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http://hdl.handle.net/10985/19196
Implementation of a reaction-diffusion process in the Abaqus finite element software
VASIKARAN, Elisabeth; CHARLES, Yann; GILORMINI, Pierre
To increase the Abaqus software capabilities, we propose a strategy to force the software to activate hidden degrees of freedom and to include extra coupled phenomena. As an illustration, we apply this approach to the simulation of a reaction diffusion process, the Gray-Scott model, which exhibits very complex patterns. Several setups have been considered and compared with available results to analyze the abilities of our strategy and to allow the inclusion of complex phenomena in Abaqus.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/191962020-01-01T00:00:00ZVASIKARAN, ElisabethCHARLES, YannGILORMINI, PierreTo increase the Abaqus software capabilities, we propose a strategy to force the software to activate hidden degrees of freedom and to include extra coupled phenomena. As an illustration, we apply this approach to the simulation of a reaction diffusion process, the Gray-Scott model, which exhibits very complex patterns. Several setups have been considered and compared with available results to analyze the abilities of our strategy and to allow the inclusion of complex phenomena in Abaqus.An introduction to the statistical theory of polymer network formation
http://hdl.handle.net/10985/6886
An introduction to the statistical theory of polymer network formation
GILORMINI, Pierre
A short but detailed introduction to the statistical theory of polymer network formation is given, including gel formation, gel structure, and sol fraction. Focus is put on the use of probability generating functions, and results that are of interest for polymer network elasticity are emphasized. Detailed derivations are supplied, and a simple 6-step procedure is provided, so that the reader is able to adapt and apply the theory to his own chemical systems, even if examples are given on polyurethanes essentially.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/68862011-01-01T00:00:00ZGILORMINI, PierreA short but detailed introduction to the statistical theory of polymer network formation is given, including gel formation, gel structure, and sol fraction. Focus is put on the use of probability generating functions, and results that are of interest for polymer network elasticity are emphasized. Detailed derivations are supplied, and a simple 6-step procedure is provided, so that the reader is able to adapt and apply the theory to his own chemical systems, even if examples are given on polyurethanes essentially.Charcaterization of the Mullins effect of carbon-black filled rubbers
http://hdl.handle.net/10985/6804
Charcaterization of the Mullins effect of carbon-black filled rubbers
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; GILORMINI, Pierre; CAILLARD, Julien
Several carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method or the tangent modulus at zero stress. The proposed parameter is used to study the effects of crosslink density and filler amount on the Mullins softening. The latter is shown to remain unaffected by a change of crosslink density and to increase with an increase of filler amount. The damage parameter exhibits mere linear dependences on the maximum Hencky strain applied and on the filler volume fraction. A simple linear expression is given finally to predict the Mullins softening of filled rubbers. The parameter also provides an objective analysis for the Mullins softening that supports comments on a better understanding of this effect.
Publisher version : http://rubberchemtechnol.org/doi/abs/10.5254/1.3592294?journalCode=rcat
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/68042011-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasGILORMINI, PierreCAILLARD, JulienSeveral carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method or the tangent modulus at zero stress. The proposed parameter is used to study the effects of crosslink density and filler amount on the Mullins softening. The latter is shown to remain unaffected by a change of crosslink density and to increase with an increase of filler amount. The damage parameter exhibits mere linear dependences on the maximum Hencky strain applied and on the filler volume fraction. A simple linear expression is given finally to predict the Mullins softening of filled rubbers. The parameter also provides an objective analysis for the Mullins softening that supports comments on a better understanding of this effect.On the account of a cohesive interface for modeling the behavior until break of highly filled elastomers
http://hdl.handle.net/10985/10434
On the account of a cohesive interface for modeling the behavior until break of highly filled elastomers
TOULEMONDE, Paul-Aymé; DIANI, Julie; GILORMINI, Pierre; DESGARDIN, Nancy
The nonlinear behavior and failure of highly filled elastomers are significantly impacted by the volume fraction, the size and nature of fillers and the matrix stiffness. Original experimental data obtained on glass beads reinforced acrylates and on propellants allow illustrating and discussing the main effects generally observed. In order to better understand the effects of the microstructure and constitutive parameters on the behavior and failure of highly filled elastomers, a composite model, represented by a 2D periodic cell with randomly dispersed particles, with an account of a cohesive zone at the filler/matrix interface is used. Finite element simulations with finite strain provide insight on the stress-strain responses dependence to the model parameters and allow defining a failure criterion perceived by the appearance of a critical fibrillar microstructure.