Example 714: Material parameter estimation: c1 with 1 load set. 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 first created by solving a boundary value problem (specified displacements). The parameter estimation here uses a linear least-squares approach to miminimise the force residuals. The parameter estimated is the c1 Mooney-Rivlin param for each of the 4 nodes.

The comfile run by this example is as follows:

#Material parameter fitting by least squares (fit c1 parameter)
#A one element membrane is solved for one loading condition
#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 de opt;r;test;example       #1 param only in fit
fem eval resid with 1,1,1,1     #this is correct c1, so get 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 matl 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 fit          #least squares fit of material params to nodal residuals

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

Files used by this example are:

Name             Modified     Size

example_714.com  10-Apr-2000  1.7k
coord1.ipnode    10-Apr-2000  993 
force1.ipnode    10-Apr-2000  985 
notes.txt        10-Apr-2000  802 
test.ipbase      10-Apr-2000  1.1k
test.ipdata      10-Apr-2000  1.2k
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_714.tar.gz  17-Aug-2010  6.7k

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

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