Nanoscale Effect Investigation for Effective Bulk Modulus of Particulate Polymer Nanocomposites Using Micromechanical Framework

Table 1

Formulae for prediction of effective bulk modulus of nanocomposites taking into account nanoscale effect.

Ref.	Expression	Interface model	Homogenization technique
Firooz et al. [52]		Simplified general interface model that recovers the elastic (stress-type) interface model	Composite sphere assemblage method
Zemlyanova and Mogilevskaya [55]	, where	Steigmann–Ogden interface model	Equivalent particle (particle-plus-interface) + Maxwell’s homogenization approach
Nazarenko et al. [56]	, where , and λc and µc in this case are the Lamé parameters of the reference medium, which is chosen as the matrix medium	Gurtin–Murdoch interface model	Energy-equivalent inhomogeneity
Duan et al. [22]	, where	Gurtin–Murdoch interface model	Equivalent particle (particle-plus-interface) + composite spheres assemblage
Gu et al. [57]	, where	Gurtin–Murdoch interface model	Equivalent particle (particle-plus-interface) + generalized self-consistent method
This work		Gurtin–Murdoch interface model	Generalized self-consistent method