Effective elastic moduli of a composite containing rigid spheres at nondilute concentrations: A multiple scattering approach

@article{citeulike:1188134, abstract = {Based on the multiple scattering technique [K. F. Freed and M. Muthukumar, J. Chem. Phys. 69, 2657 (1978); 68, 2088 (1978); M. Muthukumar and K. H. Freed, J. Chem. Phys. 70, 5875 (1979)] previously applied to the study of suspensions of spheres and polymers, we propose an approach to the computation of the effective elastic properties of a composite material containing rigid, mono-sized, randomly dispersed, spherical particles. Our method incorporates the many-body, long-range elastic interactions among inclusions. The effective medium equations are constructed and numerically solved self-consistently. We have calculated the effective shear \µ and Young E moduli, as well as the effective Poisson ratio , as functions of the particle volume fraction and of the Poisson ratio of the continuous phase. Comparisons with two sets of experimental data\&\#151;glass beads in a polymer matrix and tungsten carbide particles in a cobalt matrix (Wc/Co)\&\#151;and to a previous theoretical solution, are also presented. Our model can predict the effective Poisson ratio of the Wc/Co system for 1 and for the glass/polymer system for 0.5. In particular, the present work describes accurately composites with a high volume fraction of inclusions, where a percolation transition occurs. Very good agreement with the experimental data are obtained for E and \µ when 0.4, for both systems.\©1999 American Institute of Physics.}, author = {Mondescu, Radu P. and Muthukumar, M. }, citeulike-article-id = {1188134}, doi = {10.1063/1.478186}, journal = {The Journal of Chemical Physics}, keywords = {elasticity, greens\_function}, number = {2}, pages = {1123--1137}, posted-at = {2007-03-26 14:31:56}, priority = {2}, publisher = {AIP}, title = {Effective elastic moduli of a composite containing rigid spheres at nondilute concentrations: A multiple scattering approach}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=JCPSA6000110000002001123000001\&idtype=cvips\&gifs=yes}, volume = {110}, year = {1999} }

TY - JOUR ID - citeulike:1188134 L3 - citeulike-article-id:1188134 TI - Effective elastic moduli of a composite containing rigid spheres at nondilute concentrations: A multiple scattering approach JF - The Journal of Chemical Physics VL - 110 IS - 2 SP - 1123 EP - 1137 PB - AIP N2 - Based on the multiple scattering technique [K. F. Freed and M. Muthukumar, J. Chem. Phys. 69, 2657 (1978); 68, 2088 (1978); M. Muthukumar and K. H. Freed, J. Chem. Phys. 70, 5875 (1979)] previously applied to the study of suspensions of spheres and polymers, we propose an approach to the computation of the effective elastic properties of a composite material containing rigid, mono-sized, randomly dispersed, spherical particles. Our method incorporates the many-body, long-range elastic interactions among inclusions. The effective medium equations are constructed and numerically solved self-consistently. We have calculated the effective shear µ and Young E moduli, as well as the effective Poisson ratio , as functions of the particle volume fraction and of the Poisson ratio of the continuous phase. Comparisons with two sets of experimental data—glass beads in a polymer matrix and tungsten carbide particles in a cobalt matrix (Wc/Co)—and to a previous theoretical solution, are also presented. Our model can predict the effective Poisson ratio of the Wc/Co system for 1 and for the glass/polymer system for 0.5. In particular, the present work describes accurately composites with a high volume fraction of inclusions, where a percolation transition occurs. Very good agreement with the experimental data are obtained for E and µ when 0.4, for both systems.©1999 American Institute of Physics. KW - elasticity KW - greens_function AU - Mondescu, Radu AU - Muthukumar, M PY - 1999/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000110000002001123000001&idtype=cvips&gifs=yes ER -