  The fracture simulation of random particle reinforced composite structures
remains a challenge. Current techniques either assumed a homogeneous model,
ignoring the microstructure characteristics of composite structures, or
considered a micro-mechanical model, involving intractable computational costs.
This paper proposes a peridynamics-based statistical multiscale (PSM) framework
to simulate the macroscopic structure fracture with high efficiency. The
heterogeneities of composites, including the shape, spatial distribution and
volume fraction of particles, are characterized within the representative
volume elements (RVEs), and their impact on structure failure are extracted as
two types of peridynamic parameters, namely, statistical critical stretch and
equivalent micromodulus. At the microscale level, a bond-based peridynamic
(BPD) model with energy-based micromodulus correction technique is introduced
to simulate the fracture in RVEs, and then the computational model of
statistical critical stretch is established through micromechanical analysis.
Moreover, based on the statistical homogenization approach, the computational
model of effective elastic tensor is also established. Then, the equivalent
micromodulus can be derived from the effective elastic tensor, according to the
energy density equivalence between classical continuum mechanics (CCM) and BPD
models. At the macroscale level, a macroscale BPD model with the statistical
critical stretch and the equivalent micromodulus is constructed to simulate the
fracture in the macroscopic homogenized structures. The algorithm framework of
the PSM method is also described. Two- and three-dimensional numerical examples
illustrate the validity, accuracy and efficiency of the proposed method.
