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This ABAQUS UHYPER subroutine implements the hyperelastic energy density derived in Journal of the Mechanics and Physics of Solids 99 (2017), 438-470 for the macroscopic elastic response of isotropic and incompressible elastomers filled with liquid-like inclusions. The results applies to general non-percolative isotropic distributions of incompr…
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victorlefevre/UHYPER_Lefevre_Lopez-Pamies_Liquid_inclusions
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!********************************************************************** ! Legal notice: UHYPER_Liquid_inclusions_Lefevre_Lopez-Pamies.for ! ! Copyright (C) 2020 Victor Lefèvre ([email protected]) ! Oscar Lopez-Pamies ([email protected]) ! ! This ABAQUS UHYPER subroutine implements the hyperelastic energy ! density derived in [1] for the macroscopic elastic response of ! isotropic and incompressible elastomers filled with liquid-like ! inclusions. The results applies to general non-percolative isotropic ! distributions of incompressible inclusion whith vanishing shear ! stiffness. This result is valid for any choice of I1-based ! incompressible energy density characterizing the non-Gaussian ! isotropic elastic response of the underlying elastomer. The present ! subroutine is implemented for the choice of strain energy density ! proposed in [2]. ! ! This program is free software: you can redistribute it and/or modify ! it under the terms of the GNU General Public License as published by ! the Free Software Foundation, either version 3 of the License, or ! (at your option) any later version. ! ! This program is distributed in the hope that it will be useful, ! but WITHOUT ANY WARRANTY; without even the implied warranty of ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ! GNU General Public License for more details. ! ! You should have received a copy of the GNU General Public License ! along with this program. If not, see https://www.gnu.org/licenses/ ! !********************************************************************** ! Usage: ! ! The subroutine is to be used as an incompressible USER hyperelastic ! model with either 6 (arbitrary microstructures) or 5 (equiaxed ! particles) material properties, e.g., ! *HYPERELASTIC, USER, TYPE=INCOMPRESSIBLE, PROPERTIES=6 ! or ! *HYPERELASTIC, USER, TYPE=INCOMPRESSIBLE, PROPERTIES=5 ! in the input (.inp) file. ! ! 1/ For arbitrary microstructures, the 6 materials properties required ! by the model to be input to the subroutine via the PROPS array are ! listed in the table below: ! ! AMU1 = PROPS(1) ! PARAMETER #1 OF THE ELASTOMER ! ALPHA1 = PROPS(2) ! EXPONENT #1 OF THE ELASTOMER ! AMU2 = PROPS(3) ! PARAMETER #2 OF THE ELASTOMER ! ALPHA2 = PROPS(4) ! EXPONENT #2 OF THE ELASTOMER ! AC = PROPS(5) ! VOLUME FRACTION OF LIQUID-LIKE INCLUSIONS ! AMUT = PROPS(6) ! INITIAL SHEAR MODULUS OF THE ! ! ELASTOMER COMPOSITE ! ! The two material parameters AMU1, AMU2 characterizing the elastic ! behavior of the underlying elastomer are non-negative real numbers ! (AMU1 >= 0, AMU2 >= 0) with strictly positive sum (AMU1 + AMU2 > 0). ! The two exponents ALPHA1, ALPHA2 are non-zero real numbers ! (ALPHA1 ≠ 0, ALPHA2 ≠ 0) leading to a strongly elliptic strain ! energy (see eq. (22) in [2]). This is left to the user to check. ! ! The volume fractions of liquid-like inclusions (AC) must satisfy ! 0 <= AC <= 1. ! ! The initial shear modulus of the elastomer composite AMUT must be a ! non-negative real number (AMUT >= 0). ! ! 2/ For microstructures comprising equiaxed liquid-like inclusions, ! the 5 materials properties required by the model to be input to the ! subroutine via the PROPS array are listed in the table below: ! ! AMU1 = PROPS(1) ! PARAMETER #1 OF THE ELASTOMER ! ALPHA1 = PROPS(2) ! EXPONENT #1 OF THE ELASTOMER ! AMU2 = PROPS(3) ! PARAMETER #2 OF THE ELASTOMER ! ALPHA2 = PROPS(4) ! EXPONENT #2 OF THE ELASTOMER ! AC = PROPS(5) ! VOLUME FRACTION OF LIQUID-LIKE INCLUSIONS ! ! These 5 material properties are subjected to the same restrictions ! listed above. ! !********************************************************************** ! Additional information: ! ! This subroutine does not create solution-dependent state variables ! nor predefined field variables. ! ! Please consult the ABAQUS Documentation for additional references ! regarding the use of incompressible USER hyperelastic models with ! the UHYPER subroutine. ! ! Due the incompressible nature of this model, use of hybrid elements ! is strongly recommended. ! !********************************************************************** ! References: ! ! [1] Lefèvre, V., Lopez-Pamies, O. 2017. Nonlinear electroelastic ! deformations of dielectric elastomer composites: II — Non-Gaus- ! sian elastic dielectrics. J. Mech. Phys. Solids 99, 438--470. ! [2] Lopez-Pamies, O., 2010. A new I1-based hyperelastic model for ! rubber elastic materials. C. R. Mec. 338, 3--11. ! !**********************************************************************
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This ABAQUS UHYPER subroutine implements the hyperelastic energy density derived in Journal of the Mechanics and Physics of Solids 99 (2017), 438-470 for the macroscopic elastic response of isotropic and incompressible elastomers filled with liquid-like inclusions. The results applies to general non-percolative isotropic distributions of incompr…
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