satisfying the fiber/matrix interfacial condition and the heat transfer governing equation in each material constituent, and the independent frame temperature field is interpolated by conventional shape functions. All integrals are performed only along the element boundary such that the mesh division associated with fiber/matrix domains can be significantly simplified by the n-sided Voronoi fiber/matrix polygonal elements which allow different numbers of sides for each element and permit calculation of fields everywhere in matrix and fibers. Numerical results demonstrate that these special elements are suitable for dealing with clustering distribution of fibers.