mohr.c

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/*
%M This modules contains the MOHR COULOMB material sub-class methods and 
   definitions
%a Joao Luiz Elias Campos.
%d September 2nd, 1998.
%r $Id: mohr.c,v 1.1 2004/06/22 05:29:59 joaoluiz Exp $
%w (C) COPYRIGHT 1995-1996, Eduardo Nobre Lages.
   (C) COPYRIGHT 1997-1999, Joao Luiz Elias Campos.
   All Rights Reserved
   Duplication of this program or any part thereof without the express
   written consent of the author is prohibited.

   Modificacao: 28/04/2005    Alexandre A. Del Savio
     Foram substituídas todas as alocações dinâmicas feitas com malloc 
     por calloc.

*/

/*
** ------------------------------------------------------------------------
** Global variables and symbols:
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include "load.h"
#include "elm.h"
#include "material.h"
#include "node.h"
#include "rio.h"


/* Parent methods
 */
void MaterialTimeStep( sMaterial *, double * );
void MaterialDensity ( sMaterial *, double * );


/*
** ------------------------------------------------------------------------
** Local variables and symbols:
*/

/*
%T MOHR COULOMB material data definition
*/
typedef struct _mohrdata
{
 double E;             /* Young modulos       */
 double Nu;            /* Poisson coefficient */
 double C;             /* Coesion value       */
 double Phi;           /* Friction angle      */
} sMohrData;

#ifndef PI
#define PI 3.141592654
#endif

#ifndef THETA_MIN
#define THETA_MIN   0.5
#endif

#ifndef THETA_MAX
#define THETA_MAX   59.5
#endif

#ifndef ANM_TOL
#define ANM_TOL  1.0e-12
#endif
/*
** ------------------------------------------------------------------------
** Local functions:
*/


/*
** ------------------------------------------------------------------------
** Subclass methods:
*/
static void MohrCoulombNew         ( int, sMaterial ** );
static void MohrCoulombFree        ( sMaterial * );
static void MohrCoulombRead        ( sMaterial * );
static void MohrCoulombEParameter  ( sMaterial *, double * );
static void MohrCoulombNuParameter ( sMaterial *, double * );
static void MohrCoulombCMatrix     ( sMaterial *, double [6][6] );
static void MohrCoulombUpdateStress( sMaterial *, double, double *, double *, 
                                                  double *, double * );


/*
%F This method allocates memory for a MOHR COULOMB material and fills its 
   data with the specific values.
%i Material label (number)
%o Material descriptor.
*/
static void MohrCoulombNew( int label, sMaterial **mat )
{
 sMohrData *data = 0L;

/* Get memory for the material descriptor
 */
 (*mat) = (sMaterial *)calloc(1, sizeof(sMaterial));

/* Get memory for the MOHR COULOMB material data
 */
 data = (sMohrData *)calloc(1, sizeof(sMohrData));

/* Fill MOHR COULOMB material data
 */
 data->E   = 0.0;
 data->Nu  = 0.0;
 data->C   = 0.0;
 data->Phi = 0.0;

/* Fill material descriptor
 */
 (*mat)->type  = MOHR_COULOMB;
 (*mat)->label = label;
 (*mat)->Gamma = 0.0;
 (*mat)->data  = (void *)data;

/* Add to the material list
 */
 MatList[label-1] = (*mat);

} /* End of MohrCoulombNew */


/*
%F This method frees the MOHR COULOMB material data for a given material.
%i Material descriptor.
*/
static void MohrCoulombFree( sMaterial *mat )
{
 sMohrData *data = 0L;

/* Get MOHR COULOMB material data
 */
 data = (sMohrData *)mat->data;

/* Release allocated memory
 */
 free( data );

/* Reset material data
 */
 mat->data = 0L;

} /* End of MohrCoulombFree */


/*
%F This method reads the MOHR COULOMB material information.
%i Material descriptor.
*/
static void MohrCoulombRead( sMaterial *mat )
{
 sMohrData *data = 0L;
 double     c, nu, e, phi;

/* Get the material data
 */
 data = (sMohrData *)mat->data;

/* Read the material parameters
 */
 fscanf( nf, "%lf %lf %lf %lf", &e, &nu, &c, &phi );

/* Fill material information
 */
 data->E   = e;
 data->Nu  = nu;
 data->C   = c;
 data->Phi = phi;

} /* End of MohrCoulombRead */

/*
%F
*/
static void MohrCoulombEParameter( sMaterial *mat, double *e )
{
 sMohrData *data = 0L;

/* Get material descriptor
 */
 data = (sMohrData *)mat->data;

/* Get Young modules parameters
 */
 (*e) = data->E;

} /* End of MohrCoulombEParameter */


/*
%F 
*/ 
static void MohrCoulombNuParameter( sMaterial *mat, double *nu )
{
 sMohrData *data = 0L;

/* Get material descriptor
 */
 data = (sMohrData *)mat->data;

/* Get Poisson coefficient parameters
 */
 (*nu) = data->Nu;

} /* End of MohrCoulombNuParameter */


/*
%F This function computes the material constitutive matrix
*/
static void MohrCoulombCMatrix( sMaterial *mat, double cm[6][6] )
{
 int        i, j;
 sMohrData *data = 0L;
 double     e, nu;

/* Intialize matrix
 */
 for( i = 0; i < 6; i++ )
  for( j = 0; j < 6; j++ )
   cm[i][j] = 0.0;

/* Get material descriptor
 */ 
 data = (sMohrData *)mat->data;

