We investigate the ultimate strengths and failure types of asymmetric tilt grain boundaries (GBs) with various tilt angles with the aid of molecular dynamics simulations and analytic theory. The ...tensile strength of armchair-oriented graphene GBs shows a tendency to increase as the misorientation angle rises, while that of zigzag-oriented graphene GBs non-monotonically increases. The overall strength enhancement and weakening behaviors can be explained by a continuum stress analysis of pentagon–heptagon defects along GBs. Nevertheless, full atomistic analyses are required to predict the exact bonds from which mechanical failure initiate. Two different fracture types are observed in our studies; one with cracks growing along the GB and another with cracks growing away from the GB. Detailed understanding of the atomic arrangement along the GB, in addition to defect density, is necessary to ascertain the ultimate strength and rupture process of GBs.
Thermoelastic analysis by means of three-dimensional polyhedral elements based on the Smoothed Finite elements method (S-FEM), for example nodal Cell-based S-FEM (CS-FEM), Node-based S-FEM (NS-FEM), ...and Edge-based S-FEM (ES-FEM), was studied. S-FEM allows implicit shape functions, making it possible to construct shape functions of S-FEM based polyhedral elements in a straightforward manner. The performance of S-FEM based polyhedral elements was compared with one another and with the conventional finite elements including hexahedral and tetrahedral element. Numerical examples show that the polyhedral elements by means of CS-FEM and ES-FEM provide better accuracy and convergence rate than conventional hexahedral finite elements, while the polyhedral elements by means of NS-FEM leads to spurious mode.
The purpose of this study is to perform elastoplastic analysis using an edge-based smoothed finite element of hexahedron type. The edge-based smoothed finite element method has the best performance ...among the smoothed finite element methods, but has the problem of the volumetric locking phenomenon. Since plastic deformation is an isochoric process, it is accompanied by volumetric locking. In this study, the B-bar approach was introduced in the ESFEM to solve the volumetric locking phenomenon, and to enable elastoplastic analysis. The proposed method was verified to be efficient and accurate by comparison with results from the conventional finite element method.
An effective simulation of the eyeball containing microstructures which are optic nerves and lamina cribrosa, through homogenization method, was studied. Entire domain of the eyeball is divided into ...a fine-scale zone and a coarse-scale zone to reduce the number of degrees of freedom accompanied by modeling the microstructures. In the coarse-scale zone, homogenized material properties of the lamina cribrosa combined with the optic nerves are employed to compute overall behavior, while the optic nerves are directly modeled to obtain their local behavior in the fine-scale zone. Numerical tests with models having different size of the fine-scale zone showed that this homogenization scheme did not severely deteriorate solution accuracy and makes it possible to reflect the microstructures with reduced computational cost. Then, this multiscale method was employed to confirm a clinical result that a greater susceptibility to development of glaucoma corresponds to a larger curvature of the lamina cribrosa.
•A cell-based smoothed finite element method is proposed to make a polygonal element for analyzing FSI problems.•A sliding polygonal mesh method is developed to prevent mesh entanglement in the fluid ...domain.•The present scheme provides a seamless connection between dissimilar meshes at the interface.•The present scheme yields better accuracy compared with the conventional FEM.
A cell-based smoothed finite element method is proposed to make a polygonal type variable-node element for analyzing two-dimensional FSI problems. The gradient smoothing technique for the velocity field provides a proper softening effect, which relieves the stiff behavior of the conventional FEM. In addition, by using polygonal elements, a seamless connection is achieved between non-matching meshes satisfying the interface conditions of continuity and compatibility. In order to prevent mesh distortion along the fluid-solid interface, a sliding polygonal mesh was developed using the cell-based smoothed finite element method. Some numerical examples were presented to assess the performance and the effectiveness of the present method. The smoothed finite element methods yielded better accuracy compared with the conventional FEM, and the sliding polygonal mesh method successfully treated mesh distortion.
An equivalent continuum model for multilayer graphene sheets (MLGSs) and its plate model are developed to analyze the deformation behavior of MLGSs. Hyperelastic material models are introduced for ...the MLGS continuum model by examining the atomistic structures of MLGSs and obtaining their mechanical properties by means of molecular statics simulations. The MLGS plate model, a structural model for MLGSs, is developed by applying kinematics assumptions to the MLGS continuum model subjected to infinitesimal deformation. Finite element methods (FEM) with the corotational formulation are adopted to analyze the mechanical behavior of MLGSs under small-strain deformation and large rotation conditions. The MLGS plate element passes several basic numerical tests, including patch tests, eigenvalue analyses, and geometrically nonlinear benchmark problems. Finally, the deflections of a plane-strain cantilever and spherical indentations are analyzed by the proposed MLGS plate element and molecular dynamics (MD) simulations. These results show that the MLGS plate element properly represents the deformation behaviors of MLGSs from the atomic scale to the macroscopic continuum scale.
