Hertzian contact (sphere)

StaticPASS · 0.67%

Nonlinear contact, Hertzian pressure distribution

Tolerance:: 5%

Open & Solve in BrowserSign in or register to launch this verified model in WebCAE

Problem statement

Geometry: Elastic sphere of radius R pressed against a flat half-space (or a second sphere).
Material: Linear-elastic isotropic bodies, effective modulus E* from both E, ν.
Boundary conditions: Normal load P, frictionless contact.
Measured quantity: Contact radius a = (3PR/4E*)^(1/3) and peak pressure p₀ = 3P/(2πa²).

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units mm
material E=1000 nu=0.3
import path="half_space.step" format=step
material E=100000 nu=0.3
import path="sphere_indenter.step" format=step
contact frictionless
mesh tet size=0.25 order=1 bonding=0
fix surface number 1
fix surface number 2 component=x
fix surface number 3 component=y
load surface number 8 force=-25 component=z
solve
extract contact_pressure target="surface number 7"

Results comparison

Reference value	13.27006191604548
Our result	13.181805730512464
Deviation	0.67%
Tolerance	5%
Status	PASS · 0.67%
Element family	Solid element
Mesh details	7380 nodes, 36474 tets (graded tet quarter-model, contact zone h=0.25mm, half-space depth ~20.6mm)

Updated: 2026-10-19 · WebCAE solver