Mechanical Properties for an Arbitrary Arrangement of Rigid Spherical Particles Embedded in an Elastic Matrix (Preprint)

摘要

A computer code has been written which calculates the small deformation stress and strain fields of a medium consisting of a pack of rigid spherical particles embedded in an elastic Hookean matrix. The stress and strain tensors can be calculated at any point in the medium to within a user- specified accuracy. Average mechanical properties of the medium are also output by the code. The code has been used to simulate systems consisting of thousands of particles in a finite pack. Optionally, the code treats an infinite pack made up of repeating 3D rectangular cells of a particle pack. The multipole expansion technique used to solve the equations of small deformation for the elastic medium consists of truncated sums of complete orthogonal vector spherical harmonics. Techniques are presented which improve the convergence of the solution when the particles are in close proximity for highly filled materials. The code has been tested against exact solutions of configurations consisting of a few particles as well as infinite packs of particles in body- centered cubic, face-centered cubic, and simple cubic lattice arrangements. The code has been used to estimate mechanical properties of a variety of monomodal and bimodal particle packs of different packing densities for a matrix material with a variety of elastic constants.