Calculator Inputs
Formula Used
Generalized 3D Hooke’s law for isotropic linear elasticity:
σ = 2Gε + λ tr(ε) I
G = E / [2(1 + ν)]
λ = Eν / [(1 + ν)(1 − 2ν)]
For inverse calculations:
εx = [σx − ν(σy + σz)] / E, and similarly for εy and εz.
γxy = τxy / G, γyz = τyz / G, γzx = τzx / G.
Principal stresses come from the characteristic equation of the stress tensor. Von Mises stress is calculated from the second deviatoric invariant, which is commonly used for ductile yield assessment.
How to Use This Calculator
- Choose whether you want to convert strain to stress or stress to strain.
- Enter elastic modulus and Poisson ratio for the material.
- Fill the six independent tensor components for the active input set.
- Press calculate to show results above the form.
- Review principal values, invariants, shear limits, and the Plotly chart.
- Download the computed dataset as CSV or export a report as PDF.
Example Data Table
| Case | E (MPa) | ν | εx | εy | εz | γxy | Result Focus |
|---|---|---|---|---|---|---|---|
| Steel Bracket | 210000 | 0.30 | 0.0012 | -0.0004 | 0.0002 | 0.0008 | Check von Mises and principal stress |
| Aluminum Plate | 69000 | 0.33 | 0.0009 | 0.0001 | -0.0002 | 0.0005 | Compare hydrostatic and deviatoric response |
| Polymer Housing | 3200 | 0.38 | 0.0025 | 0.0015 | 0.0008 | 0.0011 | Estimate strain energy density |
FAQs
1. What does a 3D stress strain calculator do?
It evaluates the full three-dimensional stress or strain tensor for isotropic linear elastic materials. It also estimates principal values, invariants, von Mises stress, maximum shear stress, and strain energy density for better engineering review.
2. When should I use strain-to-stress mode?
Use strain-to-stress mode when you already know measured or simulated strain components and need the corresponding stresses. This is common with strain gauge work, finite element post-processing, and material response estimation under elastic loading.
3. When should I use stress-to-strain mode?
Use stress-to-strain mode when the applied stress state is known and you want elastic strain predictions. This helps estimate deformations, compare service conditions, and interpret linear material behavior before detailed nonlinear analysis.
4. Why is Poisson ratio limited in the calculator?
The isotropic linear elastic model becomes physically unstable near ν = 0.5 for compressible solids. Limiting the value avoids division issues and unrealistic results while keeping calculations inside a valid engineering range.
5. What is the meaning of principal stress?
Principal stresses are the normal stresses acting on planes where shear stress becomes zero. They are useful because failure criteria, fracture checks, and maximum shear calculations are commonly based on these transformed stress values.
6. Why is von Mises stress included?
Von Mises stress combines the deviatoric part of the stress state into one equivalent scalar. Designers often compare it with material yield strength to judge whether a ductile component remains within an elastic safety margin.
7. Are the shear strains engineering shear strains?
Yes. The calculator expects engineering shear strains γxy, γyz, and γzx. These are twice the tensor shear strain components, so they match the common engineering form used in constitutive relations and material handbooks.
8. Can I use this for plastic or nonlinear materials?
No. This page is intended for isotropic linear elastic behavior only. Plasticity, large deformation, anisotropy, viscoelasticity, and temperature-dependent response require more advanced constitutive models and specialized analysis methods.