skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics

Abstract

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. In order to resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. Here, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.

Authors:
 [1];  [1];  [1];  [2];  [3]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Mechanics of Materials Dept.
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Computational Materials and Data Science
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Multiscale Science
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1411597
Report Number(s):
SAND-2017-2403J
Journal ID: ISSN 0178-7675; PII: 1481; TRN: US1800240
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Computational Mechanics
Additional Journal Information:
Journal Volume: 61; Journal Issue: 1-2; Journal ID: ISSN 0178-7675
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; multiscale modeling; crystal plasticity; finite element modeling; localization

Citation Formats

Alleman, Coleman N., Foulk, James W., Mota, Alejandro, Lim, Hojun, and Littlewood, David J. Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics. United States: N. p., 2017. Web. doi:10.1007/s00466-017-1481-5.
Alleman, Coleman N., Foulk, James W., Mota, Alejandro, Lim, Hojun, & Littlewood, David J. Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics. United States. doi:10.1007/s00466-017-1481-5.
Alleman, Coleman N., Foulk, James W., Mota, Alejandro, Lim, Hojun, and Littlewood, David J. Mon . "Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics". United States. doi:10.1007/s00466-017-1481-5. https://www.osti.gov/servlets/purl/1411597.
@article{osti_1411597,
title = {Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics},
author = {Alleman, Coleman N. and Foulk, James W. and Mota, Alejandro and Lim, Hojun and Littlewood, David J.},
abstractNote = {The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. In order to resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. Here, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.},
doi = {10.1007/s00466-017-1481-5},
journal = {Computational Mechanics},
number = 1-2,
volume = 61,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Distribution-enhanced homogenization framework and model for heterogeneous elasto-plastic problems
journal, December 2015

  • Alleman, Coleman; Luscher, D. J.; Bronkhorst, Curt
  • Journal of the Mechanics and Physics of Solids, Vol. 85
  • DOI: 10.1016/j.jmps.2015.09.012

Hydrogen-enhanced localization of plasticity in an austenitic stainless steel
journal, November 1995

  • Abraham, Daniel P.; Altstetter, Carl J.
  • Metallurgical and Materials Transactions A, Vol. 26, Issue 11
  • DOI: 10.1007/BF02669644

A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity
journal, January 1993


An analysis of nonuniform and localized deformation in ductile single crystals
journal, June 1982


Can Multiscale-Multiphysics Methods Predict Softening Damage and Structural Failure?
journal, January 2010


Application of generalized non-Schmid yield law to low-temperature plasticity in bcc transition metals
journal, May 2013

  • Lim, H.; Weinberger, C. R.; Battaile, C. C.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 21, Issue 4
  • DOI: 10.1088/0965-0393/21/4/045015

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids
journal, February 2006

  • Yang, Q.; Stainier, L.; Ortiz, M.
  • Journal of the Mechanics and Physics of Solids, Vol. 54, Issue 2
  • DOI: 10.1016/j.jmps.2005.08.010

Multiscale aggregating discontinuities: A method for circumventing loss of material stability
journal, February 2008

  • Belytschko, Ted; Loehnert, Stefan; Song, Jeong-Hoon
  • International Journal for Numerical Methods in Engineering, Vol. 73, Issue 6
  • DOI: 10.1002/nme.2156

Albany: Using Component-Based Design to Develop a Flexible, Generic Multiphysics Analysis code
journal, January 2016

  • Salinger, Andrew G.; Bartlett, Roscoe A.; Bradley, Andrew M.
  • International Journal for Multiscale Computational Engineering, Vol. 14, Issue 4
  • DOI: 10.1615/IntJMultCompEng.2016017040

A concurrent multiscale method based on the alternating Schwarz scheme for coupling atomic and continuum scales with first-order compatibility
journal, August 2010


Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystals
journal, July 2004

  • Matouš, Karel; Maniatty, Antoinette M.
  • International Journal for Numerical Methods in Engineering, Vol. 60, Issue 14
  • DOI: 10.1002/nme.1045

Hydrogen in metals: A coupled theory for species diffusion and large elastic–plastic deformations
journal, April 2013


Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials
journal, February 1976

  • Hutchinson, J. W.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 348, Issue 1652
  • DOI: 10.1098/rspa.1976.0027

Dual-stage nested homogenization for rate-dependent anisotropic elasto-plasticity model of dendritic cast aluminum alloys
journal, October 2011


A micromechanics approach to the study of hydrogen transport and embrittlement
journal, April 2001


