Modeling Pure Shear with Periodic BCs in Abaqus

[EJP17708]

I am trying to invoke a state of pure shear (no normal stress) on a simple 1x1 square modeled with 9 CPS4R elements but I cannot get the normal stresses to be 0. I also want to use periodic boundary conditions because eventually I will be simulating composite RUCs.

I have pasted my input deck below. Can anyone see the mistake I am making?

This is a very simple problem, but I cannot get it to work. I even tried removing the periodic BCs and applying edge displacements

u1=x2*u
u2=x1*u

but still the normal stresses are not zero.

Is it even possible to get pure shear with finite elements?

*Node, NSET=ALLNODES
1, 0.949999988, 0.0500000007, 0.
2, 0.616666675, 0.0500000007, 0.
3, 0.283333331, 0.0500000007, 0.
4, -0.0500000007, 0.0500000007, 0.
5, 0.949999988, -0.283333331, 0.
6, 0.616666675, -0.283333331, 0.
7, 0.283333331, -0.283333331, 0.
8, -0.0500000007, -0.283333331, 0.
9, 0.949999988, -0.616666675, 0.
10, 0.616666675, -0.616666675, 0.
11, 0.283333331, -0.616666675, 0.
12, -0.0500000007, -0.616666675, 0.
13, 0.949999988, -0.949999988, 0.
14, 0.616666675, -0.949999988, 0.
15, 0.283333331, -0.949999988, 0.
16, -0.0500000007, -0.949999988, 0.
*Element, type=CPS4R, ELSET=ALLELEMS
1, 1, 2, 6, 5
2, 2, 3, 7, 6
3, 3, 4, 8, 7
4, 5, 6, 10, 9
5, 6, 7, 11, 10
6, 7, 8, 12, 11
7, 9, 10, 14, 13
8, 10, 11, 15, 14
9, 11, 12, 16, 15
*Nset, nset=TOP_EDGE, generate
1, 4, 1
*Elset, elset=TOP_EDGE, generate
1, 3, 1
*Nset, nset=LEFT_EDGE, generate
4, 16, 4
*Elset, elset=LEFT_EDGE, generate
3, 9, 3
*Nset, nset=RIGHT_EDGE, generate
1, 13, 4
*Elset, elset=RIGHT_EDGE, generate
1, 7, 3
*Nset, nset=BOT_EDGE, generate
13, 16, 1
*Elset, elset=BOT_EDGE, generate
7, 9, 1
***********************
**Reference Nodes to apply displacements on Periodic BCs
*NODE, NSET=RefNodeTB
160, 0., 0., 0.
*NODE, NSET=RefNodeLR
161, 0., 0., 0.
***********************
*EQUATION
**Top/bottom contraints
**DOF2
3
16,2,1,4,2,-1,RefNodeTB,2,-1
3
15,2,1,3,2,-1,RefNodeTB,2,-1
3
14,2,1,2,2,-1,RefNodeTB,2,-1
3
13,2,1,1,2,-1,RefNodeTB,2,-1
**DOF1
**3
**16,1,1,4,1,-1,RefNodeTB,1,-1
3
15,1,1,3,1,-1,RefNodeTB,1,-1
3
14,1,1,2,1,-1,RefNodeTB,1,-1
3
13,1,1,1,1,-1,RefNodeTB,1,-1
**Left/right contraints
**DOF1
3
16,1,1,13,1,-1,RefNodeLR,1,-1
3
12,1,1,9,1,-1,RefNodeLR,1,-1
3
8,1,1,5,1,-1,RefNodeLR,1,-1
3
4,1,1,1,1,-1,RefNodeLR,1,-1
**DOF2
**3
**16,2,1,13,2,-1,RefNodeLR,2,-1
3
12,2,1,9,2,-1,RefNodeLR,2,-1
3
8,2,1,5,2,-1,RefNodeLR,2,-1
3
4,2,1,1,2,-1,RefNodeLR,2,-1
**
*NSET,NSET=PIN
**16
5
**
**PHYSICAL AND MATERIAL PROPERTIES
**
*SOLID SECTION, ELSET=ALLELEMS, MATERIAL=ISO
**
**
*MATERIAL, NAME=ISO
*ELASTIC, TYPE=ISOTROPIC
8.963E9,0.316
*DENSITY
1.57E3
*STEP, NLGEOM=YES, INC=1000000000000
**
*STATIC
0.01,1.,1E-12,0.01
**
*CONTROLS, PARAMETERS=TIME INCREMENTATION
3,4,5,8,5,,,15,
*CONTROLS, PARAMETERS=FIELD
5.0E-6,
**
*BOUNDARY
RefNodeTB,1,,0.1
RefNodeLR,2,,0.1
**RefNodeTB,2,,
**RefNodeLR,1,,
PIN,1,3
*OUTPUT, FIELD
*NODE OUTPUT
U,RF
*ELEMENT OUTPUT
S,LE
*ENDSTEP

 

[EJP17708]

Nevermind, if I remove NLGEOM it works fine