Solid Mechanics Visualizer

Linking stress–strain, plane stress state, and Mohr’s circle in one synchronized view.

How to use this playground

Mohr’s Circle: what it is

Mohr’s Circle is a visual shortcut for the stress state at a point. It converts plane stress into a circle on a (σ, τ) graph, so you can read off principal stresses and maximum shear without doing lots of trig.

How it works (intuition)

Every point on the circle represents the stresses acting on some rotated plane through the same material point. The two original faces plot as (σx, τxy) and (σy, −τxy). Where the circle crosses the σ-axis (τ=0) gives σ1 and σ2.

Why it matters

It tells you the answers engineers care about: max normal stress (brittle fracture risk), max shear stress (ductile yielding intuition), and the orientation where these happen (θ). It’s also a fast sanity-check for FEA results.

Symbols (legend)

σ = normal stress, τ = shear stress (MPa)
σx, σy = normal stresses on x- and y-faces
τxy = shear stress on the x-face (paired on y-face as −τxy)
σ1, σ2 = principal stresses (τ = 0 on those planes)
τmax = maximum shear stress (circle radius)
θ = angle to principal plane (from x-axis)
E = Young’s modulus (GPa), ε = strain, σy = yield stress

1) Pick a mode

Use Uniaxial for a simple case driven by σ_x (with σ_y=0, τ_xy=0). Use Custom plane stress to set σ_x, σ_y, and τ_xy directly.

2) Read the results

The element shows the stress arrows. The Mohr’s circle shows the same state in (σ,τ). Use the metrics for σ₁, σ₂, τ_max, and θ.
Quick check: larger |τ_xy| → bigger radius → bigger τ_max.

Stress–Strain Lab Material & Loading

Material

Preset

E (GPa)

Yield σ_y (MPa)

Loading Mode

Uniaxial (σ_x only) Custom plane stress

Applied σ_x (MPa) 100

Current σ
100.0 MPa

Current ε
0.00048

E (Young’s modulus)
210 GPa

Region
Elastic

Linear elastic segment with yield marker; point moves as you change σ or plane stress inputs.

Plane Stress Element σ_x, σ_y, τ_xy

Arrows show normal and shear stresses on a small material element. Sign convention is standard “positive” plane stress.

Current state used for Mohr’s circle:
σx = 100 MPa, σy = 0 MPa, τxy = 0 MPa

Mohr’s Circle Principal & Max Shear

Principal σ₁
0.0 MPa

Principal σ₂
0.0 MPa

τ_max
0.0 MPa

Principal plane angle θ
0.0° (from x)

Circle center, radius, principal stresses, and max shear update live from the plane stress state.

This MVP shows:
• Plane stress (σx, σy, τxy) → Mohr’s circle
• Link to uniaxial stress–strain via σx when in “Uniaxial” mode.