A variational framework for the modeling of glassy polymers under finite strains

Farias, Jan-Michel; Stainier, Laurent; Fancello, Eduardo Alberto

doi:10.1007/s00161-019-00809-8

Cited by 5 publications

(1 citation statement)

References 54 publications

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“…In this case, they only considered the viscoelastic constitutive behaviour for the hot embossing simulation, which limited the modelling accuracy of the polymer behaviour. Farias et al [18] The influence of elastic, plastic, and viscous behaviours on the constitutive model for the filling efficiency of the micro hot embossing process has not been fully investigated in the existing literature. In this study, an original method was developed for identifying the filling efficiency of PMMA during the micro hot embossing process considering its elasticity, viscosity, and plasticity.…”

Section: Introductionmentioning

confidence: 99%

Influence of elastic-viscoplastic behaviour on the filling efficiency of amorphous thermoplastic polymer during the micro hot embossing process

Rabhi

Cheng

Barrière

et al. 2020

Journal of Manufacturing Processes

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An unsolved issue in simulating the hot embossing of polymers is modelling the unfilled structured mould. This is because the constitutive law of such polymers has not been adequately determined, especially at the microscale or smaller. The present study investigated the influence of the elastic-viscoplastic behaviour on the filling efficiency of an amorphous polymer during the micro hot embossing process. Constitutive equations based on the two-layer viscoplastic model were used to simulate the hot embossing process. The micro-cavity of the mould was completely filled by the polymer, and the elastic, viscous, and plastic behaviours were considered simultaneously in the simulation. Compression tests were performed to identify the model parameter values for poly-methyl methacrylate. A numerical simulation was performed to analyse the contributions of the polymer's elastic, viscous, and plastic behaviours. The unfilled area in the micro-cavity was evaluated after a displacement of 0.2 mm was applied to the mould. This was used as an indicator to compare the mould filling efficiency with those of the elastoplastic and elastic-viscoplastic constitutive models. The analysis led to the selection of an optimal elastic-viscoplastic model to completely fill the micro-cavity, which was consistent with the experimental results.

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Section: Introductionmentioning

confidence: 99%

Influence of elastic-viscoplastic behaviour on the filling efficiency of amorphous thermoplastic polymer during the micro hot embossing process

Rabhi

Cheng

Barrière

et al. 2020

Journal of Manufacturing Processes

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Multifield variational formulations of diffusion initial boundary value problems

Salazar

Heuzé

Stainier

2020

Continuum Mech. Thermodyn.

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We present two multifield and one single-field variational principles for the Initial Boundary Value Problem of diffusion. Chemical potential and concentration appear as conjugate variables in the multifield formulations. The main importance of the proposed formulations is the approach used to generate the variational principles, where the framework of Generalized Standard Materials is used for constitutive laws while natural boundary conditions and the balance of mass are used as constraints of the optimization problem. This approach allows to derive such principles for multiphysic problems in a generic manner. A detailed derivation and analysis of the formulations is presented, where it can be seen their equivalence with the most common strong and weak forms of the problem using Fick's laws along with the logarithmic mass action law. From the stationarity condition with respect to the mass flux of the initially proposed functional, two main relations are identified. First, the chemical potential appears as the opposite of the Lagrange multiplier that allows to enforce the balance of mass and natural boundary conditions. Second, a conjugate relation is found for a given substance between its mass flux and the opposite of the gradient of its chemical potential. Furthermore, to reduce the number of variables of the initial variational principle, a field reduction is applied, reaching the model presented by [1] for Fickean diffusion. Nevertheless, the aforementioned relations cannot be derived from the reduced model. Finally, a numerical implementation is presented for completeness where we compare the performance of the proposed formulations against the usual weak form.

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A study on the response of PLGA 85/15 under compression and heat-treatment testing cycles

Castro

Salmoria

Roesler

et al. 2020

Mech Time-Depend Mater

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A variational framework for the modeling of glassy polymers under finite strains

Cited by 5 publications

References 54 publications

Influence of elastic-viscoplastic behaviour on the filling efficiency of amorphous thermoplastic polymer during the micro hot embossing process

Influence of elastic-viscoplastic behaviour on the filling efficiency of amorphous thermoplastic polymer during the micro hot embossing process

Multifield variational formulations of diffusion initial boundary value problems

A study on the response of PLGA 85/15 under compression and heat-treatment testing cycles

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