-
Notifications
You must be signed in to change notification settings - Fork 4
/
README.txt
112 lines (111 loc) · 5.27 KB
/
README.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
!**********************************************************************
! Legal notice: UHYPER_Shrimali_Lefevre_Lopez-Pamies.for (Windows)
!
! Copyright (C) 2018 Bhavesh Shrimali ([email protected])
! 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
! non-Gaussian elastomers weakened by an isotropic and non-percolative
! distribution of equiaxed pores. 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 compressible USER hyperelastic
! model with 5 material properties, e.g.,
! *HYPERELASTIC, USER, TYPE=COMPRESSIBLE, PROPERTIES=5
! in the input (.inp) file.
!
! The 5 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
! AF0 = PROPS(5) ! INITIAL POROSITY
!
! 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 initial porosity (AF0) must satisfy 0 <= AF0 <= 1.
!
! As expected from physical considerations, this macroscopic energy
! remains finite so long the determinant of the deformation
! gradient (AJ) satisfies the condition AJ - 1 + AF0 > 0. This
! inequality constraint is enforced through a MOREAU-YOSIDA
! regularization (see, e.g. [3]). The underlying weight (ANU) is set
! here by default to ANU = 1.0e15. The subroutine issues two kinds
! of messages regarding the constraint:
! -- a WARNING message when AJ - 1 + AF0 < 1e-9 which allows the job
! to carry on
! -- an ERROR message when AJ - 1 + AF0 < -0.01 and TERMINATES the job
! In both cases, please treat the results with caution and check that
! the current local porosity given by (AJ - 1 + AF0) / AJ
! remains positive; see below on how to request it.
!
! The porosity in the deformed configuration (AJ - 1 + AF0) / AJ
! is required to be output (to check the results for instance,
! see above) as a solution-dependent state variable (SDV), e.g.,
! using the following lines in the input (.inp) file:
! *DEPVAR
! 1
! 1, Porosity, Current local porosity
! The solution-dependent state variable may be initialized using the
! following lines in the input (.inp) file:
! *INITIAL CONDITIONS, TYPE=SOLUTION
! <some element set>, AF0
!
!**********************************************************************
! Additional information:
!
! This subroutine creates a solution-dependent state variable for
! for the current porosity (see above) but does not create predefined
! field variables.
!
! Examples can be found in the article posted in the SIMULIA Learning
! Community: https://r1132100503382-eu1-3dswym.3dexperience.3ds.com/#community:39/post:mRdxC3xkRzajJ6LVk0SgwA
!
! Please consult the ABAQUS Documentation for additional references
! regarding the use of compressible USER hyperelastic models with
! the UHYPER subroutine and the use of solution-dependent
! state variables.
!
! Due the near-incompressible nature of this model at low porosities,
! the use of hybrid elements is recommended.
!
!**********************************************************************
! References:
!
! [1] Shrimali, B., Lefèvre, V., Lopez-Pamies, O. 2019. A simple
! explicit homogenization solution for the macroscopic elastic
! response of isotropic porous elastomers. J. Mech. Phys. Solids
! 122, 364--380.
! [2] Lopez-Pamies, O., 2010. A new I1-based hyperelastic model for
! rubber elastic materials. C. R. Mec. 338, 3--11.
! [3] Parikh, N., Boyd, S., 2013. Proximal algorithms. Found. Trends
! Optim. 1, 123--231.
!
!**********************************************************************