How this calculator works
Two independent constants determine isotropic linear 3D elasticity. Select the known pair; the calculator rejects combinations without positive bulk and shear stiffness. E and P-wave modulus can produce two stable solutions, so a branch selector is provided. The displayed scalar constants always describe the underlying 3D material. Plane stress or plane strain changes only the reduced in-plane constitutive matrix, whose third column uses engineering shear strain. Negative Lame lambda is allowed for some auxetic materials.
Formula
E = 9KG/(3K+G); nu = (3K-2G)/(2(3K+G)); lambda = K-2G/3; M = K+4G/3. Plane-stress normal factor = E/(1-nu^2).
Worked example
K = 100 GPa and G = 60 GPa give E = 150 GPa, nu = 0.25, lambda = 60 GPa and M = 180 GPa. E = 200 GPa and nu = 0.25 instead give G = 80 GPa and K = 133.333 GPa.
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Frequently asked questions
Does this apply to composites?
Only if an isotropic effective model is justified. A general orthotropic material needs more independent constants.
Why can E and M be ambiguous?
The relation is quadratic and can have two stable roots. Independent material information is needed to choose the correct Poisson ratio.
Do plane-stress constants become 2D material constants?
The scalar outputs remain intrinsic 3D material constants. Only the constitutive matrix is reduced for the selected stress or strain constraint.