DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

Abstract

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists of a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field in composite continua.

Multiscale Modeling of Composite Materials with DECM Approach: Shape Effect of Inclusions

“…4 and 7, it follows that the normal stress y  tends to concentrate within the round inclusions, which causes y  to decrease in the matrix around the inclusions. As shown in [7], a similar behavior also occurs for shear loads. In particular, both for shear and axial loads, the normal stresses concentrate near the boundaries of the inclusions but y  reaches its maximum value (in absolute value) at the ends of the constraint.…”

“…The DECM overcomes the drawbacks associated with the use of deformable and rigid blocks for the modeling of continua, as it has no problem generating efficient meshes for the sub-domains, even when they consist of more than one material [44]. Consequently, the DECM can provide descriptions of the stress field within single inclusions and on the interfaces between different materials [7].…”

“…The iterative analysis consists of two phases [7]: in the first phase, the DECM code processes the discrete elements with the same row index and, in the second phase, the DECM code processes the rows. Both phases, in turn, consist of two iterations, since the DECM code processes the discrete elements and the rows twice, in each phase.…”

Multiscale Discrete Element Modeling

“…The method was implemented in the Particle Flow Code (PFC2D). Some effective approaches have been developed using a combination of discrete elements and continuum mechanics methods [15][16][17][18][19]. In [20,21], the cohesive discrete element method was presented where a continuous medium is modeled by packed granular spheres, and cohesive interaction between the spheres is described with beam elements.…”

Discrete Element Simulation Analysis of Biaxial Mechanical Properties of Concrete with Large-Size Recycled Aggregate

“…The elements in the discrete element technique have normal and tangential stiffness, which are used to model the interaction between the elements, and the normal and tangential bonding strengths between the elements can be adjusted to simulate the elements cracking. Recent versions of the discrete element technique employ deformable blocks to overcome high joint displacements and modest block deformations [10][11][12][13]. He et al [14] conducted biaxial compression experiments on recycled concrete at various strain rates and discovered that while the strength of RAC rose as the strain rate increased, the concrete's failure mode remained the same.…”