## Mechanical Engineering Faculty Research

#### Title

The Elastic Response of a Cohesive Aggregate—a Discrete Element Model with Coupled Particle Interaction

#### Document Type

Article

#### Publication Date

Winter 12-2002

#### Abstract

A model is presented for the deformation of a cohesive aggregate of elastic particles that incorporates two important effects of large-sized inter-particle junctions. A finite element model is used to derive a particle response rule, for both normal and tangential relative deformations between pairs of particles. This model agrees with the Hertzian contact theory for small junctions, and is valid for junctions as large as half the nominal particle size. Further, the aggregate model uses elastic superposition to account for the coupled force–displacement response due to the simultaneous displacement of all of the neighbors of each particle in the aggregate. A particle stiffness matrix is developed, relating the forces at each junction to the three displacement degrees of freedom at all of the neighboring-particle junctions. The particle response satisfies force and moment equilibrium, so that the model is properly posed to allow for rigid rotation of the particle without introducing rotational degrees of freedom. A computer-simulated sintering algorithm is used to generate a random particle packing, and the stiffness matrix is derived for each particle. The effective elastic response is then estimated using a mean field or affine displacement calculation, and is also found exactly by a discrete element model, solving for the equilibrium response of the aggregate to uniform-strain boundary conditions. Both the estimate and the exact solution compare favorably with experimental data for the bulk modulus of sintered alumina, whereas Hertzian contact-based models underestimate the modulus significantly. Poisson's ratio is, however, accurately determined only by the full equilibrium discrete element solution, and shown to depend significantly on whether or not rigid particle rotation is permitted in the model. Moreover, this discrete element model is sufficiently robust, so it can be applied to problems involving non-homogeneous deformations in such cohesive aggregates.

#### Publication Title

Journal of the Mechanics and Physics of Solids

#### Volume

50

#### Issue

12

#### First Page

2539

#### Last Page

2575

#### Recommended Citation

Jefferson, George; Haritos, George K.; and McMeeking, Robert M., "The Elastic Response of a Cohesive Aggregate—a Discrete Element Model with Coupled Particle Interaction" (2002). *Mechanical Engineering Faculty Research*. 772.

http://ideaexchange.uakron.edu/mechanical_ideas/772