Example 715: Material parameter estimation: c1 & c2 with 2 load sets. 1 elem.

Mooney-Rivlin material parameters are estimated for an isotropic, homogeneous one element square rubber membrane undergoing biaxial stretch. The deformed geometry and force files are consistent with the material params read in. The parameter estimation here uses a linear least-squares approach to miminimise the force residuals.

The comfile run by this example is as follows:

#Material parameter fitting by least squares (fit c1 & c2 parameters)
#A one element membrane is solved for two loading conditions
#The deformed coords and corresponding forces are written to files
#These files are then read in as data for the parameter estimation.

fem de node;r;test;example      #4 nodes
fem de base;r;;example          #bilinear
fem de elem;r;;example          #1 element
fem de fibr;d
fem de elem;d fibre
fem de wind
fem dr line

fem de equa;r;;example          #finite elasticity membrane
fem de mate;r;;example          #Mooney-Rivlin c1=1, c2=0.2 both node based
fem de init;r;;example          #nodes 1,3 x_displ=0; nodes 1,2 y_displ=0
#                               !node 4 x_displ=0.1 y_disp=0.2
fem de solv;r;;example

fem solve step 1                
fem li node sol
fem dr line def rgb=blue 
fem de node;w;coord1 dep 1 nc 1 #write deformed coords to coord1.ipnode
fem de node;w;force1 dep 4 nc 1 #write reaction forces to force1.ipnode

fem solve step 1               
fem li node sol
fem dr line def rgb=blue 
fem de node;w;coord2 dep 1 nc 1 #write deformed coords to coord2.ipnode
fem de node;w;force2 dep 4 nc 1 #write boundary forces to force2.ipnode

fem de opt;r;test;example       #1 param only in fit
fem eval resid with 1,1,1,1,0.2,0.2,0.2,0.2 #correct values, so resids=0
#fem eval resid num_deriv       !gives RESJAC matrix (#resids x #params)

fem de field;r;test;example     #setup field variable for material param fit
fem de elem;r;example field

fem de fit;r;example material resid #define fit for material params to residuals
fem de node;r;coord1 dep 11 nc 1    #read in deformed coords to YP(ny,1)
fem de node;r;force1 dep 11 nc 2    #read in nodal forces to YP(ny+NYT,1)
fem de node;r;coord2 dep 12 nc 1    #read in deformed coords to YP(ny,2)
fem de node;r;force2 dep 12 nc 2    #read in nodal forces to YP(ny+NYT,2)

fem fit      #least-squares fit of material params to nodal residuals

fem list mate using solve #list original material parameters  (c1=1,c2=0.2)
fem list mate using fit   #list fitted material parameters (c1,c2 at 4 nodes)
fem

Files used by this example are:

Name             Modified     Size

example_715.com  10-Apr-2000  2.0k
coord1.ipnode    10-Apr-2000  993 
coord2.ipnode    10-Apr-2000  993 
force1.ipnode    10-Apr-2000  985 
force2.ipnode    10-Apr-2000  985 
test.ipbase      10-Apr-2000  1.1k
test.ipelem      10-Apr-2000  336 
test.ipelfd      10-Apr-2000  282 
test.ipequa      02-May-2004  2.2k
test.ipfiel      10-Apr-2000  968 
test.ipfit       13-Apr-2007  1.4k
test.ipinit      10-Apr-2000  1.1k
test.ipmate      10-Apr-2000  2.4k
test.ipnode      10-Apr-2000  837 
test.ipopti      16-Sep-2001  1.2k
test.ipsolv      16-Aug-2010  2.3k
test.ipsolv.old  13-Apr-2007  2.1k

Download the entire example:

Name                      Modified     Size

examples_7_71_715.tar.gz  17-Aug-2010  6.5k

Html last generated: Sun Mar 6 05:50:30 2016

Input last modified: Mon Aug 16 11:21:48 2010