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Research Papers

Constitutive Equations and Finite Element Implementation of Isochronous Nonlinear Viscoelastic Behavior

[+] Author and Article Information
Hossein Sepiani

Civil and Environmental Engineering Department,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: hasepian@uwaterloo.ca

Maria Anna Polak

Civil and Environmental Engineering Department,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: polak@uwaterloo.ca

Alexander Penlidis

Department of Chemical Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: penlidis@uwaterloo.ca

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 2, 2017; final manuscript received April 8, 2018; published online May 10, 2018. Assoc. Editor: Curt Bronkhorst.

J. Eng. Mater. Technol 140(4), 041004 (May 10, 2018) (11 pages) Paper No: MATS-17-1219; doi: 10.1115/1.4040003 History: Received August 02, 2017; Revised April 08, 2018

We present a phenomenological three-dimensional (3D) nonlinear viscoelastic constitutive model for time-dependent analysis. Based on Schapery's single integral constitutive law, a solution procedure has been provided to solve nonlinear viscoelastic behavior. This procedure is applicable to 3D problems and uses time- and stress-dependent material properties to characterize the nonlinear behavior of material. The equations describing material behavior are chosen based on the measured material properties in a short test time frame. This estimation process uses the Prony series material parameters, and the constitutive relations are based on the nonseparable form of equations. Material properties are then modified to include the long-term response of material. The presented model is suitable for the development of a unified computer code that can handle both linear and nonlinear viscoelastic material behavior. The proposed viscoelastic model is implemented in a user-defined material algorithm in abaqus (UMAT), and the model validity is assessed by comparison with experimental observations on polyethylene for three uniaxial loading cases, namely short-term loading, long-term loading, and step loading. A part of the experimental results have been conducted by (Liu, 2007, “Material Modelling for Structural Analysis of Polyethylene,” M.Sc. thesis, University of Waterloo, Waterloo, ON Canada), while the rest are provided by an industrial partner. The research shows that the proposed finite element model can reproduce the experimental strain–time curves accurately and concludes that with proper material properties to reflect the deformation involved in the mechanical tests, the deformation behavior observed experimentally can be accurately predicted using the finite element simulation.

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References

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Figures

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Fig. 1

Multi-Kelvin solid configuration

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Fig. 2

Single 3D element made in abaqus and meshed by one quadratic hexahedron solid element, C3D20R

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Fig. 3

Short-term (24 h) results comparison for PIPE material between test data (solid lines) [17] and present FEA (dashed lines)

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Fig. 4

Short-term (24 h) results comparison for RES1 material between test data (solid lines) [17] and present FEA (dashed lines)

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Fig. 5

Short-term (24 h) results comparison for RES2 material between test data (solid lines) [17] and present FEA (dashed lines)

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Fig. 6

Short-term (24 h) results comparison for RES4 material between test data (solid lines) [17] and present FEA (dashed lines)

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Fig. 7

Short-term (24 h) results comparison for PE80 material between test data (solid lines) [17] and present FEA (dashed lines)

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Fig. 8

Long-term (40 h) response prediction for PIPE material, test data (solid lines) [17], and present FEA (dashed lines)

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Fig. 9

Long-term (170 h) response prediction for PIPE material, test data (solid lines) [17], and present FEA (dashed lines)

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Fig. 10

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for LL-8461 at 23 °C

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Fig. 11

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for LL-8461 at 50 °C

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Fig. 12

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for LL-8461 at 60 °C

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Fig. 13

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for HD-8660 at 23 °C

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Fig. 14

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for HD-8660 at 50 °C

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Fig. 15

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for HD-8660 at 60 °C

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Fig. 16

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for Paxon 7004 at 23 °C

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Fig. 17

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for Paxon 7004 at 50 °C

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Fig. 18

Finite element (solid lines) versus experimental (dashed lines) (Courtesy of Imperial Oil Limited): creep results for Paxon 7004 at 60 °C

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Fig. 19

Two-step loading for PIPE material, test data (solid lines) [17], and present FEA (dashed lines)

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Fig. 20

Two-step loading for PIPE material, test data (solid lines) [17], and present FEA (dashed lines)

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Fig. 21

Multistep loading for PIPE material, test data (solid lines) [17], and present FEA (dashed lines)

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Fig. 22

Multistep loading and unloading for PIPE material, test data (solid lines) [17], and present FEA (dashed lines)

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