Chapter 6
Unified Micromechanics of Particulate
Composites
6.1 Introduction
Modeling the macroscopic constitutive response of heterogeneous materials starting
from local description of the microstructure is necessary. Composite materials are
heterogeneous. However, continuum mechanics formulation requires homogenization of the medium. The homogenization from local level to macro level and the
localization from macro-level quantities to the corresponding local micromechanics
variables must be well defined.
Using Eshelby method (1957), Ju and Chen (1994a, b) formulated the effective
mechanical properties of elastic multiphase composites containing many randomly
dispersed ellipsoidal inhomogeneity with perfect bonding. Within the context of the
representative volume element (REV), four governing micromechanical ensemblevolume averaged field equations are utilized to relate ensemble-volume averaged
stresses, strains, volume fractions, eigenstrains, particle shapes and orientations, and
elastic properties of constituent phases of the particulate composites. Ju and Tseng
(1996) formulated combining a micromechanical interaction approach and the
continuum plasticity to predict effective elastoplastic behavior of two-phase particulate composite containing many randomly dispersed elastic spherical inhomogeneity. Explicit pairwise interparticle interactions are considered in both the elastic and
plastic responses. Furthermore, the ensemble-volume averaging procedure is
employed and the formulation is of complete second order.
Let us consider a perfectly bonded two-phase composite consisting of an elastic
matrix (phase 0) with bulk modulus k 0 and shear modulus μ 0 and randomly dispersed
elastic spherical particles (phase 1) with bulk modulus k 1 and shear modulus μ 1 . The
effective bulk modulus k à and effective shear modulus μ à for this two-phase composite for the noninteracting solution, neglecting the interparticle interaction effects,
was derived by Ju and Chen (1994a):
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_6
277
Unified Micromechanics of Particulate
Composites
6.1 Introduction
Modeling the macroscopic constitutive response of heterogeneous materials starting
from local description of the microstructure is necessary. Composite materials are
heterogeneous. However, continuum mechanics formulation requires homogenization of the medium. The homogenization from local level to macro level and the
localization from macro-level quantities to the corresponding local micromechanics
variables must be well defined.
Using Eshelby method (1957), Ju and Chen (1994a, b) formulated the effective
mechanical properties of elastic multiphase composites containing many randomly
dispersed ellipsoidal inhomogeneity with perfect bonding. Within the context of the
representative volume element (REV), four governing micromechanical ensemblevolume averaged field equations are utilized to relate ensemble-volume averaged
stresses, strains, volume fractions, eigenstrains, particle shapes and orientations, and
elastic properties of constituent phases of the particulate composites. Ju and Tseng
(1996) formulated combining a micromechanical interaction approach and the
continuum plasticity to predict effective elastoplastic behavior of two-phase particulate composite containing many randomly dispersed elastic spherical inhomogeneity. Explicit pairwise interparticle interactions are considered in both the elastic and
plastic responses. Furthermore, the ensemble-volume averaging procedure is
employed and the formulation is of complete second order.
Let us consider a perfectly bonded two-phase composite consisting of an elastic
matrix (phase 0) with bulk modulus k 0 and shear modulus μ 0 and randomly dispersed
elastic spherical particles (phase 1) with bulk modulus k 1 and shear modulus μ 1 . The
effective bulk modulus k à and effective shear modulus μ à for this two-phase composite for the noninteracting solution, neglecting the interparticle interaction effects,
was derived by Ju and Chen (1994a):
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_6
277