An integral constitutive equation for nonlinear plasto‐viscoelastic behavior of high‐density polyethylene

Lai, J.; Bakker, A.

doi:10.1002/pen.760351703

Cited by 69 publications

(54 citation statements)

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“…A consistent tangent stiffness matrix is also formulated at the material level to accelerate convergence and avoid divergence at the structural level. In Section 3, the numerical algorithm is validated with experimental data on polyethylene reported by Lai and Bakker [1]. Convergence behaviors of the proposed algorithm under several loading histories are also investigated.…”

Section: Introductionmentioning

confidence: 98%

A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation

Kim

Muliana

2009

Numerical Meth Engineering

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SUMMARYThe present study introduces a time-integration algorithm for solving a non-linear viscoelastic-viscoplastic (VE-VP) constitutive equation of isotropic polymers. The material parameters in the constitutive models are stress dependent. The algorithm is derived based on an implicit time-integration method (Computational Inelasticity. Springer: New York, 1998) (Computational Inelasticity. Springer: New York, 1998), is also formulated to improve convergence and avoid divergence. Available experimental data on time-dependent and inelastic responses of high-density polyethylene are used to verify the current numerical algorithm. The time-integration scheme is examined in terms of its computational efficiency and accuracy. Numerical FE analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented.

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Section: Introductionmentioning

confidence: 98%

A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation

Kim

Muliana

2009

Numerical Meth Engineering

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“…For example, creep tests on high-density polyethylene (HDPE) (Lai and Bakker, 1995), polycarbonate (Frank and Brockman, 2001), and aramid and polyester fibers Davies, 2003, 2005) show a combination of both viscoelastic and viscoplastic responses even at the room temperature and for short loading times. It has been observed in many types of polymers (Crissman and Zapas, 1985;Lai and Bakker, 1995;Zapas and Crissman, 1984) and polymer composites (Megnis and Varna, 2003;Pasricha et al, 1995;Ségard et al, 2002;Tuttle and Brinson, 1986) that creep strains are not entirely recovered even after sufficiently long recovery periods. These permanent strains are attributed to the changes in polymers mulecular structure during deformation, plastic flow localization, expanding and opening of the molecular chains (rearrangement of polymer chains), that all cause micro-cracks and micro-voids in pure polymers.…”

Section: 5mentioning

confidence: 99%

“…Also, it should be clarified that in order to find the viscoelastic material parameters of PMMA, the data presented by Lai and Bakker (1995) is used. This data set is in small deformation range, and is proper for calibrating the Prony series terms and their corresponding relaxation time variables.…”

Section: Model Predictionsmentioning

confidence: 99%

“…Lai and Bakker (1995) and Hasan and Boyce (1995), the viscoplastic material constants are obtained. The loading times in these tests were rather short; hence, one can assume that the material is not damaged during these experiments, or at least the introduced damage is not signifcant at lower stress levels.…”

Section: Fig 52mentioning

confidence: 99%

“…Following the above procedure, for PMMA polymer, the Prony series and non-linear viscoelastic parameters can be extracted from the experimental data presented by Lai and Bakker (1995) and Hasan and Boyce (1995) at different stresses and temperatures.…”

Section: Application Of the Constitutive Models To Polymermentioning

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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Non‐linear Viscoelastic Behaviour

Ward

Sweeney

2012

Mechanical Properties of Solid Polymers

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This paper is concerned with the development of a quantitative analysis method that can extract the mixed linear and non-linear dynamical response of a viscoelastic process in composite materials. A tractable set of simultaneous equations with well behaved coefficients can be generated by taking time series moments of a suitably truncated Volterra series expansion. This moment hierarchy is a set of inhomogeneous non-linear integral equations, based on a vector multidimensional convolution form of the Volterra functional series expansion. The hierarchy developed is used to analyse the time dependent viscoelastic properties of fibre reinforced composite materials. Estimates of the temporal response of the measured stress to the measured mechanical force were then used to predict the out of sample stress field values. It is demonstrated that the response functions provided a good representation of the viscoelastic process. Generally speaking, the response functions estimated from the data are used to determine the dynamic and steady state transport coefficients, which can, be used to develop either an empirical field theory of the phenomena or alternatively be used in the design process.

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An integral constitutive equation for nonlinear plasto‐viscoelastic behavior of high‐density polyethylene

Cited by 69 publications

References 9 publications

A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation

A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation

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

Non‐linear Viscoelastic Behaviour

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