Elastic equilibrium of spherical particle composites with transversely isotropic interphase and incoherent material interface

The rigorous analytical solution to the unit cell model of spherical particle composite with transversely isotropic interphase and incoherent material interface has been obtained by the multipole expansion method. To this end, a general expression of the displacement vector in spherical transversely isotropic solid in terms of the vector spherical harmonics has been derived. By accurate fulfillment of the contact conditions, the model boundary value problem is reduced to the linear algebraic system. The anisotropic interface model has been developed as the first order approximation of the transversely isotropic inter phase. Relevance of this model to the theory of material interfaces and its applicability in the nanomechanics context is discussed. The developed model expands the theory of curved deformable interfaces of Gurtin et al. [Phil. Mag. A 78 (1998) 1093] on the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface elastic moduli. Taking incoherency of the nano level interfaces into account enables more realistic models and thus increases the predictive power the homogenization theory of nanostructured solids. The obtained accurate numerical data discover a significant effect of the interphase/interface anisotropy on the local stress and effective stiffness of spherical particle composite. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The rigorous analytical solution to the unit cell model of spherical particle composite with transversely isotropic interphase and incoherent material interface has been obtained by the multipole expansion method. The developed model expands the theory of curved deformable interfaces of Gurtin et al. on the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface elastic moduli. Taking incoherency of the nano level interfaces into account enables more realistic models and thus increases the predictive power the homogenization theory of nanostructured solids.