Khan, Kamran-Ahmed (2006-12). A time integration scheme for stress - temperature dependent viscoelastic behaviors of isotropic materials. Master's Thesis. Thesis uri icon

abstract

  • A recursive-iterative algorithm is developed for predicting nonlinear viscoelastic behaviors of isotropic materials that belong to the thermorheologically complex material (TCM). The algorithm is derived based on implicit stress integration solutions within a general displacement based FE structural analyses for small deformations and uncoupled thermo-mechanical problems. A previously developed recursive-iterative algorithm for a stress-dependent hereditary integral model which was developed by Haj-Ali and Muliana is modified to include time-temperature effects. The recursive formula allows bypassing the need to store entire strain histories at each Gaussian integration point. Two types of iterative procedures, which are fixed point and Newton-Raphson methods, are examined within the recursive algorithm. Furthermore, a consistent tangent stiffness matrix is formulated to accelerate convergence and avoid divergence. The efficiency and accuracy of the proposed algorithm are evaluated using available experimental data and several structural analyses. The performance of the proposed algorithm under multi-axial conditions is verified with analytical solutions of creep responses of a plate with a hole. Next, the recursive-iterative algorithm is used to predict the overall response of single lap-joint. Numerical simulations of time-dependent crack propagations of adhesive bonded joints are also presented. For this purpose, the recursive algorithm is implemented in cohesive elements. The numerical assessment of the TCM and thermorheologically simple material (TSM) behaviors has also been performed. The result showed that TCM are able to describe thermo-viscoelastic behavior under general loading histories, while TSM behaviors are limited to isothermal conditions. The proposed numerical algorithm can be easily used in a micromechanical model for predicting the overall composite responses. Examples are shown for solid spherical particle reinforced composites. Detailed unit-cell FE models of the composite systems are generated to verify the capability of the above micromechanical model for predicting the overall nonlinear viscoelastic behaviors.
  • A recursive-iterative algorithm is developed for predicting nonlinear viscoelastic
    behaviors of isotropic materials that belong to the thermorheologically complex material
    (TCM). The algorithm is derived based on implicit stress integration solutions within a
    general displacement based FE structural analyses for small deformations and uncoupled
    thermo-mechanical problems. A previously developed recursive-iterative algorithm for
    a stress-dependent hereditary integral model which was developed by Haj-Ali and
    Muliana is modified to include time-temperature effects. The recursive formula allows
    bypassing the need to store entire strain histories at each Gaussian integration point.
    Two types of iterative procedures, which are fixed point and Newton-Raphson methods,
    are examined within the recursive algorithm. Furthermore, a consistent tangent stiffness
    matrix is formulated to accelerate convergence and avoid divergence. The efficiency and
    accuracy of the proposed algorithm are evaluated using available experimental data and
    several structural analyses. The performance of the proposed algorithm under multi-axial
    conditions is verified with analytical solutions of creep responses of a plate with a hole.
    Next, the recursive-iterative algorithm is used to predict the overall response of single lap-joint. Numerical simulations of time-dependent crack propagations of adhesive
    bonded joints are also presented. For this purpose, the recursive algorithm is
    implemented in cohesive elements. The numerical assessment of the TCM and
    thermorheologically simple material (TSM) behaviors has also been performed. The
    result showed that TCM are able to describe thermo-viscoelastic behavior under general
    loading histories, while TSM behaviors are limited to isothermal conditions. The
    proposed numerical algorithm can be easily used in a micromechanical model for
    predicting the overall composite responses. Examples are shown for solid spherical
    particle reinforced composites. Detailed unit-cell FE models of the composite systems
    are generated to verify the capability of the above micromechanical model for predicting
    the overall nonlinear viscoelastic behaviors.

publication date

  • December 2006