Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures

In this paper, a two scale Finite Element method (FE2), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic microstructure that exhibit a time-dependent response. The sensitivity to the strain rate requires an homogenization scheme to bridge the scale...

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Vydáno v:Composite structures Ročník 193; s. 165 - 179
Hlavní autoři: Tikarrouchine, E., Chatzigeorgiou, G., Praud, F., Piotrowski, B., Chemisky, Y., Meraghni, F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.06.2018
Elsevier
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ISSN:0263-8223, 1879-1085
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Abstract In this paper, a two scale Finite Element method (FE2), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic microstructure that exhibit a time-dependent response. The sensitivity to the strain rate requires an homogenization scheme to bridge the scales between the macroscopic boundary conditions applied and the local evaluation of the strain rate. In the present work, the effective response of composite materials where the matrix has a local elasto-viscoplastic behavior with ductile damage are analyzed using periodic homogenization, solving simultaneously finite element problems at the microscopic scale (unit cell) and at the macroscopic scale. This approach can integrate any kind of periodic microstructure with any type of non-linear behavior for the constituents (without the consideration of non-linear geometric effects), allowing to treat complex mechanisms that can occur in every phase and at their interface. The numerical implementation of this simulation strategy has been performed with a parallel computational technique in ABAQUS/Standard,with the implementation of a set of dedicated scripts. The homogenization process is performed using a user-defined constitutive law that solve a set full-field non-linear simulations of a Unit Cell and perform the necessary homogenization of the mechanical quantities. The effectiveness of the method is demonstrated with three examples of 3D composite structures with plastic or viscoplastic and ductile damage matrix. In the first example, the numerical results obtained by this full field approach are compared with a semi-analytical solution on elastoplastic multilayer composite structure. The second example investigates the macroscopic response of a complex viscoplastic composite structure with ductile damage and is compared with the mean field Mori-Tanaka method. Finally, 3D corner structure consisting of periodically aligned short fibres composite is analysed under complex loading path. These numerical simulations illustrate the capabilities of the FE2 strategy under non-linear regime. when time dependent constitutive models describe the response of the constituents.
AbstractList In this paper, a two scale Finite Element method (FE2 ), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic microstructure that exhibit a time-dependent response. The sensitivity to the strain rate requires an homogenization scheme to bridge the scales between the macroscopic boundary conditions applied and the local evaluation of the strain rate. In the present work, the effective response of composite materials where the matrix has a local elasto-viscoplastic behavior with ductile damage are analyzed using periodic homogenization, solving simultaneously finite element problems at the microscopic scale (unit cell) and at the macroscopic scale. This approach can integrate any kind of periodic microstructure with any type of non-linear behavior for the constituents (without the consideration of non-linear geometric effects), allowing to treat complex mechanisms that can occur in every phase and at their interface. The numerical implementation of this simulation strategy has been performed with a parallel computational technique in ABAQUS/Standard,with the implementation of a set of dedicated scripts. The homogenization process is performed using a user-defined constitutive law thatsolve a set full-field non-linear simulations of a Unit Cell and perform the necessary homogenization of the mechanical quantities. The effectiveness of the method is demonstrated with three examples of 3D composite structures with plastic or viscoplastic and ductile damage matrix. In the first example, the numerical results obtained by this full field approach are compared with a semi-analytical solution on elastoplastic multilayer composite structure. The second example investigates the macroscopic response of a complex viscoplastic composite structure with ductile damage and is compared with the mean field Mori-Tanaka method. Finally, 3D corner structure consisting of periodically aligned short fibres composite is analysed under complex loading path. These numerical simulations illustrate the capabilities of the FE2 strategy under non-linear regime, when time dependent constitutive models describe the response of the constituents
In this paper, a two scale Finite Element method (FE2), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic microstructure that exhibit a time-dependent response. The sensitivity to the strain rate requires an homogenization scheme to bridge the scales between the macroscopic boundary conditions applied and the local evaluation of the strain rate. In the present work, the effective response of composite materials where the matrix has a local elasto-viscoplastic behavior with ductile damage are analyzed using periodic homogenization, solving simultaneously finite element problems at the microscopic scale (unit cell) and at the macroscopic scale. This approach can integrate any kind of periodic microstructure with any type of non-linear behavior for the constituents (without the consideration of non-linear geometric effects), allowing to treat complex mechanisms that can occur in every phase and at their interface. The numerical implementation of this simulation strategy has been performed with a parallel computational technique in ABAQUS/Standard,with the implementation of a set of dedicated scripts. The homogenization process is performed using a user-defined constitutive law that solve a set full-field non-linear simulations of a Unit Cell and perform the necessary homogenization of the mechanical quantities. The effectiveness of the method is demonstrated with three examples of 3D composite structures with plastic or viscoplastic and ductile damage matrix. In the first example, the numerical results obtained by this full field approach are compared with a semi-analytical solution on elastoplastic multilayer composite structure. The second example investigates the macroscopic response of a complex viscoplastic composite structure with ductile damage and is compared with the mean field Mori-Tanaka method. Finally, 3D corner structure consisting of periodically aligned short fibres composite is analysed under complex loading path. These numerical simulations illustrate the capabilities of the FE2 strategy under non-linear regime. when time dependent constitutive models describe the response of the constituents.
Author Tikarrouchine, E.
Chemisky, Y.
Meraghni, F.
Praud, F.
Piotrowski, B.
Chatzigeorgiou, G.
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  surname: Chatzigeorgiou
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  surname: Meraghni
  fullname: Meraghni, F.
  email: fodil.meraghni@ensam.eu
  organization: Arts et Metiers ParisTech, LEM3-UMR 7239 CNRS, 4 rue Augustin Fresnel, 57078 Metz, France
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Keywords FE2 method
Multi-scale finite element computation
Elastoviscoplastic behavior
Composite materials
Periodic homogenization
Ductile damage
periodic homogenization
ductile damage
elastoviscoplastic behavior
composite materials
Language English
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Snippet In this paper, a two scale Finite Element method (FE2), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic...
In this paper, a two scale Finite Element method (FE2 ), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic...
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SubjectTerms Composite materials
Ductile damage
Elastoviscoplastic behavior
Engineering Sciences
FE2 method
Materials
Materials and structures in mechanics
Mechanics
Mechanics of materials
Multi-scale finite element computation
Periodic homogenization
Solid mechanics
Title Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures
URI https://dx.doi.org/10.1016/j.compstruct.2018.03.072
https://hal.science/hal-01762458
Volume 193
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