Analyses on composite materials using an element overlay technique

岡田, 裕; 田中, 智行; 福井, 泰好; 熊澤, 典良; Ninomiya, Takashi; Sakasegawa, Yosuke

doi:10.1299/jsmecmd.2004.17.467

Cited by 10 publications

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“…Since the global and local meshes can be generated independently, mesh generation efforts, which are drawing a dominant bottleneck in recent computer-aided engineering (Arai et al, 2015), are reduced remarkably. S-FEM has been applied to basic problems (Fish, 1992;Fish and Markolefas, 1993), multiscale structural problems (Suzuki et al, 1999), linear elastic fracture problems (Okada et al, 2005;Maitireyimu et al, 2009;Kamaya et al, 2010;Wada et al, 2014), elastic-plastic fracture problems (Okada et al, 2007), and composite material problems (Okada et al, 2004;Tanaka et al, 2006;Kikuchi et al, 2014). However, s-FEM has a common issue.…”

Section: Introductionmentioning

confidence: 99%

An s-version finite element method without generation of coupling stiffness matrix by using iterative technique

Yumoto

Yusa

Okada

2016

Mechanical Engineering Journal

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In s-version finite element method (s-FEM) proposed by Fish (1992), a local mesh that represents the local feature such as a hole or a crack is superposed on a global mesh that represents the shape of the whole analysis model. The interaction between global and local meshes is represented by coupling stiffness matrices. Since the global and local meshes can be generated independently, mesh generation efforts are reduced remarkably. However, s-FEM has a common issue. The generation of coupling stiffness matrices takes a considerable amount of program development efforts, which include constructing accurate cross-element integration methodology and programming it for various element types. For such an issue, we propose an iterative s-FEM that does not require the generation of coupling stiffness matrices at all. The coupling term is now evaluated by global and local stresses that are computed on the respective mesh and then transferred to the other by interpolation techniques. The global and local stresses are treated as initial stress in the finite element computations. The global and local analyses are performed alternately under assumed initial stress, and converged solution is achieved by iteration with a monitored residual being sufficiently small. In proposed iterative s-FEM, an issue about linear independence of global and local elements, which is known to occur in the original s-FEM, does not occur. In numerical experiments, converged solution was successfully obtained within several hundred iteration counts. Accurate stress distribution for a stress concentration problem and an accurate stress intensity factor for a linear elastic fracture mechanics problem were computed by proposed iterative s-FEM. In addition, several stress interpolation techniques were compared in the numerical experiments. Nearest neighbor interpolation for the global stress and local least squares interpolation for the local stress showed good convergence and accurate solution.

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Section: Introductionmentioning

confidence: 99%

An s-version finite element method without generation of coupling stiffness matrix by using iterative technique

Yumoto

Yusa

Okada

2016

Mechanical Engineering Journal

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“…The other is called "local finite element model" or "local model" that is superposed on the global model, as depicted in Figure 3. Typically, the local model has a finer spatial resolution than the global model and is typically placed at the portion of stress concentration, such as crack (see Okada, Endoh and Kikuchi [7]), and second phase material and its vicinity (see Okada et al [8] and Okada et al [9]). In Okada et al …”

Section: The S-version Finite Element Methods (S-fem)mentioning

confidence: 99%

“…When the damage constitutive law is adopted in an analysis, we perform an incremental analysis, just like the case of elastoplasticity (see Okada et al [9]). We briefly describe the formulations of present s-FEM.…”

Section: The S-version Finite Element Methods (S-fem)mentioning

confidence: 99%

“…The constitutive model was implemented in the in-house s-FEM computer program. The s-FEM computer program of Okada et al [3] can model particulate composite materials by superposing the finite element models for the particles on that for the global structure or for the region of unit cell. A finite element model for a particle and its surrounding material region needs to be built only once.…”

Section: Damage Constitutive Lawmentioning

confidence: 99%

“…From equation (6), the rate of damage parameter can be derived to be: Substituting equation (9) in equation (8), we arrive at: …”

Section: Isotropic Damagementioning

confidence: 99%

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Numerical Investigation for the Microstructural Effects on the Crack Growth Behavior of Particulate Composite Materials

Okada¹

2006

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. In present investigation, analyses for the damage evolution behavior of particulate composite materials by using the finite element method (FEM) and the s-version finite element method (s-FEM) were carried out. The analyses were carried out in particular interest in the phenomenon of crack propagation. Prior to crack propagation, material damage develops in the material. The material damage may be in the forms of microviod and/or microcracks in the binder (matrix) and in the form of binder (matrix)/particle separation that is known to be dewetting. In a macroscopic sense, the reinforcing particles distribute evenly in matrix. However, at microscopic level, the density of the distributed particles varies. This means that the stiffness and strength of the material also have some spatial variations. Material damages initiate at the weak material locations and then propagate the surroundings. When cracks are present in the material, the cracks interact with the surroundings and the material To simulate such scenarios, we adopted two kinds of damage constitutive models. One is isotropic damage model and the other is ?separate dilatational/deviatoric damage constitutive model? in which the contributions of hydrostatic and of deviatoric stresses are accounted for independently. A parameter in the separate dilatational/ deviatoric damage model can characterize which, hydrostatic or deviatoric stress component, has dominant influence to the damage behavior of the material. A series of analyses on uncracked and cracked specimen with statistically varying material stiffness at a microscopic level were carried out. The results revealed that the damage behavior is highly influenced by the damage mode. SUBJECT TERMS Fracture Mechanics

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A moving superimposed finite element method for structural topology optimization

Wang

2006

Int. J. Numer. Meth. Engng

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SUMMARYLevel set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures. In this paper, a dynamic implicit boundary-based moving superimposed finite element method (s-version FEM or S-FEM) is developed for structural topology optimization using the level set methods, in which the variational interior and exterior boundaries are represented by the zero level set. Both a global mesh and an overlaying local mesh are integrated into the moving S-FEM analysis model. A relatively coarse fixed Eulerian mesh consisting of bilinear rectangular elements is used as a global mesh. The local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function. In numerical integration using the Gauss quadrature rule, the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes. A double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co-ordinate systems. An element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency. A simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint. A physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated PDE solving procedure. The proposed moving S-FEM is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems. For the classical elasticity problems in the literature, the present S-FEM can achieve numerical results in good agreement with those from the theoretical solutions and/or numerical results from the standard FEM. For the minimum compliance topology optimization problems in structural optimization, the present approach significantly outperforms the well-recognized 'ersatz material' approach as expected in the accuracy of the strain field, numerical stability, and representation fidelity at the expense of increased computational time. It is also shown that the present approach is able to produce structures near the theoretical optimum. It is suggested that the present S-FEM can be a promising tool for shape and topology optimization using the level set methods.

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Analyses on composite materials using an element overlay technique

Cited by 10 publications

References 0 publications

An s-version finite element method without generation of coupling stiffness matrix by using iterative technique

An s-version finite element method without generation of coupling stiffness matrix by using iterative technique

Numerical Investigation for the Microstructural Effects on the Crack Growth Behavior of Particulate Composite Materials

A moving superimposed finite element method for structural topology optimization

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