A Stochastic Nonlocal Model for Materials with Multiscale Behavior

Jianxu Shi; Roger Ghanem

doi:10.1615/IntJMultCompEng.v4.i4.70

International Journal for Multiscale Computational Engineering

Jacob Fish (open in a new tab) Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA

J. Tinsley Oden (open in a new tab) Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA

Somnath Ghosh (open in a new tab) Departments of Civil & Systems Engineering, Mechanical Engineering, and Material Science Engineering, Johns Hopkins University, Baltimore, MD, USA

Arif Masud (open in a new tab) Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 3129E Newmark Civil Engineering Laboratory, MC-250, Urbana, Illinois 61801-2352, USA

Klaus Hackl (open in a new tab) Institute of Mechanics of Materials, Ruhr-University Bochum, Bochum, 44721, Germany

Karel Matous (open in a new tab) Department of Aerospace and Mechanical Engineering, Center for Shock Wave-Processing of Advanced Reactive Materials, University of Notre Dame, Notre Dame, Indiana 46556, USA

Thomas J.R. Hughes (open in a new tab) Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 East 24th Street, C0200, Austin, TX 78712-1229, USA

Caglar Oskay (open in a new tab) Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA

Tamar Schlick (open in a new tab) Department of Chemistry, New York University, New York, New York 10003, USA; Courant Institute of Mathematical Sciences, New York University, New York, New York, 10012, USA; NYU-ECNU Center for Computational Chemistry, NYU Shanghai, China

Indexed in

A Stochastic Nonlocal Model for Materials with Multiscale Behavior

pages 501-520

DOI: 10.1615/IntJMultCompEng.v4.i4.70

Get access

Jianxu Shi
ABAQUS, Inc., Rising Sun Mills, 166 Valley Street, Providence, RI02909-2499

Roger Ghanem
Sony Astani Department of Aerospace and Mechanical Engineering, University of Southern California, 210 KAP Hall, Los Angeles, CA 90089, USA

Краткое описание

Integral-type nonlocal mechanics is employed to model the macroscale behavior of multiscale materials, with the associated nonlocal kernel representing the interactions between mesoscale features. The nonlocal model is enhanced by explicitly considering the spatial variability of subscale features as stochastic contributions resulting in a stochastic characterization of the kernel. By appropriately representing the boundary conditions, the nonlocal boundary value problem (BVP) of the macroscale behavior is transformed into a system of equations consisting of a classical BVP together with two Fredholm integral equations. The associated integration kernels can be calibrated using either experimental measurements or micromechanical analysis. An efficient and computationally expedient representation of a resulting stochastic kernel is achieved through its polynomial chaos decomposition. The coefficients in this decomposition are evaluated from statistical samples of the disturbance field associated with a random distribution of microcracks. The new model is shown to be capable of predicting nonlocal features, such as the size effect and boundary effect, of the behavior of materials with random microstructures.

Begell Recommend

Electrospinning of Micro- and Nanofibers: Fundamentals in Separation and Filtration Processes Y. Filatov
A. Budyka
V. Kirichenko

TSFP DIGITAL LIBRARY ONLINE