The elastic response of a cohesive aggregate - a discrete element model with coupled particle interaction

被引:57
作者
Jefferson, G
Haritos, GK
McMeeking, RM [1 ]
机构
[1] Univ Calif Santa Barbara, Coll Engn, Dept Mech & Environm Engn, Santa Barbara, CA 93106 USA
[2] Univ Calif Santa Barbara, Coll Engn, Dept Mat, Santa Barbara, CA 93106 USA
[3] USAF, Inst Technol, Dept Aeronaut & Astronaut, Wright Patterson AFB, OH 45433 USA
关键词
ceramic material; porous material; granular material; elastic material; discrete elements;
D O I
10.1016/S0022-5096(02)00051-0
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
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. Published by Elsevier Science Ltd.
引用
收藏
页码:2539 / 2575
页数:37
相关论文
共 22 条
[1]   THE INFLUENCE OF AN INCREASING PARTICLE COORDINATION ON THE DENSIFICATION OF SPHERICAL POWDERS [J].
ARZT, E .
ACTA METALLURGICA, 1982, 30 (10) :1883-1890
[2]   A MICROMECHANICAL DESCRIPTION OF GRANULAR MATERIAL BEHAVIOR [J].
CHRISTOFFERSEN, J ;
MEHRABADI, MM ;
NEMATNASSER, S .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1981, 48 (02) :339-344
[3]   THE EFFECTIVE ELASTIC-MODULI OF POROUS GRANULAR ROCKS [J].
DIGBY, PJ .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1981, 48 (04) :803-808
[4]   YIELDING OF METAL-POWDER BONDED BY ISOLATED CONTACTS [J].
FLECK, NA ;
KUHN, LT ;
MCMEEKING, RM .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1992, 40 (05) :1139-1162
[5]  
Green DJ, 1990, CERAMICS T, V7, P347
[6]   HOT-ISOSTATIC PRESSING DIAGRAMS - NEW DEVELOPMENTS [J].
HELLE, AS ;
EASTERLING, KE ;
ASHBY, MF .
ACTA METALLURGICA, 1985, 33 (12) :2163-2174
[7]   THE ELASTIC BEHAVIOUR OF A CRYSTALLINE AGGREGATE [J].
HILL, R .
PROCEEDINGS OF THE PHYSICAL SOCIETY OF LONDON SECTION A, 1952, 65 (389) :349-355
[8]   MICROMECHANICAL MODELING OF POWDER COMPACTS .1. UNIT PROBLEMS FOR SINTERING AND TRACTION INDUCED DEFORMATION [J].
JAGOTA, A ;
DAWSON, PR .
ACTA METALLURGICA, 1988, 36 (09) :2551-2561
[9]   Particle spin in anisotropic granular materials [J].
Jenkins, JT ;
La Ragione, L .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2001, 38 (6-7) :1063-1069
[10]   MEAN-FIELD INELASTIC BEHAVIOR OF RANDOM ARRAYS OF IDENTICAL SPHERES [J].
JENKINS, JT ;
STRACK, ODL .
MECHANICS OF MATERIALS, 1993, 16 (1-2) :25-33