************************************************************************************* Legal notice: UHYPER_Lopez-Pamies.for (Windows) and UHYPER_Lopez-Pamies.f (Linux) Copyright (C) 2018 Oscar Lopez-Pamies (pamies@illinois.edu) This ABAQUS UHYPER subroutine implements the incompressible hyperelastic model proposed in [1]. The present subroutine implements specifically the two-term version of this model (see eq. (13) in [1]) 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 4 material properties, e.g., *HYPERELASTIC, USER, TYPE=INCOMPRESSIBLE, PROPERTIES=4 in the input (.inp) file. The 4 materials properties for the model to be provided as 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 The two material parameters AMU1, AMU2 are non-negative real numbers (AMU1 >= 0, AMU2 >= 0). The two exponents ALPHA1, ALPHA2 are real numbers chosen so that the resulting strain energy is trongly elliptic (see eq. (22) in [1]). This is left to the user to check. ************************************************************************************* 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. ************************************************************************************* Reference: [1] Lopez-Pamies, O., 2010. A new I1-based hyperelastic model for rubber elastic materials. C. R. Mec. 338, 3--11. *************************************************************************************