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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i6.50
pages 615-629

On the Canonical Structure of the Eigendeformation-Based Reduced-Order Homogenization

Wei Wu
Rensselaer Polytechnic Institute
Zheng Yuan
Multiscale Design Systems, LLC 280 Park Avenue South New York, NY 10010, USA
Jacob Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA
Venkat Aitharaju
Senior Manufacturing Project Engineer, 2000 Centerpoint Parkway, Pontiac, MI 48341, USA

ABSTRACT

The manuscript focuses on the computational aspects of the eigendeformation-based, reduced-order homogenization developed in Fish and Yuan (2008), Oskay and Fish (2007), and Yuan and Fish (2009) with regard to its compatibility to commercial finite element code architecture and on standard user-defined material interfaces. Most commercial finite element software codes provide functionality for adding user-defined material models. The eigendeformation-based homogenization formulation has a lot of specificity that limits its flexibility to add user-defined material models. In the present manuscript we recast the original formulation referred to above into a more transparent and flexible form that enables easy addition of new material models of microconstituents. Several nonlinear examples, including damage, plasticity, and viscoplasticity, are used to demonstrate the canonical structure of the proposed formulation and its verification against the direct computational homogenization method.

REFERENCES

  1. ABAQUS 6.8 Documentation, User Subroutines Reference Manual.

  2. Fish, J., Shek, K., Pandheeradi, M., and Shephard, M. S., Computational plasticity for composite structure based on mathematical homogenization: Theory and practice. DOI: 10.1016/S0045-7825(97)00030-3

  3. Fish, J. and Yu, Q., Multiscale damage modeling for composite materials: Theory and computational framework. DOI: 10.1002/nme.276

  4. Fish, J. and Yuan, Z., N-scale model reduction theory. DOI: 10.1093/acprof:oso/9780199233854.003.0003

  5. Guedes, J. M. and Kikuchi, N., Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. DOI: 10.1016/0045-7825(90)90148-F

  6. Hill, R., A self-consistent mechanics of composite materials. DOI: 10.1016/0022-5096(65)90010-4

  7. Mori, T. and Tanaka, K., Average stress in the matrix and average elastic energy of materials with misfitting inclusions. DOI: 10.1016/0001-6160(73)90064-3

  8. Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2006.08.015

  9. Tachibana, Y. and Krempl, E., Modeling of high homologous temperature deformation behavior using the viscoplasticity theory based on overstress (VBO): Part I. Creep and tensile behavior. DOI: 10.1115/1.2804739

  10. Tachibana, Y. and Krempl, E., Modeling of high homologous temperature deformation behavior using the viscoplasticity theory based on overstress (VBO): Part II. Characteristics of the VBO model. DOI: 10.1115/1.2805967

  11. Tachibana, Y. and Krempl, E., Modeling of high homologous temperature deformation behavior using the viscoplasticity theory based on overstress (VBO): Part III. A simplified model. DOI: 10.1115/1.2812341

  12. Terada, K. and Kikuchi, N., Nonlinear homogenization method for practical applications.

  13. Yu, Q., Fish, J., and Shek, K. L., Computational damage mechanics for composite materials based on mathematical homogenization. DOI: 10.1002/(SICI)1097-0207(19990820)45:11<1657::AID-NME648>3.0.CO;2-H

  14. Yuan, Z. and Fish, J., Towards realization of computational homogenization in practice. DOI: 10.1002/nme.2074

  15. Yuan, Z. and Fish, J., Multiple scale eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2008.12.038


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