Direct FE<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2583" altimg="si141.svg"><mml:msup><mml:mrow/><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> for concurrent multilevel modeling of heterogeneous thin plate structures

Xu, Jian; Li, Pei; Poh, Leong Hien; Zhang, Yingying; Tan, V.B.C.

doi:10.1016/j.cma.2022.114658

Cited by 22 publications

(6 citation statements)

References 47 publications

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“…Substituting Equation (56) into Equation ( 55), we yield the cell problems for two unknown cell functions N mn (y, z) and D 𝛼 1 (y, z) as…”

Section: 2mentioning

confidence: 99%

“…The semi‐concurrent multiscale methods are more accurate but less efficient than the hierarchical multiscale methods because there exists a data exchange between the small scale and large scale during the whole numerical modeling, 40 that is, the data can be transferred from the small scale to the large scale and vice versa. The FE2 methods, 53 or their extension forms, Direct FE2, 54–56 are the typical semi‐concurrent multiscale methods. In FE2 methods, the weak form of the equilibrium equation is constructed by the principle of virtual work, which demonstrates the internal virtual work is equal to the external virtual work 54 .…”

Section: Hm Coupling Problems In Heterogeneous Pm With Macro‐meso Con...mentioning

confidence: 99%

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High‐order models for hydro‐mechanical coupling problems in multiscale porous media

Zuo,

Yang,

Cui

et al. 2024

Numerical Meth Engineering

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An accurate prediction of nonlinear hydro‐mechanical (HM) coupling in subsurface structures with pronounced heterogeneity at multiple spatial scales is still an open topic and crucial for numerous engineering applications, for example, hydraulic fracturing and enhanced geothermal systems. In this study, novel high‐order multi‐scale asymptotic solutions are developed to accurately capture the locally oscillating characteristics of gas flow and solid displacement fields at multiple scales. First, the formal macro‐meso two‐scale asymptotic expansion is performed to establish the homogenized solutions and macro‐meso high‐order models which can predict the HM coupling problems at the macroscale and mesoscale. By directly expanding the cell functions defined at the mesoscale to the microscopic levels, the high‐order two‐scale expansion for the mesoscopic cell functions is built, and the upscaled relations for the flow parameters and constitutive coefficients from the microscale to the mesoscale and macroscale are developed correspondingly. The multi‐scale low/high‐order models are established by combining the high‐order expansion of all cell functions at the mesoscale and the developed macro‐meso two‐scale models. The main contributions are that the present approaches follow the reverse thought processes of reiteration homogenization methods, and offer a very innovative and efficient way to establish high‐accuracy high‐order models for the nonlinear HM coupling problems in the heterogeneous porous medium with any number of spatial scales. The effectiveness and accuracy of the present solution are validated by several representative cases with different constitutive coefficient contrasts. The results demonstrate that the high‐order solutions provide an accurate prediction for gas transport and solid deformation of heterogeneous porous media with multi‐scale configurations.

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“…Substituting Equation (56) into Equation ( 55), we yield the cell problems for two unknown cell functions N mn (y, z) and D 𝛼 1 (y, z) as…”

Section: 2mentioning

confidence: 99%

Section: Hm Coupling Problems In Heterogeneous Pm With Macro‐meso Con...mentioning

confidence: 99%

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

Zuo,

Yang,

Cui

et al. 2024

Numerical Meth Engineering

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“…Differences in material modulus, strength, and influences of microscopic geometry produce various possibilities of material degradation modes. Numerous computational approaches are proposed including the reduced-order-homogenization (ROH) method (Fish et al, 1999;Fish and Yuan, 2005;Oskay and Fish, 2007;Yuan andFish, 2008, 2009), FE2 method (Eidel and Fischer, 2018;Özdemir et al, 2008;Xu et al, 2022), and second-order problem (Kouznetsova et al, 2004).…”

Section: Test On Composite Materials With Reduced-order-homogenizatio...mentioning

confidence: 99%

“…Later, Zhang et al (2021) developed a dissipation-based arc-length method to capture the snap-back loading-deflection curve with the global cracking elements method. In addition, Xu et al (2022) studied the damage development from micro-to macroscale through the two-finite-element (FE2) method of heterogeneous thin plate structures. The energy dissipation also takes place in porous media.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Dissipation Energy of Isotropic Continuum Damage Mechanics Model With Adaptive Time-Step Control Approach

Liu

Yuan

2023

Int J Mult Comp Eng

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This paper proposes an algorithm to evaluate dissipation energy of an isotropic continuum damage mechanics model with an adaptive time-step control approach. The algorithm takes place at each integration point under the scope of finite element analysis. The total amount of the dissipation energy of one structure can be used to verify the conservation law of energy, where the summation of the elastic strain energy and the dissipation energy should be equal to the total work by external force. However, the paper shows that this condition may not be valid when the unstable crack propagation occurs. When the crack propagation is unstable, the development of damage can be driven by stored strain energy without external load. The strains at the beginning and ending time within one increment at the damaged elements will give inaccurate dissipation energy by the classic trapezoidal integration scheme. In addition, this paper proposes a new damage evolution shape function with C1 continuity of the strain-stress curve under the uniaxial tension test, which is used to demonstrate the numerical procedure of the adaptive algorithm.

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“…In addition, the method can be directly performed on existing mature commercial FE codes (e.g., ABAQUS) without extensive programming knowledge and constitutive modeling expertise, which facilitates the use of FE 2 and expands its application [19]. The method also has good applications in geometric nonlinear and material nonlinear models [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE2 Method

Zhao

Tan

et al. 2023

Mathematics

Self Cite

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The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE2 method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE2 model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results.

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Direct FE2 for concurrent multilevel modeling of heterogeneous thin plate structures

Cited by 22 publications

References 47 publications

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

Evaluation of Dissipation Energy of Isotropic Continuum Damage Mechanics Model With Adaptive Time-Step Control Approach

A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE2 Method

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