Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials

Zhang, H. W.; Wu, Jia; Fu, Zhendong

doi:10.1007/s00466-010-0475-3

Cited by 71 publications

(47 citation statements)

References 31 publications

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“…Considering groups of coarse-elements that bare the same geometrical and mechanical properties these coarse element types can be grouped into sets of representative volume elements (RVE). In this work the term RVE will be used to denote the coarse element together with its underlying fine mesh structure as in [62]. For each RVE a homogeneous equilibrium equation is established considering specific boundary conditions.…”

Section: Numerical Evaluation Of Micro-scale Basis Functionsmentioning

confidence: 99%

“…EMsFEM is based on the assumption that the discrete micro-displacements within the coarse element are interpolated at the macro-nodes using the following scheme: [20,62] that a necessary and sufficient condition for relations (39) to hold is that the microbasis functions adhere to the following property…”

Section: Numerical Evaluation Of Micro-scale Basis Functionsmentioning

confidence: 99%

“…The boundary conditions considered are similar to the boundary conditions implemented for the evaluation of the micro to macro mapping [Eq. (47)] [62,63] .…”

Section: Macro Equivalent Micro-nodal Forcesmentioning

confidence: 99%

“…Poisson's effect). To overcome this problem, the enhanced multiscale finite element method (EMsFEM) has been proposed for the analysis of heterogeneous structures [62]. EMsFEM introduces additional coupling terms into the fine-scale interpolation functions to consider the coupling effect among different directions in multi-dimensional vector problems.…”

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confidence: 99%

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A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Triantafyllou

Chatzi

2014

Comput Mech

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A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments.

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Section: Numerical Evaluation Of Micro-scale Basis Functionsmentioning

confidence: 99%

Section: Numerical Evaluation Of Micro-scale Basis Functionsmentioning

confidence: 99%

“…The boundary conditions considered are similar to the boundary conditions implemented for the evaluation of the micro to macro mapping [Eq. (47)] [62,63] .…”

Section: Macro Equivalent Micro-nodal Forcesmentioning

confidence: 99%

mentioning

confidence: 99%

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A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Triantafyllou

Chatzi

2014

Comput Mech

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“…By doing this, the microscopic heterogeneous features of elements can be well captured by the numerical base functions in the solid deformation. The EMsFEM has been successfully used for the elastic [38] and elasto-plastic [39] analyses of the periodic lattice truss materials. The above-mentioned researches show that, the downscaling computation in the EMsFEM can be implemented easily and the detailed microscopic stress and strain fields can be obtained simultaneously as well as the macroscopic responses.…”

Section: Introductionmentioning

confidence: 99%

A new multiscale computational method for elasto-plastic analysis of heterogeneous materials

Zhang

2011

Comput Mech

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A new multiscale computational method is developed for the elasto-plastic analysis of heterogeneous continuum materials with both periodic and random microstructures. In the method, the multiscale base functions which can efficiently capture the small-scale features of elements are constructed numerically and employed to establish the relationship between the macroscopic and microscopic variables. Thus, the detailed microscopic stress fields within the elements can be obtained easily. For the construction of the numerical base functions, several different kinds of boundary conditions are introduced and their influences are investigated. In this context, a two-scale computational modeling with successive iteration scheme is proposed. The new method could be implemented conveniently and adopted to the general problems without scale separation and periodicity assumptions. Extensive numerical experiments are carried out and the results are compared with the direct FEM. It is shown that the method developed provides excellent precision of the nonlinear response for the heterogeneous materials. Moreover, the computational cost is reduced dramatically.

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General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

Zhang

Lü

Zheng

et al. 2014

Num Anal Meth Geomechanics

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SUMMARY This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.

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Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials

Cited by 71 publications

References 31 publications

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

A new multiscale computational method for elasto-plastic analysis of heterogeneous materials

General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

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