A homogenization theory for time-dependentnonlinear composites with periodic internal structures |
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| Institution: | 1. Henan Provincial Key Laboratory of Intelligent Manufacturing of Mechanical, Mechanical and Electrical Engineering Institute, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, China;2. College of Mechanical Engineering, Hunan University of Technology, Zhuzhou 412007, Hunan, China;1. Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge, MA 02139, USA;2. Brown University, Division of Applied Mathematics, Providence, RI 02912, USA;3. IBM T.J. Watson Research Center, Cambridge, MA 02142, USA;4. Lehigh University, Department of Mathematics, 27 Memorial Dr W, Bethlehem, PA 18015, USA;5. Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA |
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| Abstract: | A homogenization theory for time-dependent deformation such as creep andviscoplasticity of nonlinear composites with periodic internal structures is developed. To beginwith, in the macroscopically uniform case, a rate-type macroscopic constitutive relation betweenstress and strain and an evolution equation of microscopic stress are derived by introducing twokinds of Y-periodic functions, which are determined by solving two unit cell problems.Then, the macroscopically nonuniform case is discussed in an incremental form using thetwo-scale asymptotic expansion of field variables. The resulting equations are shown to beeffective for computing incrementally the time-dependent deformation for which the history ofeither macroscopic stress or macroscopic strain is prescribed. As an application of the theory,transverse creep of metal matrix composites reinforced undirectionally with continuous fibers isanalyzed numerically to discuss the effect of fiber arrays on the anisotropy in such creep. |
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