TY - JOUR
T1 - Elastic fields and effective moduli of particulate nanocomposites with the Gurtin-Murdoch model of interfaces
AU - Kushch, Volodymyr I.
AU - Mogilevskaya, Sofia G.
AU - Stolarski, Henryk K.
AU - Crouch, Steven L.
N1 - Funding Information:
VK gratefully acknowledges the MTS Professorship Grant from the University of Minnesota, Minneapolis, USA.
PY - 2013/4
Y1 - 2013/4
N2 - A complete solution has been obtained for periodic particulate nanocomposite with the unit cell containing a finite number of spherical particles with the Gurtin-Murdoch interfaces. For this purpose, the multipole expansion approach by Kushch et al. [Kushch, V.I.; Mogilevskaya, S.G.; Stolarski, H.K.; Crouch, S.L.; 2011. Elastic interaction of spherical nanoinhomogeneities with Gurtin-Murdoch type interfaces. J. Mech. Phys. Solids 59, 1702-1716] has been further developed and implemented in an efficient numerical algorithm. The method provides accurate evaluation of local fields and effective stiffness tensor with the interaction effects fully taken into account. The displacement vector within the matrix domain is found as a superposition of the vector periodic solutions of Lamé equation. By using local expansion of the total displacement and stress fields in terms of vector spherical harmonics associated with each particle, the interface conditions are fulfilled precisely. Analytical averaging of the local strain and stress fields in matrix domain yields an exact, closed form formula (in terms of expansion coefficients) for the effective elastic stiffness tensor of nanocomposite. Numerical results demonstrate that elastic stiffness and, especially, brittle strength of nanoheterogeneous materials can be substantially improved by an appropriate surface modification.
AB - A complete solution has been obtained for periodic particulate nanocomposite with the unit cell containing a finite number of spherical particles with the Gurtin-Murdoch interfaces. For this purpose, the multipole expansion approach by Kushch et al. [Kushch, V.I.; Mogilevskaya, S.G.; Stolarski, H.K.; Crouch, S.L.; 2011. Elastic interaction of spherical nanoinhomogeneities with Gurtin-Murdoch type interfaces. J. Mech. Phys. Solids 59, 1702-1716] has been further developed and implemented in an efficient numerical algorithm. The method provides accurate evaluation of local fields and effective stiffness tensor with the interaction effects fully taken into account. The displacement vector within the matrix domain is found as a superposition of the vector periodic solutions of Lamé equation. By using local expansion of the total displacement and stress fields in terms of vector spherical harmonics associated with each particle, the interface conditions are fulfilled precisely. Analytical averaging of the local strain and stress fields in matrix domain yields an exact, closed form formula (in terms of expansion coefficients) for the effective elastic stiffness tensor of nanocomposite. Numerical results demonstrate that elastic stiffness and, especially, brittle strength of nanoheterogeneous materials can be substantially improved by an appropriate surface modification.
KW - Effective stiffness
KW - Gurtin-Murdoch interface
KW - Multipole expansion
KW - Spherical inhomogeneity
KW - Unit cell model
UR - http://www.scopus.com/inward/record.url?scp=84873713218&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84873713218&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2012.12.016
DO - 10.1016/j.ijsolstr.2012.12.016
M3 - Article
AN - SCOPUS:84873713218
SN - 0020-7683
VL - 50
SP - 1141
EP - 1153
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 7-8
ER -