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Geotechnical Stress Simulation

Apply stress horizontally (σₓ) and vertically (σᵧ) to see how a material deforms. The grid will dynamically animate to show strain. The graph shows the material's full constitutive behavior, including elastic, plastic, and failure phases.

Material Properties

Applied Stresses

Legend

Spring in Compression
Spring in Tension
An interactive animation showing a grid of springs deforming under simulated stress.
Definition will appear here.
A graph plotting Load vs. Deformation, showing the material's elastic, plastic, and failure phases.

Theoretical Detail

3D Stress Matrix (Cauchy Stress Tensor)

In continuum mechanics, the stress state at a point is described by the Cauchy stress tensor, a 3x3 matrix. It relates the force vector to the normal vector of a surface. Diagonal elements are normal stresses; off-diagonals are shear stresses.

$$\sigma = \begin{bmatrix} \sigma_{xx} & \tau_{xy} & \tau_{xz} \\ \tau_{yx} & \sigma_{yy} & \tau_{yz} \\ \tau_{zx} & \tau_{zy} & \sigma_{zz} \end{bmatrix}$$

2D Plane Stress Matrix (Current State)

For this simulation, we assume a plane stress condition. The matrix shows the internal shear stress for the highlighted grid element, which is maximum at 45°.