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Finite Element Simulation and Analysis of Local Stress Concentration in Polymers with a Nonlinear Viscoelastic Constitutive Model


Chea, Limdara Ong (1997) Finite Element Simulation and Analysis of Local Stress Concentration in Polymers with a Nonlinear Viscoelastic Constitutive Model. Engineer's thesis, California Institute of Technology. doi:10.7907/13SD-9N16.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Given a nonlinear viscoelastic (NLVE) constitutive model for a polymer, this numerical study aims at simulating local stress concentrations in a boundary value problem with a corner stress singularity. A rectangular sample of Polyvinyl Acetate (PVAc)-like cross-linked polymer clamped by two metallic rigid grips and subjected to a compression and tension load is numerically simulated. A modified version of the finite element code FEAP, that incorporated a NLVE model based on the free volume theory, was used. First, the program was validated by comparing numerical and analytical results. Two simple mechanical tests (a uniaxial and a simple shear test) were performed on a Standard Linear Solid material model, using a linear viscoelastic (LVE) constitutive model. The LVE model was obtained by setting the proportionality coefficient [...] to zero in the free volume theory equations. Second, the LVE model was used on the corner singularity boundary value problem for three material models with different bulk relaxation functions K(t). The time-dependent stress field distribution was investigated using two sets of plots: the stress distribution contour plots and the stress time curves. Third, using the NLVE constitutive model, compression and tension cases were compared using the stress results (normal stress [...] and shear stress [...]). These two cases assessed the effect of the creep retardation-creep acceleration phenomena. The shift between the beginning of the relaxation moduli was shown to play an important role. This parameter affects strongly the fluctuation pattern of the stress curves. For two different shift values, in one case, the stress response presents a 'double peak' and 'stress inversion' characteristic whereas, in the other case, it presents a 'single peak' and no 'inversion'. Another important factor was the material's compressibility. In the case of a nearly-incompressible material, the LVE and NLVE models yielded identical results; thus, the simpler LVE model is preferable. However, in the case of sufficient volume dilatation (or contraction), the NLVE model predicted correct characteristic responses, whereas LVE results were erroneous. This proves the necessity of using the NLVE model over the LVE model.

Item Type:Thesis (Engineer's thesis)
Subject Keywords:(Aeronautics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Knauss, Wolfgang Gustav
Thesis Committee:
  • Unknown, Unknown
Defense Date:4 October 1996
Record Number:CaltechETD:etd-01082008-095104
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67
Deposited By: Imported from ETD-db
Deposited On:25 Jan 2008
Last Modified:11 Aug 2022 20:40

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PDF (Chea_l_1997.pdf) - Final Version
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