Dongwoo Sohn

Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions

A three-level finite element scheme is proposed for simulation of crack propagation in heterogeneous media including randomly distributed voids or inclusions. To reduce total degrees of freedom in the view of mesh gradation, the entire domain is categorized into three regions of different-level meshes: a region of coarse-level mesh, a region of intermediate-level mesh, and a region of fine-level mesh. The region of coarse-level mesh is chosen to be far from the crack to treat the material inhomogeneities in the sense of coarse-graining through homogenization, while the region near the crack is composed of the intermediate-level mesh to model the presence of inhomogeneities in detail. Furthermore, the region very near the crack tip is refined into the fine-level mesh to capture a steep gradient of elastic field due to the crack tip singularity. Variable-node finite elements are employed to satisfy the nodal connectivity and compatibility between the neighboring different-level meshes. Local remeshing is needed for readjustment of mesh near the crack tip in accordance with crack growth, and this is automatically made according to preset values of parameters determining the propagation step size of crack, and so the entire process is fully automatic. The effectiveness of the proposed scheme is demonstrated through several numerical examples. Meanwhile, the effect of voids and inclusions on the crack propagation is discussed in terms of T-stresses, with the aid of three-level adaptive scheme.

An efficient scheme for coupling dissimilar hexahedral meshes with the aid of variable-node transition elements

Three-dimensional transition elements are proposed achieve efficient and accurate connections of nonmatching meshes with different resolutions. These elements, termed variable-node elements, allow additional nodes on element faces of conventional hexahedral elements, as well as on element edges. By taking proper polynomial bases and their absolute values that correspond to the additional nodes, compatible trilinear shape functions are systematically derived in master domains of the elements. When one hexahedral element meets many other hexahedral elements at its faces or edges, the variable-node elements enable one-to-many connection of the dissimilar hexahedral elements in a seamless way. The effectiveness of the proposed scheme is demonstrated through numerical examples of local mesh refinement and subdivision modeling involving nonmatching mesh problems.

Effect of interlayer sliding on the estimation of elastic modulus of multilayer graphene in nanoindentation simulation

Nanoindentation experiments and simulations are carried out to estimate the elastic modulus of freely-suspended-multilayer graphene. However, due to the difficulty of clamping all layers of multilayer graphene in experiments, and to the ambiguity of imposing the clamped boundary conditions in numerical simulations, the estimated values of elastic modulus exhibit large variation. In particular, interlayer sliding can affect the estimation of elastic modulus. From a series of molecular dynamics simulations, we demonstrate that the estimated elastic modulus of multilayer graphene depends on the level of interlayer sliding involved in boundary conditions. Under fully clamped boundary conditions that prevent interlayer sliding, the elastic modulus is constant regardless of the number of layers. In contrast, under weakly clamped boundary conditions that involve interlayer sliding, the elastic modulus decreases with increasing number of layers. In the case of weakly clamped conditions, a few wrinkles form in the interlayer and then coalesce into a single large wrinkle due to interlayer sliding. Our findings provide an understanding of the variation of elastic modulus observed in other experimental and numerical studies.

MULTISCALE FINITE ELEMENT METHOD FOR HETEROGENEOUS MEDIA WITH MICROSTRUCTURES: CRACK PROPAGATION IN A POROUS MEDIUM

A novel multiscale FE scheme is proposed for simulation of crack propagation in heterogeneous media. A fine scale mesh is constructed to model the crack tip and the microstructures around the near-tip field, while a coarse scale mesh is introduced to model the far field, wherein the effect of the microstructures is averaged through the homogenization theory to yield the average macroscopic constitutive relationship. The so-called variable node elements are subsequently employed to connect the fine scale zone in a seamless way to the coarse scale zone. The moving crack tip is modeled in a straightforward manner with the conventional quarter-point singular element. Several numerical examples are presented to demonstrate the scheme as an effective tool for multiscale simulation of crack propagation in consideration of the microstructures in a heterogeneous body.

A microstructure modeling scheme for unidirectional composites using signed distance function based boundary smoothing and element trimming

Abstract A simple and accurate scheme for modeling microstructures is proposed with the help of element trimming combined with signed distance function based boundary smoothing. To accommodate randomly distributed fibers in unidirectional composites, digital image processing is used. The interfaces of multi-materials are identified by introducing a signed distance function, and then, square background elements crossing the interfaces are simply trimmed and divided to represent a single material behavior by a single element. After element trimming, the elements that are polygon-shaped in the two-dimensional domain are split into conventional three-node triangle elements (six-node prism elements in the three-dimensional domain) available in many commercial software packages. The present modeling scheme was verified through benchmark examples in terms of the accuracy and efficiency and then applied to the modeling of unidirectional composites based on real microscopic images to evaluate the equivalent elastic properties.

Temperature dependence of screw dislocation mobility on shuffle-set of silicon

Large-scale atomistic simulations are performed in order to observe local behaviors of screw dislocations located on the shuffle set of (111) in single crystal silicon, focusing on the propagation process of the screw dislocations. A quadrupolar arrangement of screw dislocations is utilized to impose the periodic boundary conditions along each of the three spatial directions. With the aid of molecular dynamics simulations, the dislocation mobility is investigated in terms of the critical resolved shear stress. Based on the results from the simulations, we discuss effects of the model size and temperature on the critical resolved shear stress. After choosing the proper model size to reduce undesirable interference between the dislocations, we further estimate the Peierls stress by fitting from a set of the critical resolved shear stresses at various temperatures. Meanwhile, we observe a double kink mechanism in the dislocation propagation which is the most energetically favorable dislocation movement in silicon. We investigate the formation and migration of kink pairs on an undissociated screw dislocation in silicon.