Elastic Constants Calculator
Calculate all elastic moduli from any two known constants for isotropic materials
Problem Conditions
Three-dimensional conditions
Elastic Constants Results
Example Calculation
Steel Properties (3D)
Given: Young's modulus E = 200 GPa, Poisson's ratio ν = 0.3
Material: Structural steel (isotropic)
Calculated Results
Shear modulus: G = E/(2(1+ν)) = 76.92 GPa
Bulk modulus: K = E/(3(1-2ν)) = 166.67 GPa
Lamé constant: λ = Eν/((1+ν)(1-2ν)) = 115.38 GPa
P-wave modulus: M = E(1-ν)/((1+ν)(1-2ν)) = 269.23 GPa
Elastic Constants
Typical Values
Quick Tips
Any two independent constants define all others
Valid for isotropic, homogeneous materials only
Poisson's ratio: -1 < ν < 0.5 (physically realizable)
2D vs 3D gives different relationships
All moduli must be non-negative
Understanding Elastic Constants
What Are Elastic Constants?
Elastic constants are material properties that describe how a material responds to applied stress. They quantify the relationship between stress (force per unit area) and strain (deformation) in the elastic regime where the material returns to its original shape when the load is removed.
Isotropic Materials
This calculator assumes isotropic and homogeneous materials. Isotropic means the material properties are the same in all directions, while homogeneous means the properties are uniform throughout the material. Examples include metals like steel and aluminum.
Key Relationships
3D Relationships
G = E / [2(1 + ν)]
K = E / [3(1 - 2ν)]
λ = Eν / [(1 + ν)(1 - 2ν)]
M = E(1 - ν) / [(1 + ν)(1 - 2ν)]
Physical Constraints
E ≥ 0: Materials cannot have negative stiffness
K ≥ 0: Materials cannot expand under compression
G ≥ 0: Materials cannot have negative shear resistance
-1 < ν < 0.5: Thermodynamic stability requirement