How this calculator works
Von Mises stress combines the distortional part of a stress state into a nonnegative scalar. General mode uses a symmetric stress tensor; principal mode sets all shears to zero. Plane stress sets the out-of-plane components to zero. Inverse normal-stress calculations can have two roots, so choose a branch explicitly. An inverse shear result is a magnitude; both signs give the same equivalent stress. The criterion is commonly used for isotropic ductile yielding and is not a universal fracture criterion.
Formula
sigma_vm^2 = ((sx-sy)^2 + (sy-sz)^2 + (sz-sx)^2)/2 + 3(txy^2 + tyz^2 + tzx^2). Pure shear: sigma_vm = sqrt(3) |tau|.
Worked example
Principal stresses 100 MPa, 50 MPa and 0 MPa give sigma_vm = 86.60254 MPa. Pure shear of 50 MPa gives the same equivalent stress.
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Frequently asked questions
Does hydrostatic stress contribute?
No. Adding the same normal stress to all three axes leaves the equivalent stress unchanged.
Can normal stress be compressive?
Yes. Enter signed normal or principal components. Shear inverse modes return a nonnegative magnitude.
Why are there two inverse roots?
Equivalent stress depends quadratically on a normal component. The same target can occur on either side of the minimum.