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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1146 |
| Date | 15 May 2009 |
| Creators | Khan, Kamran-Ahmed |
| Contributors | Muliana, Hanifah |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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