/* Get element parameters
 */
 e  = data->E;
 nu = data->Nu;

/* Compute matrix elements
 */
 if( NDof == 3 )
 {
  cm[0][0] =
  cm[1][1] =
  cm[2][2] =  e*(nu*nu-1.0) / (nu*(nu+nu*nu)+nu*(nu*nu+nu)+nu*nu-1.0);
  cm[1][0] =
  cm[2][0] =
  cm[0][1] =
  cm[2][1] =
  cm[0][2] =
  cm[1][2] = -e*(nu*nu+nu) / (nu*(nu+nu*nu)+nu*(nu*nu+nu)+nu*nu-1.0);
  cm[3][3] =
  cm[4][4] =
  cm[5][5] = (e * e) / (e + e * (1.0 + 2.0 * nu));
 }
 else
 {
  cm[0][0] = cm[1][1] = (e * (1.0 - nu)) / ((1.0 + nu) * (1.0 - (2.0 * nu)));
  cm[0][1] = cm[1][0] = (e * nu) / ((1.0 + nu) * (1.0 - (2.0 * nu)));
  cm[2][2] = e / (2.0 * (1.0 + nu));
 }

} /* End of MohrCoulombCMatrix */


/*
%F
*/
static void MohrCoulombUpdateStress( sMaterial *mat, double dtime,
                                                     double *yield,
                                                     double *effdef, 
                                                     double *str,
                                                     double *def )
{
 sMohrData *data = 0L;
 double     sig1, sig3, sig2;
 double     c, phi, pf, mult, aldp, ni;
 double     cm[6][6];
 double     sigaux;
 double     num, den;

/* Get material data
 */
 data = (sMohrData *)mat->data;

/* Get material contitutive matrix
 */
 MohrCoulombCMatrix( mat, cm );
 
/* Get material poisson coef.
 */
 MohrCoulombNuParameter( mat, &ni );

/* Get material plastic properties
 */ 
 c   = data->C;
 phi = data->Phi;

/* Computes the principal stresses (Sigma 1 and Sigma 3)
 */
 sigaux = ((str[0] + str[1]) / 2.0) -
        sqrt( (str[0] - str[1])*(str[0] - str[1])/4.0 + str[2] * str[2] );
 sig3 = ((str[0] + str[1]) / 2.0) +
        sqrt( (str[0] - str[1])*(str[0] - str[1])/4.0 + str[2] * str[2] );
        
 if(sigaux <= sig3){
  sig1 = sigaux;
 }
 else{
  sig1 = sig3;
  sig3 = sigaux;
 }        
        
 sig2 = ni * (sig1 + sig3);

/* Computes the angle
 */
 phi *= PI / 180.0;
 phi  = (1.0 + sin(phi)) / (1.0 - sin(phi));

/* Compute plastic function
 */
 (*yield) = pf = sig1 - (sig3 * phi) + (2.0 * c * sqrt(phi));

/* Correct the stress if necessery
 */
 if( pf <= 0.0 )
 {
  if( sig1 == str[0]) aldp = 0.0;
  else                aldp = atan2( (sig1 - str[0]), str[2] );

  mult = pf / (-cm[0][0] * (1.0 + (phi*phi)) + (2.0 * phi * cm[0][1]));

  sig1 += mult * (cm[0][0] - (cm[0][1] * phi));
  sig3 += mult * (cm[0][1] - (cm[0][0] * phi));
  sig2 += mult * cm[0][0] * (1.0 - phi);

  str[0] = ((sig1 + sig3) / 2.0) + ((sig1-sig3) * cos(2.0 * aldp) / 2.0);
  str[1] = ((sig1 + sig3) / 2.0) - ((sig1-sig3) * cos(2.0 * aldp) / 2.0);
  str[2] = ((sig1 - sig3) * (sin(2.0 * aldp))) / 2.0;
  str[3] = sig2; 
 }
 
 num = fabs(2.0 * c * sqrt(phi));
 den = fabs(sig1 - sig3 * phi);
 
 if(num <= den){         
  str[4] = ( num / den );
 }
 else{
  str[4] = ( den / num );
 }
 
 if(str[4] > 1.0) (str[4] = 1.0);
 
} /* End of MohrCoulombUpdateStress */


/*
** ------------------------------------------------------------------------
** Public functions:
*/

/*
%F This function initializes the sub-class "MOHR COULOMB".
*/
void MohrCoulombInit( void );
void MohrCoulombInit( void )
{
/* Initialize MOHR COULOMB material sub-class
 */
 MatClass[MOHR_COULOMB].new       = MohrCoulombNew;
 MatClass[MOHR_COULOMB].free      = MohrCoulombFree;
 MatClass[MOHR_COULOMB].read      = MohrCoulombRead;
 MatClass[MOHR_COULOMB].epar      = MohrCoulombEParameter;
 MatClass[MOHR_COULOMB].nupar     = MohrCoulombNuParameter;
 MatClass[MOHR_COULOMB].cmatrix   = MohrCoulombCMatrix;
 MatClass[MOHR_COULOMB].updatestr = MohrCoulombUpdateStress;
 MatClass[MOHR_COULOMB].updatepar = 0L;
 MatClass[MOHR_COULOMB].timestep  = MaterialTimeStep;
 MatClass[MOHR_COULOMB].density   = MaterialDensity;
 MatClass[MOHR_COULOMB].vstrain   = 0L;

} /* End of MohrCoulombInit */


/* =======================================================  End of File  */

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