Direct numerical simulation of complex nano‐structured composites, considering interface stretching and bending effects, using nano‐computational grains

Abstract

Driven by the promising applications of nano-composites, the Steigmann-Ogden (S-O) interface stress model is used together with the classical Elasticity theory to model the effective mechanical properties of nano-composites, considering both interface stretching and bending effects. However, no literature has been reported on analytical or numerical solutions for composites containing multiple three-dimensional nano-inclusions with SO interfaces. In order to overcome this difficulty, a new type of computational grain (CG) is developed with an embedded spherical inclusion and SO matrix/inclusion interface. The stiffness matrix of each CG is computed by a new boundary-type multifield variational principle together with Papkovich-Neuber potentials. By evaluating and assembling stiffness matrices of CGs along with parallel computations, very efficient direct numerical simulations of complex nano-composites with a large number of inclusions in a Representative Volume Element of the nanocomposite are essentially realized. Numerical examples demonstrate the validity and the power of the currently developed CGs. Especially, material models with 10,000 nano-inclusions are simulated in around 50 min on the 16-core workstation. The influence of interface elastic bending parameters and spatial distributions of the nano-inclusions on the overall properties of nano-composites is also investigated in this study.

3D viscoelastic computational grains with spherical inclusions with or without interphases/coatings for micromechanical modeling of heterogeneous materials

“…29 It should also be noted that simple parallelization can further speed the computation by CGs, where microstructures with 10,000 inclusions are simulated in around 50 min on a 16-core workstation. 30 For more details of the appropriate size of the RVE, please refer to Reference 31.…”