Test No. VNL09 Find out reactions at the punch pressed
on large block for perfectly plastic and isotropic hardening materials.
Definition
A 2D plane strain punch is pressed on larger block of finite dimensions. Punch is
assumed rigid and contact condition between punch and the block are assumed
frictionless sliding (line BC). Vertical downward displacement D is applied to the
punch (Figure 1). Symmetry condition is assumed along
line ABL, and sliding condition is applied along line LK.Figure 1.
Dimensions: AB = 40 mm, BC = 80 mm, BL = 160 mm, LK = 200 mm
The material properties are:
Properties
Value
Modulus of Elasticity
1.e+3 MPa
Poisson's Ratio
0.3
Two plasticity models are used:
Elastic perfectly plastic with yield stress 1 MPa
Isotropic hardening with tangent modulus 0.1e+3 MPa
Results
Geometry of rigid punch and the base was simulated with
two 3D solid plates with thickness 10 mm (Figure 2a). Plane strain condition assumes zero
strain perpendicular to the plate side. In order to meet the condition zero normal
displacements were applied to both sides of the plates (Figure 2b).Figure 2.
Prescribed displacement of the punch was applied in six steps. The
following table contains values of the reaction force at the punch per 1 mm of the
plates thickness.
SimSolid Reaction, N
Reference Reaction, N
D, mm
Perfect Plasticity
Hardening
Perfect Plasticity
Hardening
0.04
29.70
29.68
30
30
0.12
91.03
92.7
86
87
0.14
103.3
107.25
99
100
0.16
105.6
112.3
109
113
0.18
106.7
116.5
110
114
0.24
-109.4
126.36
111
125
1 Test
PL-7 from NAFEMS Publication R0049, “Background to Material Non-Linear
Benchmarks”.
