A regularized phenomenological multiscale damage model

Liu, Yang; Filonova, Vasilina; Hu, Nan; Yuan, Zifeng; Fish, Jacob; Yuan, Zheng; Belytschko, Ted

doi:10.1002/nme.4705

Cited by 45 publications

(36 citation statements)

References 39 publications

(69 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Herein, the magnitude of failure strains for each phase is rescaled based on the element sized to keep the fracture energy constant and alleviate mesh dependency.…”

Section: Numerical Resultsmentioning

confidence: 99%

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Yuan

Aitharaju

Fish

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Summary We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo‐chemo‐mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale‐multiphysics approach. To address the enormous computational complexity involved, a reduced‐order homogenization was originally developed for a single physics problem is employed. The proposed reduced‐order two‐scale thermo‐chemo‐mechanical model has been validated for predicting part distortion beam strength in three‐point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.

show abstract

“…Herein, the magnitude of failure strains for each phase is rescaled based on the element sized to keep the fracture energy constant and alleviate mesh dependency.…”

Section: Numerical Resultsmentioning

confidence: 99%

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Yuan

Aitharaju

Fish

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…In step (i), the coarse‐scale incremental strain

normalΔ {normalϵ}_{n + 1 / 2}^{c} ((), boldx, t)

is obtained from the solution of the coarse‐scale problem at each quadrature point, in each time step. Because of strong size dependence that has been observed in granular materials, we define a nonlocal coarse‐scale strain increment

{(〈〉, normalΔ {normalϵ}_{n + 1 / 2}^{c} ((), {boldx}_{I}))}_{R}

as follows:

\begin{matrix} {〈Δ ϵ_{n + 1 / 2}^{c} (x_{I})〉}_{R} & = \sum_{ξ_{J} \in Q_{I}} α^{*} (x_{I}, ξ_{J}) ϕ^{*} (ξ_{J}) \\ ϕ^{*} (ξ_{J}) & = \{\begin{matrix} normalΔ {normalϵ}_{n + 1 / 2}^{c} ({normalξ}_{I}) if {normalξ}_{J} = {boldx}_{I} \\ normalΔ {normalϵ}_{n + α}^{c} ({normalξ}_{J}) if {normalξ}_{J} \neq {boldx}_{I} \end{matrix} \end{matrix}

where

normalΔ {normalϵ}_{n + α}^{c}

denotes the coarse‐scale strain computed on the fly, that is, α is

\pm ((), 1 / 2)

, which represents either ...…”

Section: Methodsmentioning

confidence: 99%

“…Previous hierarchical DEM–FEM coupling schemes have proven to be mesh dependence in after the onset of strain localization. The proposed multiscale approach remedies this issue by applying a modified staggered nonlocal approach proposed in to define the unit cell problem for the stress homogenization. Formulating the two‐scale discrete‐continuum problem via the GMH framework. This treatment allows us to derive the Cauchy stress expression directly from the equilibrium equations of particles and provide a consistent framework that links the continuum (coarse-scale) and discrete (fine‐scale) representations of the granular assemblies based on the multiscale asymptotic analysis.…”

Section: Introductionmentioning

confidence: 99%

A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials

Liu

Sun

Yuan

et al. 2015

Int. J. Numer. Meth. Engng

Self Cite

View full text Add to dashboard Cite

Summary A three‐dimensional nonlocal multiscale discrete‐continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information‐passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete‐continuum coupling method retains the simplicity and efficiency of a continuum‐based finite element model, while circumventing mesh pathology in the post‐bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure‐sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single‐scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

“…7. The singlescale local and nonlocal models [32] assume that the material is homogeneous, whereas the multiscale models Physical field class -DOF subclass -Field gradient subclass -Flux and state variable subclass -Sparse matrix subclass -Convergent test subclass Step class -Dirichlet boundary condition subclass -Neumann boundary condition class -Initial condition subclass -Multi-point constraint subclass -Step property subclass …”

Section: Constitutive Law Library Classmentioning

confidence: 99%

Nonlinear multiphysics finite element code architecture in object oriented Fortran environment

Yuan

Fish

2015

Finite Elements in Analysis and Design

Self Cite

View full text Add to dashboard Cite

A regularized phenomenological multiscale damage model

Cited by 45 publications

References 39 publications

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials

Nonlinear multiphysics finite element code architecture in object oriented Fortran environment

Contact Info

Product

Resources

About