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/104342016-01-01T00:00:00ZTOULEMONDE, Paul-AyméDIANI, JulieGILORMINI, PierreDESGARDIN, NancyThe nonlinear behavior and failure of highly filled elastomers are significantly impacted by the volume fraction, the size and nature of fillers and the matrix stiffness. Original experimental data obtained on glass beads reinforced acrylates and on propellants allow illustrating and discussing the main effects generally observed. In order to better understand the effects of the microstructure and constitutive parameters on the behavior and failure of highly filled elastomers, a composite model, represented by a 2D periodic cell with randomly dispersed particles, with an account of a cohesive zone at the filler/matrix interface is used. Finite element simulations with finite strain provide insight on the stress-strain responses dependence to the model parameters and allow defining a failure criterion perceived by the appearance of a critical fibrillar microstructure.Testing some implementations of a cohesive-zone model at finite strain
http://hdl.handle.net/10985/10171
Testing some implementations of a cohesive-zone model at finite strain
GILORMINI, Pierre; DIANI, Julie
This study shows how the results given by a cohesive-zone model at finite strain may depend strongly on its numerical implementation. A two-dimensional four-node cohesive element is considered, which includes several variants depending on a part of the strain-displacement matrix, on the quadrature rule applied, and on the configuration chosen to perform integration. Finite element simulations combine these variants with a very simple, bilinear, cohesive-zone model, in two tests. The first test involves a single element and illustrates some features of the various implementations. The other test simulates the peeling of an elastomer strip from a rigid substrate.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/101712015-01-01T00:00:00ZGILORMINI, PierreDIANI, JulieThis study shows how the results given by a cohesive-zone model at finite strain may depend strongly on its numerical implementation. A two-dimensional four-node cohesive element is considered, which includes several variants depending on a part of the strain-displacement matrix, on the quadrature rule applied, and on the configuration chosen to perform integration. Finite element simulations combine these variants with a very simple, bilinear, cohesive-zone model, in two tests. The first test involves a single element and illustrates some features of the various implementations. The other test simulates the peeling of an elastomer strip from a rigid substrate.Crosslink Density Changes during the Hydrolysis of Tridimensional Polyesters
http://hdl.handle.net/10985/8276
Crosslink Density Changes during the Hydrolysis of Tridimensional Polyesters
RICHAUD, Emmanuel; GILORMINI, Pierre; COQUILLAT, Marie; VERDU, Jacques
The hydrolysis of almost ideal networks based on macrodiols of average molar mass about 2 kg mol 1, with L¼18 ester groups per chain is studied. Tensile testing is used to evaluate the crosslink density through the statistical theory of rubber elasticity at two temperatures and three values of relative humidity. A kinetic model for ester consumption including an autocatalysis term is proposed and combined with two original approaches for modeling the crosslink density changes. This allows kinetic parameters of hydrolysis to be determined, and very good predictions are obtained for the variations of crosslink density (or elastic modulus) in the three aging conditions considered. The initial curvature of elastic modulus versus time is predicted positive for weak autocatalysis and negative for strong autocatalysis. The obtained conversion ratio at degelation is found to decrease sharply with the number of esters per elastically active chain
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/82762014-01-01T00:00:00ZRICHAUD, EmmanuelGILORMINI, PierreCOQUILLAT, MarieVERDU, JacquesThe hydrolysis of almost ideal networks based on macrodiols of average molar mass about 2 kg mol 1, with L¼18 ester groups per chain is studied. Tensile testing is used to evaluate the crosslink density through the statistical theory of rubber elasticity at two temperatures and three values of relative humidity. A kinetic model for ester consumption including an autocatalysis term is proposed and combined with two original approaches for modeling the crosslink density changes. This allows kinetic parameters of hydrolysis to be determined, and very good predictions are obtained for the variations of crosslink density (or elastic modulus) in the three aging conditions considered. The initial curvature of elastic modulus versus time is predicted positive for weak autocatalysis and negative for strong autocatalysis. The obtained conversion ratio at degelation is found to decrease sharply with the number of esters per elastically active chainSome features of the PPR cohesive-zone model combined with a linear unloading/reloading relationship
http://hdl.handle.net/10985/11537
Some features of the PPR cohesive-zone model combined with a linear unloading/reloading relationship
GILORMINI, Pierre; DIANI, Julie
A loading/unloading/reloading process is applied to a cohesive zone where the model proposed by Park, Paulino and Roesler in 2009 is combined with a linear unloading/reloading relationship. The applied loading and unloading use the same mixed mode and reloading is in mode I. When the amplitude of preloading is varied, several features are evidenced: jumps of the dissipated energy, reversibility maintained after a traction peak, nonlinear traction variations during unloading, increasing traction during unloading, finite traction after a fracture criterion has been fulfilled, different traction values at the beginning of unloading and when dissipative reloading begins. Moreover, the results depend strongly on the path followed during unloading. Simple modifications of the model allow none of these questionable features to appear.