The invention designs a three-dimensional Voronoi unit
simulation method aiming at the elasticity problem of a particle reinforced
composite material containing an interface phase, and a three-dimensional correction complementary
energy functional containing inclusions, a matrix and an interface is deduced, so that the method can be used for calculating a three-dimensional three-phase
composite material; besides,
stress functions are constructed in the three integral domains respectively, Maxwell complete polynomials are adopted and comprise a stress function polynomial and an interaction
force function polynomial, and good convergence and continuity are achieved for three-dimensional interface units with different node numbers. Compared with
commercial software, the method is faster and more efficient when the Voronoi model of the three-dimensional interface is calculated, and results of hundreds of thousands of units in the
commercial software can be obtained with fewer units when the same model is calculated. Compared with a traditional displacement
finite element method, the method is more targeted when solving the
stress problem of the particle composite reinforced material.