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Two-Dimensional Modeling of Behavior of Composite Laminates Using Microplane Method

Poorsolhjouy, Payam | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40369 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Kazemi, Mohammad Taghi
  7. Abstract:
  8. This study presents a modified Microplane model in two-dimensional space which is capable of modeling anisotropic materials accurately. The main idea of Microplane model is to write constitutive equations in terms of vectors rather than tensors. Material constitutive laws are written for planes of every possible orientation to calculate the response of each plane to a given loading. Then the results of all the planes, called microplanes, are added up using Principle of Virtual Work (PVW) to form together the macroscopic response of the material. Microplane model with kinematic constraint is used in this study. Kinematic constraint states that microscopic (local) strain vector acting on each generic plane is the projection of macroscopic (global) strain tensor. In microplane model it is generally possible to define the constitutive equations of each microplane as functions of that specific plane’s orientation. In addition it is also admissible to define each component of stress vector on a microplane as a function of all strain components acting on that particular microplane. These two characteristics make Microplane model a powerful tool for modeling behavior of anisotropic materials. In this study, at first the general framework of Microplane model in two-dimensional coordinates is developed and microplane stiffness components for both models with and without volumetric-deviatoric split are calculated. Then it is proved that the reason why existing Microplane models (except the relatively complicated Spectral Stiffness Microplane) fail in modeling severely anisotropic materials is that they do not take account for the interaction between normal and shear components of stress and strain vectors acting on a microplane. It is then proved that in modeling anisotropic materials volumetric-deviatoric split is not useful. Constitutive equations in microplane level are redefined to take account for interaction between normal and shear components of stress and strain vectors. Stiffness components presenting this interaction are defined in the form of an odd Fourier series. For modeling nonlinear behavior of unidirectional composite laminates which include severe softening, concept of stress-strain boundaries is used. Different boundaries are defined for normal tension, normal compression and inplane shear loadings. In defining boundaries, also, the aforementioned interaction between normal and shear components of strain and stress vectors is taken into account. They are defined using bilinear functions of strain components. Parameters of these functions are calibrated for AS4/3501-6 epoxy unidirectional composite laminate. Since fibre composite laminates exhibit a strong energetic size effect, in addition to the statistical size effect, formulation of boundaries is also modified in order to take account for different finite element sizes. Using aforementioned modifications, the model presented here is capable of modeling unidirectional composite laminates behavior in linear and nonlinear softening regimes.
  9. Keywords:
  10. Microplane Model ; Two Dimensional Behavior ; Fourir Series ; Unidirectional Composites ; Anisotropic Materials ; Stress-Strain Boundary

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