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

More documents

Recommendations

Info

all the elements, e, connected to node i. This error measure is satisfied when each component of the force vector satisfies the criterion. 30
4.0 CONSTITUTIVE MODELS One of the primary reasons for developing SANTOS was to take advantage of the many state-of-the-art features available in PRONTO and adapt them to quasistatic mechanics problems. One of those features is the flexible material model interface which allows a constitutive model to be added to the code with minimal effort. The constitutive developer does not have to be familiar with the internal workings of SANTOS but only needs to modify a few well documented subroutines to add a new material model. The material model implementation requires the user to provide entries in a few data statements to define the limits of the internal data structure. The code also requires the constitutive developer to provide estimates of the initial dilatationrd and shear moduli so that the program can compute an initial stable time step. The material model may contain internal state variables that define the state or evolution of the material. The implementation requires that the developer provide names and any required initialization for the internal state variables. The internal state variable names for each material currently implemented are provided in the User Guide section. These quantities may be individually selected for output to the plotting data base. The final changes to the material model subroutines require the developer to provide names for any necessary input quantities such as Young’s modulus or Poisson’s ratio. The input names for the material models currently implemented are given in the User Guide section. The code currently contains twelve continuum material models with more models being developed as our applications require them. The models range from purely elastic behavior to time-dependent viscoplastic response. SANTOS utilizes an indirect solution technique which can require hundreds of thousands of calls to the constitutive model during a complex analysis. Thus, efficient implementation of the constitutive model is a primary concern. Considerable effort has gone into writing each material model subroutine such that the routine vectorizes on a vector supercomputer. The material model routine is written in terms of the unrotated Cauchy stress, o, and the deformation rate in the unrotated configuration, d. The basic assumption is that the deformation or strain rate is constant over the step. The deformation rate that is available to the constitutive subroutine is the mechanical strain rate, i.e., any thermal strain rate contribution to the total strain rate has already been removed. During each iteration, the latest kinematic quantities are used to update the stress. Stresses written to the plotting data base are rotated to the current configuration. 4.1 Integration of the Rate Equations The constitutive models are written in a rate form and must be integrated forward at each time step. In - SANTOS, a forward Euler or a backward Euler integration of the rate equations, is used for many of the constitutive models. The forward Euler integration assumes that f ‘+* =fn +f(fn)At (4.1.1) where f is the quantity to be integrated, n refers to the current step for which values off are available and n+ 1 refers to the next step for which values off are being sought. The quantity f is defined using the known quantities at step n, and At is the time step increment. l%e forward Euler scheme is simple and computationally efilcient but is conditionally stable. The time step size allowed is controlled by a stability criterion that varies with each material model. 31
Page 1 and 2: SANDIA REPORT SAND90-0543 l UC-721
Page 3 and 4: SAND90-0543 Unlimited Release Print
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$=2 y 4 L x I 1 2 1- 1 I I
Page 21 and 22: Consequently, the gradient operator
Page 23 and 24: We are now faced with a three-dimen
Page 25 and 26: We now see that the internal force
Page 27 and 28: ‘t+At = QAt % (3.3.2) For a const
Page 29 and 30: If the strain increments are insign
Page 31 and 32: The mean coordinates Z, correspond
Page 33 and 34: for arbitrary Ui]. Using Equation (
Page 35 and 36: TRI-6348-6-O Figure 3.7.1. A model
Page 37: 3.8 Convergence Measures When an it
Page 41 and 42: where y is a column vector containi
Page 43 and 44: ~=~y —=Kdkk (4.3.3) where K is th
Page 45 and 46: Q TRI-6348-7-O Figure 4.5.1. Yield
Page 47 and 48: @r=R . (4.5.16) Because S is deviat
Page 49 and 50: and (4.5.27) Combining Equations (4
Page 51 and 52: TRI-6348-1o-o Figure 4.5.4. Effect
Page 53 and 54: The subscripts n and n+ 1 refer to
Page 55 and 56: The elastic plastic material model
Page 57 and 58: (a) a. P, Compression (b) 16 a. ‘
Page 59 and 60: The mean volumetric strain is updat
Page 61 and 62: ~=$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 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
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
Page 139 and 140:
To obtain a solution to the gravity
Page 141 and 142:
Figure E-5. Deformed Shape of the B
Page 143 and 144:
P= () 4:(1-V) 1-: pc3 +2(1-m)lllpc
Page 145 and 146:
L < 1 t i I I t I , I 1 3 3 1 1 I i
Page 147 and 148:
Side Set ID for the Rigid Surface C
Page 149 and 150:
TITLE UPSETTING OF A CYLINDRICAL BI
Page 151 and 152:
Table 1: M-D Argillaceous Salt Cree
Page 153 and 154:
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
Page 159 and 160:
Mr. Steven Crouch GeoLogic Research
Page 161:
[:1 . 1 .i i- ) r
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?