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/115372017-01-01T00:00:00ZGILORMINI, PierreDIANI, JulieA loading/unloading/reloading process is applied to a cohesive zone where the model proposed by Park, Paulino and Roesler in 2009 is combined with a linear unloading/reloading relationship. The applied loading and unloading use the same mixed mode and reloading is in mode I. When the amplitude of preloading is varied, several features are evidenced: jumps of the dissipated energy, reversibility maintained after a traction peak, nonlinear traction variations during unloading, increasing traction during unloading, finite traction after a fracture criterion has been fulfilled, different traction values at the beginning of unloading and when dissipative reloading begins. Moreover, the results depend strongly on the path followed during unloading. Simple modifications of the model allow none of these questionable features to appear.Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers
http://hdl.handle.net/10985/11439
Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers
DIANI, Julie; GILORMINI, Pierre
A three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecularmobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/114392017-01-01T00:00:00ZDIANI, JulieGILORMINI, PierreA three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecularmobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.Study on the temperature dependence of the bulk modulus of polyisoprene by molecular dynamics simulations
http://hdl.handle.net/10985/6677
Study on the temperature dependence of the bulk modulus of polyisoprene by molecular dynamics simulations
DIANI, Julie; FAYOLLE, Bruno; GILORMINI, Pierre
The temperature dependence of the bulk modulus of polyisoprene has been studied using molecular dynamics simulations. Virtual polyisoprenes have been submitted to volume contractions above and below the glass transition. Bulk modulus has been observed to be linearly dependent on temperature both above and below the glass transition respectively, and it dropped by a factor of about 2 while temperatures was risen above the glass transition. By monitoring the energy changes during volume contractions, it was observed that the bulk modulus arises mainly from the Van de Waals interactions. Nevertheless, the entropy contribution to the bulk modulus becomes significant above the glass transition. At a first order, the entropy part of the bulk modulus can be considered as independent on the temperature.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/66772008-01-01T00:00:00ZDIANI, JulieFAYOLLE, BrunoGILORMINI, PierreThe temperature dependence of the bulk modulus of polyisoprene has been studied using molecular dynamics simulations. Virtual polyisoprenes have been submitted to volume contractions above and below the glass transition. Bulk modulus has been observed to be linearly dependent on temperature both above and below the glass transition respectively, and it dropped by a factor of about 2 while temperatures was risen above the glass transition. By monitoring the energy changes during volume contractions, it was observed that the bulk modulus arises mainly from the Van de Waals interactions. Nevertheless, the entropy contribution to the bulk modulus becomes significant above the glass transition. At a first order, the entropy part of the bulk modulus can be considered as independent on the temperature.Effect of the microstructure parameters on the Mullins softening in carbon-black filled SBRs
http://hdl.handle.net/10985/6805
Effect of the microstructure parameters on the Mullins softening in carbon-black filled SBRs
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; GILORMINI, Pierre; CAILLARD, Julien
A quantitative estimate of the Mullins softening is proposed and tested on various carbon-black filled styrene-butadiene rubbers. In order to model the behaviour of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. The amplification factor is grounded on the representation of filled rubbers as heterogeneous materials made of hard rigid domains and soft deformable domains. In the present work, this factor is splitted into two parts with opposite effects that account for the Mullins softening and for the filler reinforcement, respectively. Evolutions of both parts are obtained through a direct analysis of cyclic uniaxial tensile tests performed on a series of materials. The Mullins softening part is shown to linearly depend on the filler volume fraction and on the maximum strain applied, when defined as the first invariant of the Hencky tensor. Its changes with the gum crosslink density parameter are insignificant. The reinforcement part of the amplification factor shows quadratic dependence on the filler volume fraction.
[The definitive version is available at www3.interscience.wiley.com]
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/68052012-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasGILORMINI, PierreCAILLARD, JulienA quantitative estimate of the Mullins softening is proposed and tested on various carbon-black filled styrene-butadiene rubbers. In order to model the behaviour of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. The amplification factor is grounded on the representation of filled rubbers as heterogeneous materials made of hard rigid domains and soft deformable domains. In the present work, this factor is splitted into two parts with opposite effects that account for the Mullins softening and for the filler reinforcement, respectively. Evolutions of both parts are obtained through a direct analysis of cyclic uniaxial tensile tests performed on a series of materials. The Mullins softening part is shown to linearly depend on the filler volume fraction and on the maximum strain applied, when defined as the first invariant of the Hencky tensor. Its changes with the gum crosslink density parameter are insignificant. The reinforcement part of the amplification factor shows quadratic dependence on the filler volume fraction.