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

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(a) Surfacel isthe master and (b) Surface 1 k the slave and surface 2 is the slave sutiace 2 is the master TFII-6348-20-O Figure 5.1. Schematic showing the effect of changing the master-slave designation between two surfaces. wouldbe to check every slave node against every master surface at every time step. This, however, is inefficient. The current strategy is to use a global search to determine which slave nodes are in close proximity to a master surface. The search process accumulates these potential interactions by constructing a local neighborhood around the nmster surface and globally searching for all slave nodes that fall within the neighborhood. The algorithm is based on a particle search technique, Heinstein et al., 1993. It sorts the slave nodes by location and uses a binary search to construct a list of slave nodes in a master surface neighborhood. The search algorithm depends only on the number of slave nodes and not on the geometry of the problem. It takes advantage of the known positions of the slave nodes and master surfaces. After gathering a list of potential interactions, a detailed contact check is done for each slave-nodehna.ster surface ptir. This check determines: (1) which of the candidate master surfaces is in contact with the slave node, (2) the point of contact. (3) the amount of penetration,and (4) the direction the slave node should be pushed back. The contact check also tries to resolve pushback ambiguities that arise due to discretization of the master surface. A complete discussion of these ambiguities and their resolution can be found in Heinstein et al., 1993. The benefits of reducing the time spent in the contact surface algorithms can be significant. For iterative solvers, such as dynamic relaxation, inaccuracies in the location phase lead to an increase in the number of iterations required for convergence. These inaccuracies arise mainly fkom incorrectly determining the location of contact as a slave node slides across another surface. For large finite element simulations with large numbers of slave nodes and master surfaces, as much ~as50°A of the total CPU time ii spent in the Ioeation phase. Thus, the speed ,and efficiency of the contact detection algorithms are important. 80
5.2 Application Phase The operation of the master-slave scheme can be demonstrated in the following example where slave node I lies between master nodes M and N, as shown in Figure 5.2.1. The location phase algorithm has already determined that node I has penetrated the master surface segment connecting nodes M and N. Because node I has penetrated the master surface, the normal force (Rn) and tangential force (Rt) at node I me determined. me coefficient of friction> ~, is used in conjunction with Rn to determine the threshold valuefor slip, @n. If Rt is less than @n,, then no sliP occurs and both the values of Rn and Rt are transferred to the master swface nodes using a weighting Procedure based on the position of the slave node along the master segment. TRI-S348-21-O Figure 5.2.1. Schematic showing the penetration of the master surface by slave node I. Node I is cinematically restored to the master surface, and its nodal forces are transfemed to the master surface nodes M and N. 81
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SANDIA REPORT SAND90-0543 l UC-721
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SAND90-0543 Unlimited Release Print
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CONTENTS 1.0 IN~ODUCTION . . . . .
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Figures 2.1.1 2.2.1 2.2.2 3.1.1 3.7
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1.0 INTRODUCTION SANTOS is a finite
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2.0 GOVERNING EQUATIONS In this cha
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Using the left decomposition of Equ
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1.5 1.0 0.5 a 0.0 i% \ +7797 / \ &
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3.0 NUMERICAL FORMULATION In this c
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m’ I 2$=2 y 4 L x I 1 2 1- 1 I I
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Consequently, the gradient operator
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We are now faced with a three-dimen
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We now see that the internal force
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‘t+At = QAt % (3.3.2) For a const
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If the strain increments are insign
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The mean coordinates Z, correspond
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for arbitrary Ui]. Using Equation (
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TRI-6348-6-O Figure 3.7.1. A model
Page 37 and 38: 3.8 Convergence Measures When an it
Page 39 and 40: 4.0 CONSTITUTIVE MODELS One of the
Page 41 and 42: where y is a column vector containi
Page 43 and 44: ~=~y —=Kdkk (4.3.3) where K is th
Page 45 and 46: Q TRI-6348-7-O Figure 4.5.1. Yield
Page 47 and 48: @r=R . (4.5.16) Because S is deviat
Page 49 and 50: and (4.5.27) Combining Equations (4
Page 51 and 52: TRI-6348-1o-o Figure 4.5.4. Effect
Page 53 and 54: The subscripts n and n+ 1 refer to
Page 55 and 56: The elastic plastic material model
Page 57 and 58: (a) a. P, Compression (b) 16 a. ‘
Page 59 and 60: The mean volumetric strain is updat
Page 61 and 62: ~=$s:s . (4.6.9) J The yield condit
Page 63 and 64: 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
Page 69 and 70: law secondary creep model is reques
Page 71 and 72: PROP(3) - Modulus function identifi
Page 73 and 74: where K @ () n+l is the O;:l =3K @n
Page 75 and 76: 2 11 F=exp-1-~ 6 for q>&; . (4.12.8
Page 77 and 78: Accuracy of the method is assured i
Page 79 and 80: The volumetric part of the model ca
Page 81 and 82: for the bulk response, where G(t) a
Page 83 and 84: then G(t,@) = G(g) . (4.14.9) This
Page 85 and 86: PROP(7) - Third Short Time Shear Mo
Page 87: 5.0 CONTACT SURFACES Many structure
Page 91 and 92: 6.0 LOADS AND BOUNDARY CONDITIONS S
Page 93 and 94: 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
Page 99 and 100: Schreyer,H.L., R.F. Kulak, and J.M.
Page 101 and 102: APPENDIX A: SANTOS Users Manual A-1
Page 103 and 104: SANTOS Users Manual Listed below, i
Page 105 and 106: tol ... tolerance value used for co
Page 107 and 108: See the theory section for definiti
Page 109 and 110: omega ... specified angular velocit
Page 111 and 112: dence of the pressure scale factor
Page 113 and 114: TWO MU(2P) BULK MODULUS (K) AO Al A
Page 115 and 116: RN3 (exponent of workhardening and
Page 117 and 118: APPENDIX B: User Subroutines B-1 ,.
Page 119 and 120: ‘ser Subroutines SANTOS allows th
Page 121 and 122: 600 CONTINUE END IF 1000 CONTINUE R
Page 123 and 124: APPENDIX C: Printed Output Descript
Page 125 and 126: Printed Output Description The SANT
Page 127 and 128: FUNCTION DEFI NIT IONS FUNCTION ID
Page 129 and 130: 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
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To obtain a solution to the gravity
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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
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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
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WIPP UC721 - DISTRIBUTIONLIST SAND9
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Sue B. Clark University of Georgia
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Mr. Steven Crouch GeoLogic Research
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[: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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