II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy

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Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831 Prices available from (615) 576-8401, FTS 626-8401 Available to the public from National Technical Information Service U.S. Department of Commerce 5285 Port Royal Rd Springfield, VA 22161 NTIS price codes Printed copy: A08 Microfiche copy: AO1
SAND90-0543 Unlimited Release Printed July 1997 Distribution Category UC-721 SANTOS—A Two-Dimensional Finite Element Program for the Quasistatic, Large Deformation, Inelastic Response of Solids Charles M. Stone Engineering and Manufacturing Mechanics Department Sandia National Laboratories P.O. Box 5800 Albuquerque, NM 87185-0443 ABSTRACT SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived from the transient dynamic code PRONTO 2D. The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided.
Page 1: SANDIA REPORT SAND90-0543 l UC-721
Page 5 and 6: CONTENTS 1.0 IN~ODUCTION . . . . .
Page 7 and 8: Figures 2.1.1 2.2.1 2.2.2 3.1.1 3.7
Page 9 and 10: 1.0 INTRODUCTION SANTOS is a finite
Page 11 and 12: 2.0 GOVERNING EQUATIONS In this cha
Page 13 and 14: Using the left decomposition of Equ
Page 15 and 16: 1.5 1.0 0.5 a 0.0 i% \ +7797 / \ &
Page 17 and 18: 3.0 NUMERICAL FORMULATION In this c
Page 19 and 20: m’ I 2$=2 y 4 L x I 1 2 1- 1 I I
Page 21 and 22: Consequently, the gradient operator
Page 23 and 24: We are now faced with a three-dimen
Page 25 and 26: We now see that the internal force
Page 27 and 28: ‘t+At = QAt % (3.3.2) For a const
Page 29 and 30: If the strain increments are insign
Page 31 and 32: The mean coordinates Z, correspond
Page 33 and 34: for arbitrary Ui]. Using Equation (
Page 35 and 36: TRI-6348-6-O Figure 3.7.1. A model
Page 37 and 38: 3.8 Convergence Measures When an it
Page 39 and 40: 4.0 CONSTITUTIVE MODELS One of the
Page 41 and 42: where y is a column vector containi
Page 43 and 44: ~=~y —=Kdkk (4.3.3) where K is th
Page 45 and 46: Q TRI-6348-7-O Figure 4.5.1. Yield
Page 47 and 48: @r=R . (4.5.16) Because S is deviat
Page 49 and 50: and (4.5.27) Combining Equations (4
Page 51 and 52: TRI-6348-1o-o Figure 4.5.4. Effect
Page 53 and 54:
The subscripts n and n+ 1 refer to
Page 55 and 56:
The elastic plastic material model
Page 57 and 58:
(a) a. P, Compression (b) 16 a. ‘
Page 59 and 60:
The mean volumetric strain is updat
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~=$s:s . (4.6.9) J The yield condit
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in Section 4.6, use such decomposit
Page 65 and 66:
not amenable to vectorization. Vect
Page 67 and 68:
We make use of the following identi
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law secondary creep model is reques
Page 71 and 72:
PROP(3) - Modulus function identifi
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where K @ () n+l is the O;:l =3K @n
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2 11 F=exp-1-~ 6 for q>&; . (4.12.8
Page 77 and 78:
Accuracy of the method is assured i
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The volumetric part of the model ca
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for the bulk response, where G(t) a
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then G(t,@) = G(g) . (4.14.9) This
Page 85 and 86:
PROP(7) - Third Short Time Shear Mo
Page 87 and 88:
5.0 CONTACT SURFACES Many structure
Page 89 and 90:
5.2 Application Phase The operation
Page 91 and 92:
6.0 LOADS AND BOUNDARY CONDITIONS S
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TRI-6348-43-O Figure 6.2.1. Definit
Page 95 and 96:
diagonal mass matrix routines with
Page 97 and 98:
Biffle, J. H., and M.L. Blanford. 1
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Schreyer,H.L., R.F. Kulak, and J.M.
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APPENDIX A: SANTOS Users Manual A-1
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SANTOS Users Manual Listed below, i
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tol ... tolerance value used for co
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See the theory section for definiti
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omega ... specified angular velocit
Page 111 and 112:
dence of the pressure scale factor
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TWO MU(2P) BULK MODULUS (K) AO Al A
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RN3 (exponent of workhardening and
Page 117 and 118:
APPENDIX B: User Subroutines B-1 ,.
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‘ser Subroutines SANTOS allows th
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600 CONTINUE END IF 1000 CONTINUE R
Page 123 and 124:
APPENDIX C: Printed Output Descript
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Printed Output Description The SANT
Page 127 and 128:
FUNCTION DEFI NIT IONS FUNCTION ID
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1 SANTOS, VERSION SANTOS 2.0 ,RUN O
Page 131 and 132:
APPENDIX D: Adding a New Constituti
Page 133 and 134:
Adding A New Constitutive Model to
Page 135 and 136:
APPENDIX E: Verification and Sample
Page 137 and 138:
Verification and Sample Problems Sa
Page 139 and 140:
To obtain a solution to the gravity
Page 141 and 142:
Figure E-5. Deformed Shape of the B
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P= () 4:(1-V) 1-: pc3 +2(1-m)lllpc
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L < 1 t i I I t I , I 1 3 3 1 1 I i
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Side Set ID for the Rigid Surface C
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TITLE UPSETTING OF A CYLINDRICAL BI
Page 151 and 152:
Table 1: M-D Argillaceous Salt Cree
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4.0 3.5 3.0 1.0 0.5 0.0 I I I 1 1 1
Page 155 and 156:
WIPP UC721 - DISTRIBUTIONLIST SAND9
Page 157 and 158:
Sue B. Clark University of Georgia
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Mr. Steven Crouch GeoLogic Research
Page 161:
[:1 . 1 .i i- ) r
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II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy

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