3-D schapery representation for non-linear viscoelasticity and finite element implementation

Lai, J.; Bakker, A.

doi:10.1007/bf00369936

Cited by 165 publications

(92 citation statements)

References 11 publications

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“…(4.47) to (4.51) and those presented by other researchers (Haj-Ali and Muliana, 2004;Huang et al, 2011a;Lai and Bakker, 1996) is that they are stated in the undamaged (effective) configuration allowing one to couple the viscoelastic model to any damage evolution law. The other difference comes from the nature and definition of Lagrangian strain and II-PK stress (for finite strain) which deliver a volumetric tensor instead of a scalar value (in small deformation form).…”

Section: Decoupling Volumetric and Deviatoric Strains And Hierarchicamentioning

confidence: 94%

“…For more detail the reader is referred to (Haj-Ali and Muliana, 2004;Lai and Bakker, 1996). On the other hand, if the assumption of linear change of 2 g S is not considered, the hereditary decomposition can be derived as …”

Section: Decoupling Volumetric and Deviatoric Strains And Hierarchicamentioning

confidence: 99%

“…The Schapery's viscoelastic one-dimensional convolution single integral model is expressed in terms of the Cauchy stress,  , as by Lai and Bakker (1996), the one-dimensional nonlinear viscoelastic model in Eq. …”

Section: Non-linear Viscoelastic Model In Small Strain Frameworkmentioning

confidence: 99%

“…Using the Schapery's integral constitutive law, Eq. (7.1), and after some mathematical manipulations (Lai and Bakker, 1996), the deviatoric and volumetric non-linear viscoelastic strain components can be partitioned and expressed at time t , as Table 7.1 and 7.2. (Lai and Bakker, 1996).…”

Section: Non-linear Viscoelastic Model In Small Strain Frameworkmentioning

confidence: 99%

“….1: Viscoelastic material parameters for the PMMA (Lai and Bakker, 1996) Table 7.2: Non-linear viscoelastic parameters for the PMMA (Lai and Bakker, 1996) …”

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confidence: 99%

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Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

Tehrani¹

2013

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Lightweight advanced materials are critical in the manufacturing of many Army vehicles. Recently, numerical tools have been utilized to customize experiments to achieve optimized behavior of micro/nano polymer composites (MNPCs). Most numerical studies are based on characterizing the MNPCs through simple microstructures, as circular particles or straight fibers embedded in a specific polymer matrix. Although these geometries are effective in virtually modeling some types of composite material behavior, they fail to address some critical key Names of Under Graduate students supportedPERCENT_SUPPORTED NAME FTE Equivalent:Total Number:The number of undergraduates funded by this agreement who graduated during this period with a degree in science, mathematics, engineering, or technology fields:The number of undergraduates funded by your agreement who graduated during this period and will continue to pursue a graduate or Ph.D. degree in science, mathematics, engineering, or technology fields:Number of graduating undergraduates who achieved a 3.5 GPA to 4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education, Research and Engineering:The number of undergraduates funded by your agreement who graduated during this period and intend to work for the Department of DefenseThe number of undergraduates funded by your agreement who graduated during this period and will receive scholarships or fellowships for further studies in science, mathematics, engineering or technology fields: Student Metrics This section only applies to graduating undergraduates supported by this agreement in this reporting periodThe number of undergraduates funded by this agreement who graduated during this period: 0.00 ...... Names of Personnel receiving masters degrees Inventions (DD882) Scientific ProgressBecause the mechanical responses of polymers and many types of polymer composites are in the large deformation range, the Eulerian or Lagrangian concept is required for measuring the stress and strain. On the other hand, developing a large deformation based constitutive model requires a number of considerations, and should be performed from a thermodynamics point of view to study the motion of each component of the material. Even though such approach is precise and physically sound, it is limited to just one type of material. Furthermore, polymers show high dependency to the rate and time of the applied load; hence, employing viscoelastic, viscoplastic and viscodamage models is necessary. To address these issues, a consistent framework is developed to generalize elastic/viscoelastic and plastic/viscoplastic models from small strain to the large deformation range. The developed continuum based app...

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Section: Decoupling Volumetric and Deviatoric Strains And Hierarchicamentioning

confidence: 94%

Section: Decoupling Volumetric and Deviatoric Strains And Hierarchicamentioning

confidence: 99%

Section: Non-linear Viscoelastic Model In Small Strain Frameworkmentioning

confidence: 99%

Section: Non-linear Viscoelastic Model In Small Strain Frameworkmentioning

confidence: 99%

“….1: Viscoelastic material parameters for the PMMA (Lai and Bakker, 1996) Table 7.2: Non-linear viscoelastic parameters for the PMMA (Lai and Bakker, 1996) …”

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confidence: 99%

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Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

Tehrani¹

2013

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A finite element constitutive update scheme for anisotropic, viscoelastic solids exhibiting non-linearity of the Schapery type

Poon

Ahmad

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThis study presents a new scheme for performing integration point constitutive updates for anisotropic, small strain, non-linear viscoelasticity, within the context of implicit, non-linear "nite element structural analysis. While the basic scheme has been presented earlier by the authors for linear viscoelasticity, the present work illustrates the generality of the underlying fundamentals by extending to Schapery's non-linear model. The method features a judicious choice of state variables, a stable backward Euler integration step, and a consistent tangent operator. Its greatest strength lies in ready incorporation into existing FEM codes. Numerical examples involving homogeneous stress states such as uniaxial extension and simple shear, and non-uniform stress states such as a beam under tip load, were carried out by incorporating the present scheme into a general purpose FEM package. Excellent agreement with analytical results is observed.

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Ultra High Molecular Weight Polyethylene and its Reinforcement with Carbon Nanotubes in Medical Devices

Guedes

Kanagaraj

Sreekanth

et al. 2015

Polyethylene‐Based Blends, Composites and Nanocomposites

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This chapter discusses the advantages and complexities of ultra high molecular weight polyethylene (UHMWPE) when used as a bearing material for total joint arthroplasty (TJA) and total knee arthroplasty (TKA). The UHMWPE internal structure and its mechanical response depend strongly on a diversity of factors that include radiation crosslinking, fiber reinforcement, and the addition of antioxidants such as Vitamin E or Vitamin C. All these manufacturing procedures induce morphological changes and simultaneously alter the mechanical properties of UHMWPE. The importance of UHMWPE on arthroplasty, including the advantages, the limitations and the strategies devised to overcome the known drawbacks are discussed in the first section. The following sections revise and discuss the biocompatibility, the manufacturing processes, the tribological behaviour, the aging by oxidation and irradiation of UHMWPE and UHMWPE-CNT nanocomposites. The last section analyses the viscoelastic behavior of UHMWPE and its implications on the long-term survival of total joint arthroplasty.

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3-D schapery representation for non-linear viscoelasticity and finite element implementation

Cited by 165 publications

References 11 publications

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

A finite element constitutive update scheme for anisotropic, viscoelastic solids exhibiting non-linearity of the Schapery type

Ultra High Molecular Weight Polyethylene and its Reinforcement with Carbon Nanotubes in Medical Devices

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