•We present a plate finite element able to analyze deformation of MLGSs.•Interlayer slip and layer deformation are described by kinematics assumptions.•Corotational formulation is employed for small-strain deformations & large rotations.•The element is verified as a structural element and a continuum description of MLGSs.
•Distinct buckling modes of BLGSs on a foundation are studied.•New morphology evolutions of the post-buckling deformation are reported.•Novel finite element for analyzing atomic van der Waals ...interactions is developed.
The buckling and the post-buckling of bilayer graphene sheets (BLGSs) on an elastic foundation subjected to an axial compressive load in plane-strain condition are studied. The solutions for the buckling strain and the characteristic wavelength at the onset of the buckling are obtained by using proposed continuum models describing deformations of BLGSs. The buckling analysis reveals that the buckling of BLGSs on an elastic foundation could be categorized into four. When the foundation is very soft, the Euler beam kinematics prevails in the entire BLGSs. On the stiffer foundation, the shear deformation on the cross-section of BLGSs occurs, and the characteristic wavelength changes sensitively as the stiffness of the foundation varies. With the foundation whose stiffness is almost the same as the shear modulus of the graphene interlayer, the buckling strain and the characteristic wavelength are nearly linear versus the elastic modulus of the foundation in logarithmic scale. When the foundation is much stiffer than the rigidities of the graphene interlayer, detachment between graphene layers could occur. Finally, we conduct the post-buckling analysis by using the proposed finite element model and obtain various morphology evolutions which contain detachment between graphene layers, period doubling, localization, period switching, and folding. Also, we present a diagram includes distinct deformation patterns according to the stiffness of the foundation and the magnitude of the applied compressive strain.
•An automatic algorithm for generating polyhedral meshes was systematically developed.•Hexahedral elements near the given STL surface were categorized into polyhedral volume topologies based on the ...MC algorithm.•Topology ambiguities of the MC algorithm were effectively resolved to provide an appropriate mesh for complex geometry.•The effectiveness was demonstrated through numerical analysis using the smoothed finite element method.
Hexahedral meshes that exhibit the superiority in terms of solution accuracy and convergence rate are preferred to other types of meshes in the finite element analysis. However, the construction of the hexahedral meshes for complex geometries is still considered troublesome due to their poor geometric adaptability. This paper presents an efficient grid-based scheme to automatically generate polyhedral meshes including the hexahedral elements, and thus to provide hexahedral-dominant meshes for three-dimensional geometry with complex shapes. On the basis of the marching cube algorithm with a background grid composed of a regular arrangement of cubes, surface topologies for the background cubes are defined to represent the three-dimensional boundaries of a given domain. Then, in order to generate a three-dimensional finite element mesh, the surface topologies of the marching cube algorithm are systematically expanded to polyhedral volume topologies. Meanwhile, a topology ambiguity problem inherent in the marching cube algorithm is effectively resolved to generate an appropriate polyhedral mesh even for an arbitrary complex geometry. Several examples including biostructure modeling demonstrate that the proposed mesh generation scheme can easily discretize complex three-dimensional domains with hexahedral-dominant meshes, which are composed of the polyhedral elements near the domain boundaries and the hexahedral elements that come from the background cubes inside the domains. Furthermore, to show the applicability and effectiveness of polyhedral meshes in the finite element analysis, some structural analyses are performed using the smoothed finite element method that can be straightforwardly adapted to polyhedral elements of arbitrary shape.
•A new formulation of VNEs (variable-node elements) based on S-FEM is proposed.•The application of CS-FEM is extended to three-dimensional elastoplastic analysis.•The proposed VNEs are useful for ...connecting nonmatching FE meshes.•The effectiveness of the proposed VNEs is demonstrated through numerical examples.
In this paper, variable-node elements (VNEs) based on the cell-based smoothed finite element method (CS-FEM) are proposed with emphasis on their applications for elasto-plastic finite deformation. The formulation of CS-FEM is extended to cover elastic–plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elasto-plastic deformations is remedied by relaxing volumetric strain through its mean value. In addition, the existing VNEs limited to linear elastic analysis is extended to analysis of elasto-plastic deformations with the aid of CS-FEM. The comparison with the conventional finite elements and Abaqus demonstrates the effectiveness and accuracy of the present approach.
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