Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
15
2
2017
CONCURRENT ATOMISTIC-CONTINUUM MODEL FOR DEVELOPING SELF-CONSISTENT ELASTIC CONSTITUTIVE MODELING OF CRYSTALLINE SOLIDS WITH CRACKS
99-119
10.1615/IntJMultCompEng.2017020072
Jiaxi
Zhang
Department of Civil Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
Subhendu
Chakraborty
Department of Civil Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
Somnath
Ghosh
Departments of Civil & Systems Engineering, Mechanical Engineering, and Material Science
Engineering, Johns Hopkins University, Baltimore, MD, USA
self-consistent elastic model
concurrent atomistic-continuum coupling
crack tip field
molecular dynamics
finite element analysis
Damage of materials inherently involves coupling of deformation and failure mechanisms at multiple length and time scales. This paper develops self-consistent elastic constitutive relations of crystalline materials containing atomistic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The self-consistent constitutive model incorporates both nonlinearity and nonlocality to account for atomic level interactions and deformation mechanisms, especially near crack tips. Atomistic modeling in the concurrent model is done using molecular dynamics (MD), while the continuum modeling is done using a crystal elasticity finite element (FE) analysis code. The atomistic-continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in an interface region. The constitutive model is calibrated by comparing with the results of MD predictions in the concurrent model. For validation, the crack tip stress field is investigated using both the coupled concurrent model and a FE model with the constitutive law. The self-consistent model exhibits excellent accuracy and enhanced efficiency in comparison with pure MD and concurrent model results.
MULTI-YIELD SURFACE MODELING OF VISCOPLASTIC MATERIALS
121-142
10.1615/IntJMultCompEng.2017020087
Hao
Yan
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville,
Tennessee 37235, USA
Caglar
Oskay
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville,
Tennessee 37235, USA
multi-yield surface plasticity
viscoelastic-viscoplastic behavior
cyclic loading
This manuscript presents a multi-yield surface model to idealize the mechanical behavior of viscoplastic solids subjected to cyclic loading. The multi-yield surface model incorporates the evolution of nonlinear viscoplastic flow through a piece-wise linear hardening approximation. A kinematic hardening law is employed to account for the evolution of backstress with respect to the viscoplastic strain rate. The new backstress evolution strategy is proposed to ensure that all yield surfaces remain consistent (i.e., satisfying collinearity) throughout the viscoplastic process. The multi-yield surface model is coupled with viscoelasticity to approximate the relaxation behavior of high-temperature metal alloys. The model is implemented using a mixed finite element approach. The capabilities of the proposed approach are demonstrated using experiments conducted on a high-temperature titanium alloy (Ti-6242S) subjected to static, cyclic, and relaxation conditions.
ITERATIVE GLOBAL-LOCAL APPROACH TO CONSIDER THE EFFECTS OF LOCAL ELASTO-PLASTIC DEFORMATIONS IN THE ANALYSIS OF THIN-WALLED MEMBERS
143-173
10.1615/IntJMultCompEng.2017019767
R. Emre
Erkmen
School of Civil and Environmental Engineering, Centre for Built-Infrastructure and Research, University of Technology, Sydney, NSW 2007, Australia
Ali
Saleh
School of Civil and Environmental Engineering, Centre for Built-Infrastructure and Research, University of Technology, Sydney, NSW 2007, Australia
global-local analysis
convergence acceleration
thin-walled members
local effects
The aim of this study is to develop an iterative global-local analysis method to efficiently model the local deformation effects for the nonlinear elasto-plastic analysis of thin-walled beams. Thin-walled members are usually modeled by using beam-type one-dimensional finite elements, which are based on rigid cross-section assumption. Therefore, only deformations associated with the beam axis behavior such as flexural-, torsional-, or lateral buckling can be considered in these formulations, whereas local deformations, namely flange or web local buckling, can be captured by shell-type models. The proposed method allows the local use of shell elements in critical areas to incorporate the local deformation effects on the overall behavior of the thin-walled beam without necessitating a shell model for the whole structure. In this study, the local shell formulation is able to capture the elasto-plastic metal behavior based on the von Mises
yield criterion and the associated flow rule for plane stress, which may cause unstable post-buckling response. In order to trace an unstable post-buckling curve, the iterative global-local analysis method is incorporated into the arc-length solution procedure. In order to improve the convergence characteristics, the procedure introduces strong discontinuities in the beam element formulation in the region of the local shell elements. These discontinuities are in the form of an internal enrichment considering additional local degrees of freedom associated with some penalty terms which adjust the tangent stiffness matrix of the beam for the prediction in the next step according to the effects of the local shell model in the previous step. Comparisons with full shell-type analysis are provided in order to illustrate the accuracy and efficiency of the method developed herein.
BAYESIAN MULTISCALE FINITE ELEMENT METHODS. MODELING MISSING SUBGRID INFORMATION PROBABILISTICALLY
175-197
10.1615/IntJMultCompEng.2017019851
Yalchin
Efendiev
Department of Mathematics and Institute for Scientific Computation (ISC),
Texas A&M University, College Station, TX 77840, USA; Multiscale Model Reduction Laboratory, North-Eastern Federal University,
Yakutsk, 677980, Russia
Wing Tat
Leung
Department of Mathematics and Institute for Scientific Computation (ISC), Texas A&M University, College Station, Texas 77843-3368, USA
S. W.
Cheung
Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M
University, College Station, Texas, 77843-3368, USA
N.
Guha
Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M
University, College Station, Texas, 77843-3368, USA; Department of Statistics, Texas A&M University, College Station, Texas, 77843-3368, USA
V. H.
Hoang
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang
Technological University, Singapore, 637371
B.
Mallick
Department of Statistics, Texas A&M University, College Station, Texas, 77843-3368, USA
Bayesian
multiscale
MCMC
Gibbs
multiscale finite element method
In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models cannot resolve all scales. Various subgrid models are proposed to represent unresolved scales. Here, we consider a probabilistic approach for modeling unresolved scales using the multiscale finite element method [cf., Chkrebtii et al., Bayesian Anal., vol. 11, no. 4, pp. 1239-1267, 2016; Mallick et al., Bayesian Anal., vol. 11, no. 4, p. 1279, 2016]. By representing dominant modes using the generalized multiscale finite element, we propose a Bayesian framework, which provides multiple inexpensive (computable) solutions for a deterministic problem. These approximate probabilistic solutions may not be very close to the exact solutions and, thus, many realizations are needed. In this way, we obtain a rigorous probabilistic description of approximate solutions. In the paper, we consider parabolic and wave equations in heterogeneous media. In each time interval, the domain is divided into subregions. Using residual information, we design appropriate prior and posterior distributions. The likelihood consists of the residual minimization. To sample from the resulting posterior distribution, we consider several sampling strategies. The sampling involves identifying important regions and important degrees of freedom beyond permanent basis functions, which are used in residual computation. Numerical results are presented. We consider two sampling algorithms. The first algorithm uses sequential sampling and is inexpensive. In the second algorithm, we perform full sampling using the Gibbs sampling algorithm, which is more accurate compared to the sequential sampling. The main novel ingredients of our approach consist of: defining appropriate permanent basis functions and the corresponding residual; setting up a proper posterior distribution; and sampling the posteriors.