#############################################################
# This illustrates the classical Hertz contact problem of a
# rigid cylinder indenting an elastic half-space. The
# governing equation is linear elasticity and the constitutive
# law is a simple compressible linear isotropic function
# requiring a Young's modulus (E) and Poisson's ratio (v).
# The half-space is trilinear and the cylinder is bicubic-linear.
# Even though the problem is linear, the addition of contact makes
# the problem non-linear requiring a Newton-Raphson solution approach.
#############################################################
# Define parameters, regions, coordinate system and bases
fem def para;r;hertz;example
fem def region;r;two;example
fem def coord 3,1
fem def bases;r;collapsed;example
# Read in half-space described by trilinear elements
fem def nodes;r;half;example reg 1
fem def elem;r;half;example reg 1
# Refine half-space with dense mesh in region of contact
fem refine xi 1 element 101 ntimes 2 reg 1
fem refine xi 1 element 101,103 ntimes 2 reg 1
fem refine xi 1 element 101,107,105,108 ntimes 1 reg 1
fem refine xi 1 element 101,107,111,112 ntimes 1 reg 1
fem refine xi 3 ntimes 3 reg 1
# Define fibre directions
fem def fibre;r;half;example reg 1
fem def elem;r;half;example fibre reg 1
# Read in rigid cylinder described by bicubic-linear elements
fem def nodes;r;cylinder;example reg 2
fem def elem;r;cylinder;example reg 2
# Update derivatives and scale-factors
fem up node deriv 1 linear reg 2
fem up node deriv 2 linear reg 2
fem up node deriv 3 linear reg 2
fem up scale_factors normalise reg 2
# Align cylinder for contact
fem change nodes rotate by -90 reg 2
fem change nodes translate by -2,2,0 reg 2
# Define fibre directions
fem def fibre;r;cylinder;example reg 2
fem def elem;r;cylinder;example fibre reg 2
## Export cylinder (master surface)
#fem export nodes;cylinder as cylinder reg 2
#fem export elem;cylinder as cylinder reg 2
# Node groups for fixed boundary conditions
fem group nodes 101,305,221,301,179,297,217,293,107,103,303,219,299,177,295,215,291,105 as fixedx reg 1
fem group nodes 105,161,145,169,129,165,149,173,121,153,133,157,113,137,125,141,109,117,106 as fixedy1 reg 1
fem group nodes 107,162,146,170,130,166,150,174,122,154,134,158,114,138,126,142,110,118,108 as fixedy2 reg 1
fem group nodes 101..442 as fixedz reg 1
fem group nodes 1..20 as cylinderfixedz reg 2
fem group nodes 1..20 as cylinderfixedy reg 2
fem group nodes 1..20 as cylinderfixedx reg 2
# Define equations
fem def equa;r;half;example reg 1
fem def equa;r;cylinder;example reg 2
# Define material properties
fem def mat;r;half;example reg 1
fem def mat;r;cylinder;example reg 2
# Define initial fixed boundary conditions
fem def init;r;half;example reg 1
fem def init;r;cylinder;example reg 2
# Move cylinder through prescribed displacement
fem change nodes translate by 0,-0.02,0 nodes cylinderfixedy reg 2
# define contact parameters
fem def contact;r;contact;example
# Define solve for problem reg 1
fem def solve;r;half;example reg 1
$j=0;
$CONVERGED=0;
while ($CONVERGED==0)
{
$j++;
######################################Projection
# Set contact xi points on specified faces (8x8)
fem def xi;c contact_points faces 381,575,531,593,479,584,548 points 8 reg 1
# Define data at xi positions
fem def data;c from_xi reg 1
# Update slave info
fem update data field to slave
# Project onto target face
fem def xi;c closest_face faces 623 region 2
# Store projection gap in data fields
fem update data field from gap region 2
# Update master info
fem update data field to master
# Place initial geometry YP(ny,3) into XP
if ($j>1)
{
FEM up geom from sol YP_index 3 to 1..3 reg 1
}
#####################################Mechanics problem
# Solve contact problem
fem solve error 0.01 iterate 5 reg 1
FEM up geom from sol to 1..3 reg 1
}
# Place initial geometry YP(ny,3) into XP
FEM up geom from sol YP_index 3 to 1..3 reg 1
# Only need displacements for stresses
fem update solution geometry subtract reg 1
# Fit stresses at Gauss points to nodal fields
fem def field;r;half;example
fem def elem;r;half;example field
fem up gauss stress ref
fem de fit;r;half;example gauss
fem fit
## Export undeformed slave with stresses
#fem export nodes;half as half reg 1
#fem export elem;half as half reg 1
# Add undeformed geometry to displacements
fem update solution geometry add reg 1
# Update XP from YP
FEM up geom from sol to 1..3 reg 1
## Export deformed slave
#fem export nodes;half_def as half_def reg 1 offset 1000
#fem export elem;half_def as half_def reg 1 offset_elem 1000
## Export deformed master
#fem export nodes;cylinder_def as cylinder_def reg 2 offset 2000
#fem export elem;cylinder_def as cylinder_def reg 2 offset_elem 2000