Sandia fracture challenge 2: Sandia California’s modeling approach
journal, March 2016

  • Karlson, Kyle N.; Foulk, James W.; Brown, Arthur A.
  • International Journal of Fracture, Vol. 198, Issue 1-2
  • DOI: 10.1007/s10704-016-0090-1

The computer simulation of microstructural evolution
journal, September 2001


An approach to micro-macro modeling of heterogeneous materials
journal, January 2001

  • Kouznetsova, V.; Brekelmans, W. A. M.; Baaijens, F. P. T.
  • Computational Mechanics, Vol. 27, Issue 1
  • DOI: 10.1007/s004660000212

Elastic constants of polycrystals
journal, January 1970


Constitutive analysis of elastic-plastic crystals at arbitrary strain
journal, December 1972


Elastic properties of reinforced solids: Some theoretical principles
journal, September 1963


FETI-DP: a dual-primal unified FETI method?part I: A faster alternative to the two-level FETI method
journal, January 2001

  • Farhat, Charbel; Lesoinne, Michel; LeTallec, Patrick
  • International Journal for Numerical Methods in Engineering, Vol. 50, Issue 7
  • DOI: 10.1002/nme.76

The Schwarz alternating method in solid mechanics
journal, June 2017

  • Mota, Alejandro; Tezaur, Irina; Alleman, Coleman
  • Computer Methods in Applied Mechanics and Engineering, Vol. 319
  • DOI: 10.1016/j.cma.2017.02.006

Connecting Atomistic-to-Continuum Coupling and Domain Decomposition
journal, January 2008

  • Parks, Michael L.; Bochev, Pavel B.; Lehoucq, Richard B.
  • Multiscale Modeling & Simulation, Vol. 7, Issue 1
  • DOI: 10.1137/070682848

Hybrid atomistic–continuum method for the simulation of dense fluid flows
journal, May 2005

  • Werder, Thomas; Walther, Jens H.; Koumoutsakos, Petros
  • Journal of Computational Physics, Vol. 205, Issue 1
  • DOI: 10.1016/j.jcp.2004.11.019

Brittle fracture in austenitic steel
journal, July 1994


A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems
journal, September 1992

  • Armero, F.; Simo, J. C.
  • International Journal for Numerical Methods in Engineering, Vol. 35, Issue 4
  • DOI: 10.1002/nme.1620350408

The role of localized deformation in hydrogen-assisted crack propagation in 21Cr–6Ni–9Mn stainless steel
journal, August 2009


Novel boundary conditions for strain localization analyses in microstructural volume elements: BCS FOR LOCALIZATION ANALYSIS IN MICROSTRUCTURES
journal, October 2011

  • Coenen, E. W. C.; Kouznetsova, V. G.; Geers, M. G. D.
  • International Journal for Numerical Methods in Engineering, Vol. 90, Issue 1
  • DOI: 10.1002/nme.3298

Predicting Mesoscale Microstructural Evolution in Electron Beam Welding
journal, March 2016


FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials
journal, March 2000

  • Feyel, Frédéric; Chaboche, Jean-Louis
  • Computer Methods in Applied Mechanics and Engineering, Vol. 183, Issue 3-4
  • DOI: 10.1016/S0045-7825(99)00224-8

Heterogeneous Atomistic-Continuum Representations for Dense Fluid Systems
journal, August 1997

  • Hadjiconstantinou, Nicolas G.; Patera, Anthony T.
  • International Journal of Modern Physics C, Vol. 08, Issue 04
  • DOI: 10.1142/S0129183197000837

Hierarchical crystal plasticity FE model for nickel-based superalloys: Sub-grain microstructures to polycrystalline aggregates
journal, March 2015


The effect of microstructural representation on simulations of microplastic ratcheting
journal, May 2010

  • Dingreville, Rémi; Battaile, Corbett C.; Brewer, Luke N.
  • International Journal of Plasticity, Vol. 26, Issue 5
  • DOI: 10.1016/j.ijplas.2009.09.004

Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems
journal, January 2005

  • Engel, Martin; Griebel, Michael
  • International Journal for Numerical Methods in Fluids, Vol. 50, Issue 4
  • DOI: 10.1002/fld.1067

Elastic-Plastic Deformation at Finite Strains
journal, March 1969


Grain-scale experimental validation of crystal plasticity finite element simulations of tantalum oligocrystals
journal, September 2014


The Mortar finite element method with Lagrange multipliers
journal, December 1999


Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation
journal, July 1992