Structural Analysis
Contact Stress Simulators
A focused Structural Analysis hub for contact stress tools, keeping related formulas, assumptions, and engineering checks together.
9 simulators
Adjacent categories
Simulator list
Elliptical Hertz Contact Simulator — General Hertzian Contact
Contact Stress
Compute the elliptical contact patch of general Hertzian contact: major semi-axis a, minor semi-axis b and peak pressure p_max from normal load and principal curvatures.
Hertz Contact Mechanics Calculator — Contact Radius, Pressure & Deflection
Contact Stress
Calculate Hertz contact pressure, radius, and deflection for spheres, cylinders, or flat geometries. Input materials and load for instant results.
DMT Adhesive Contact Simulator — Derjaguin-Muller-Toporov Theory
Contact Stress
For hard elastic spheres, the DMT model adds the long-range attraction outside the contact area to a Hertzian profile. The pull-off force F_po = -2 pi R gamma is 4/3 tim…
Hertz Contact Stress Calculator
Contact Stress
Based on Hertz contact theory, compute contact pressure distribution, contact radius, and subsurface maximum shear stress for sphere and cylinder contacts in real time.
Hertz Line Contact Simulator — Two Parallel Cylinders
Contact Stress
Visualize Hertzian line contact between two parallel cylinders. Adjust line load, radii and Young's modulus to see the contact half-width and maximum contact pressure fo…
JKR Adhesive Contact Simulator — Johnson-Kendall-Roberts Theory
Contact Stress
Real-time computation of how surface energy γ enlarges the contact radius of soft elastic spheres and creates a pull-off force. Compare with Hertz to see adhesion at a g…
Rolling Contact Stress Calculator — Hertz Contact Theory & Subsurface Stress
Contact Stress
Calculate rolling contact stress using Hertz theory. Input geometry, materials, and load to get contact radius, peak pressure, and subsurface shear stress.
Hertz Subsurface Stress Simulator — σz, σr and τmax versus Depth
Contact Stress
Hertz subsurface stress simulator. Compute centerline σz, σr and τmax under a Hertzian sphere contact in real time; peak shear at z≈0.48a is the pitting origin.
Wheel-Rail Contact Simulator — Elliptical Hertz Contact and Adhesion Limit
Contact Stress
Visualize elliptical Hertz contact between a railway wheel and rail head. Change the axle load, wheel radius, rail crown radius and friction coefficient to learn about t…
How to Use
- Select material pairing (steel-on-steel, aluminum-on-steel, ceramic-on-steel) and enter elastic moduli (E₁, E₂) in GPa
- Input contact geometry: radius of curvature for both bodies (R₁, R₂ in mm), applied normal load (N in kN), and contact width or diameter
- Apply Hertzian contact stress formulas; simulator computes peak contact pressure, subsurface stress distribution, and von Mises equivalent stress at depth z
- Review stress contours, compare against material yield strength, and export results for fatigue assessment
Worked Example
Rolling element bearing contact: steel ball (E=200 GPa, ν=0.3, R=5 mm) on steel raceway (R=15 mm), radial load N=2 kN. Effective radius R_eff = 1/(1/5 + 1/15) = 3.75 mm. Contact pressure P_max = 1.5(N·K/π·R_eff)^(2/3) yields approximately 1840 MPa. Maximum shear stress occurs at depth z ≈ 0.47·a (contact half-width), critical for spalling prediction in fatigue life calculations.
Practical Notes
- Use reduced elastic modulus E* = 1/[(1-ν₁²)/E₁ + (1-ν₂²)/E₂] for dissimilar materials; ignoring Poisson ratio mismatches can underestimate stress by 5–15%
- Verify contact geometry remains elastic; plastic yield occurs when P_max exceeds 0.6·material hardness (MPa), invalidating Hertzian theory
- Account for lubrication regime (elastohydrodynamic pressure spike adds 20–40% to dry contact values) and surface roughness friction when modeling power loss