Elastic Constants Calculator

Calculate all elastic moduli from any two known constants for isotropic materials

Problem Conditions

Three-dimensional conditions

GPa

Elastic Constants Results

Enter two known elastic constants to calculate all others
Choose different constants and ensure values are within valid ranges
0

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

Young's Modulus (E)
Resistance to axial deformation
Bulk Modulus (K)
Resistance to volume change
Shear Modulus (G)
Resistance to shear deformation
Poisson's Ratio (ν)
Lateral to axial strain ratio
Lamé Constant (λ)
Relates normal and lateral strains
P-wave Modulus (M)
Longitudinal wave modulus

Typical Values

SteelE: 200 GPa, ν: 0.30
AluminumE: 70 GPa, ν: 0.33
ConcreteE: 30 GPa, ν: 0.20
GlassE: 70 GPa, ν: 0.22
RubberE: 0.01 GPa, ν: 0.50
CorkE: 0.02 GPa, ν: 0.00

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