Thermo-mechanical analysis of nonlinear heterogeneous materials by second-order reduced asymptotic expansion approach

Yang, Zhiqiang; Hao, Zhiwei; Sun, Yi; Liu, Yizhi; Dong, Hao

doi:10.1016/j.ijsolstr.2019.06.021

Cited by 18 publications

(7 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, the governing equations of the nonlinear shell structures with orthogonal periodic configurations are given as follows 34,[47][48][49] :…”

Section: Governing Equations For the Nonlinear Shell Structuresmentioning

confidence: 99%

“…Obviously, the equalities (8) always hold owing to the previous assumptions on the homogenized solutions u (0) i . Following, [48][49][50] the asymptotic expansion forms of ( 9) are given by u (1) i (𝛂, 𝛃)…”

Section: First-order Asymptotic Formulas and Homogenized Equationmentioning

confidence: 99%

“…For 𝜉 = 0, it reduces to the zeroth-order homogenization methods. [47][48][49] Once the partitioned eigenstrain is obtained, the Equations ( 51)-( 54) are utilized to obtain the coarse-scale strain and stress solutions.…”

Section: Order Reduction Form Of the Homogenization Problemsmentioning

confidence: 99%

“…Bhattacharjee and Matouš 46 applied a manifold-based order reduction model to predict the macro performance of the hyperelastic heterogenous composites. Yuan, 47 Fish, 48 and Yang et al 49 constructed and applied the multiscale reduced models to evaluate any inelastic deformations of the heterogeneous composites, and could greatly save the computing time. Further, Yang et al, 50 expanded the multiscale reduced-order approach to compute the nonlinear axisymmetric structure with periodic configuration.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A second‐order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurations

Yang

Liu

Sun

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

This article develops an efficient second-order reduced multiscale (SORM) method to study the nonlinear shell structure with orthogonal periodic configurations. The heterogenous shell structure is periodically distributed in orthogonal curvilinear coordinate systems. At first, the nonlinear problems for the shell structure are introduced, and the detailed higher-order nonlinear multiscale formulas based on the asymptotic homogenization approach are given including microscale unit cell functions, effective material parameter and the homogenized equation. Also, since it requires a large number of computation cost to solve the nonlinear multiscale problems by the traditional high-order homogenization methods, the novel reduced order multiscale model is constructed.Further, according to the reduced-order multiscale models and higher-order nonlinear formulas, an effective SORM algorithm is provided for studying the nonlinear shell structures. The main characteristics of the proposed algorithm are that the novel reduced forms established to investigate the nonlinear shell structures and an efficient higher-order homogenized solution evaluated by postprocessing that does not need higher-order continuities of the homogenization solutions. Finally, according to some typical nonlinear examples including block structures, cylindrical shell and double-curved shallow shell, the availabilities of the SORM algorithm are confirmed.

show abstract

“…In this section, the governing equations of the nonlinear shell structures with orthogonal periodic configurations are given as follows 34,[47][48][49] :…”

Section: Governing Equations For the Nonlinear Shell Structuresmentioning

confidence: 99%

Section: First-order Asymptotic Formulas and Homogenized Equationmentioning

confidence: 99%

Section: Order Reduction Form Of the Homogenization Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A second‐order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurations

Yang

Liu

Sun

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Yang [7] investigates asymptotic expansions for the Laplace transforms. An effective second-order reduced asymptotic expansion approach is proposed by Yang et al [8] to analyze the thermo-mechanical coupling problems of nonlinear periodic heterogeneous materials.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Coupled Settlement by Using Three Asymptotic Expansion Parameters

Lu¹,

Liao²,

Lin³

2019

Proceedings of the 2019 International Conference on Modeling, Simulation and Big Data Analysis (MSBDA 2019)

View full text Add to dashboard Cite

Based on Biot's coupled theory of poroelasticity, the uniform loading induced settlement is investigated by applying asymptotic expansion approach. Using three small asymptotic expansion parameters, the variables of settlement and excess pore fluid pressure are expressed in this study. Substituting these variables into the non-dimensional mathematical model, the coupled settlement model of the porous medium can be simplified into the uncoupled ones. The results are verified by the closed-form solutions to show the value of applying asymptotic expansion.

show abstract

Superposition‐based concurrent multiscale approaches for porodynamics

Sun,

Zhang,

Fish

et al. 2024

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

The current study presents superposition‐based concurrent multiscale approaches for porodynamics, capable of capturing related physical phenomena, such as soil liquefaction and dynamic hydraulic fracture branching, across different spatial length scales. Two scenarios are considered: superposition of finite element discretizations with varying mesh densities, and superposition of peridynamics (PD) and finite element method (FEM) to handle discontinuities like strain localization and cracks. The approach decomposes the acceleration and the rate of change in pore water pressure into subdomain solutions approximated by different models, allowing high‐fidelity models to be used locally in regions of interest, such as crack tips or shear bands, without neglecting the far‐field influence represented by low‐fidelity models. The coupled stiffness, mass, compressibility, permeability, and damping matrices were derived based on the superposition‐based current multiscale framework. The proposed FEM‐FEM porodynamic coupling approach was validated against analytical or numerical solutions for one‐ and two‐dimensional dynamic consolidation problems. The PD‐FEM porodynamic coupling model was applied to scenarios like soil liquefaction‐induced shear strain accumulation near a low‐permeability interlayer in a layered deposit and dynamic hydraulic fracturing branching. It has been shown that the coupled porodynamic model offers modeling flexibility and efficiency by taking advantage of FEM in modeling complex domains and the PD ability to resolve discontinuities.

show abstract

Thermo-mechanical analysis of nonlinear heterogeneous materials by second-order reduced asymptotic expansion approach

Cited by 18 publications

References 58 publications

A second‐order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurations

A second‐order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurations

Analysis of Coupled Settlement by Using Three Asymptotic Expansion Parameters

Superposition‐based concurrent multiscale approaches for porodynamics

Contact Info

Product

Resources

About