A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation

Ames, Nicoli M.; Srivastava, Vipin; Chester, Shawn A.; Anand, Lallit

doi:10.1016/j.ijplas.2008.11.004

Cited by 250 publications

(126 citation statements)

References 24 publications

(31 reference statements)

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“…An essential kinematical ingredient of elastic-viscoplastic constitutive theories for amorphous polymers below their glass transition temperatures, is the classical Kröner (1960) -Lee (1969 multiplicative decomposition 6 F = F e F p , with det F e > 0 and det F p > 0, (3.1) of the deformation gradient F into elastic and plastic parts F e and F p (e.g., Boyce et al, 1988;Govaert et al, 2000;Anand and Gurtin, 2003;Anand et al, 2009). Since we wish to model the behavior of glassy polymers in the technologically important temperature range which spans their glass transition temperatures, and since the number of microscopic relaxation mechanisms in these polymers increases as the temperature is increased, we base our theory on a "multimechanism" generalization of the decomposition (3.1), F = F e (α) F p (α) , with det F e (α) > 0 and det F p (α) > 0, α = 1, .…”

Section: Theorymentioning

confidence: 99%

“…The details are easily worked out by using the kinematical decomposition (3.2) instead of (3.1), and mimicking the development of the below-ϑ g theory detailed in Anand et al (2009).…”

Section: Theorymentioning

confidence: 99%

“…13 This is a useful free energy function for moderately large elastic stretches, Anand (1979Anand ( , 1986.…”

Section: Specialization Of the Theorymentioning

confidence: 99%

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A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition

Srivastava

Chester

Ames

et al. 2010

International Journal of Plasticity

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213

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Amorphous thermoplastic polymers are important engineering materials; however, their nonlinear, strongly temperature-and rate-dependent elastic-viscoplastic behavior is still not very well understood, and is modeled by existing constitutive theories with varying degrees of success. There is no generally agreed upon theory to model the large-deformation, thermo-mechanically-coupled, elastic-viscoplastic response of these materials in a temperature range which spans their glass transition temperature. Such a theory is crucial for the development of a numerical capability for the simulation and design of important polymer processing operations, and also for predicting the relationship between processing methods and the subsequent mechanical properties of polymeric products. In this paper we extend our recently published theory , IJP 25, 1474-1494Ames et al., 2009, IJP 25, 1495-1539 to fill this need.We have conducted large strain compression experiments on three representative amorphous polymeric materials -a cyclo-olefin polymer (Zeonex-690R), polycarbonate (PC), and poly(methyl methacrylate) (PMMA) -in a temperature range from room temperature to approximately 50C above the glass transition temperature, ϑ g , of each material, in a strain-rate range of ≈ 10 −4 to 10 −1 s −1 , and compressive true strains exceeding 100%. We have specialized our constitutive theory to capture the major features of the thermomechanical response of the three materials studied experimentally.We have numerically implemented our thermo-mechanically-coupled constitutive theory by writing a usermaterial subroutine for a widely-used finite element program. In order to validate the predictive capabilities of our theory and its numerical implementation, we have performed the following validation experiments: (i) a plane-strain forging of PC at a temperature below ϑ g , and another at a temperature above ϑ g ; (ii) blowforming of thin-walled semi-spherical shapes of PC above ϑ g ; and (iii) microscale hot-embossing of channels in Zeonex and PMMA above ϑ g . By comparing the results from this suite of validation experiments of some key features, such as the experimentally-measured deformed shapes and the load-displacement curves, against corresponding results from numerical simulations, we show that our theory is capable of reasonably accurately reproducing the experimental results obtained in the validation experiments.

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Section: Theorymentioning

confidence: 99%

“…The details are easily worked out by using the kinematical decomposition (3.2) instead of (3.1), and mimicking the development of the below-ϑ g theory detailed in Anand et al (2009).…”

Section: Theorymentioning

confidence: 99%

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A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition

Srivastava

Chester

Ames

et al. 2010

International Journal of Plasticity

Self Cite

213

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“…The constitutive models considering the kinematic hardening can account for this nonlinear response at large strains Ames et al, 2009), however they do not adequately account for this effect at small strains (Anand and Ames, 2006). Additionally, the heat generation and thermal conduction due to plastic dissipation become important at large strains and can affect both loading and unloading responses as demonstrated by Anand et al (2009);Ames et al (2009). A nonlinear viscoelastic model, heat generation, and thermal conduction will be considered in a future work in a fully thermo-mechanically-coupled simulation.…”

Section: Resultsmentioning

confidence: 99%

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Nguyễn

Lani

Pardoen

et al. 2016

International Journal of Solids and Structures

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A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A corotational formulation is used through the total Lagrange formalism. At small strains, the viscoelastic behavior is captured using the generalized Maxwell model. At large strains beyond a viscoelastic limit characterized by a pressure-sensitive yield function, which is extended from the Drucker-Prager one, a viscoplastic region follows. The viscoplastic flow is governed by a non-associated Perzyna-type flow rule incorporating this pressure-sensitive yield function and a quadratic flow potential in order to capture the volumetric deformation during the plastic process. The stress reduction phenomena arising from the post-peak plateau and during the failure stage are considered in the context of a continuum damage mechanics approach.The post-peak softening is modeled by an internal scalar, so-called softening variable, whose evolution is governed by a saturation law. When the softening variable is saturated, the rehardening stage is naturally obtained since the isotropic and kinematic hardening phenomena are still developing. Beyond the onset of failure characterized by a pressure-sensitive failure criterion, the damage process leading to the total failure is controlled by a second internal scalar, so-called failure variable. The final failure occurs when the failure variable reaches its critical value. To avoid the loss of solution uniqueness when dealing with the continuum damage mechanics formalism, a non-local implicit gradient formulation is used for both the softening and failure variables, leading to a multi-mechanism non-local damage continuum. The pressure sensitivity considered in both the yield and failure conditions allows for the distinction under compression and tension loading conditions. It is shown through experimental comparisons that the proposed constitutive model has the ability to capture the complex behavior of amorphous glassy polymers, including their failure.

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“…Various models were developed and tested to simulate these responses. Rheological models extended to three-dimensional case under finite strain assumption have been proposed, for instance, by (Alcoutlabi and MartinezVega, 2003;Anand and Ames, 2006;Dupaix and Boyce, 2007;Ames et al, 2009;Anand et al, 2009;Srivastava et al, 2010;Shim and Mohr, 2011;Fleischhauer et al, 2012;Helbig and Seelig, 2012). Some of them were devoted to phenomenological modeling (Zaïri et al, 2005b;Cheng and Ghosh, 2013) or developed within a thermodynamics framework (Drozdov, 1999;Miehe et al, 2009;Bouvard et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Multi-mechanism modeling of amorphous polymers

Jeridi

Chouchene

Kéryvin

et al. 2014

Mechanics Research Communications

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The paper is devoted to a multimechanism (MM) model for the mechanical behavior of amorphous glassy polymers. A finite strain formulation through updated lagrangian formalisms is used. In the proposed phenomenological model, three mechanisms are respectively associated to three physical regimes for plastic deformation. The model was successful in describing the stress-strain behavior of glassy polymers for different strain rates and range of temperatures. The description of the three regions observed in the monotonic stress-strain curves is obtained through a coupling matrix between the isotropic hardening variables. A modular strategy based on the determination of the material parameters in three steps is proposed.

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A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation

Cited by 250 publications

References 24 publications

A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition

A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Multi-mechanism modeling of amorphous polymers

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