Formula Home Mechanics of Materials Stress Strain Hooke's Law Orthotropic Material Transverse Isotropic Isotropic Material Plane Stress Plane Strain Finding E and n Finding G and K Applications Pressure Vessels Rosette Strain Gages Failure Criteria Calculators Stress Transform Strain Transform Principal Stress Principal Strain Elastic Constants Resources Bibliography
STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste.

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

3D Scanners

A white paper to assist in the evaluation of 3D scanning hardware solutions.

more free publications
 Isotropic Definition Most metallic alloys and thermoset polymers are considered isotropic, where by definition the material properties are independent of direction. Such materials have only 2 independent variables (i.e. elastic constants) in their stiffness and compliance matrices, as opposed to the 21 elastic constants in the general anisotropic case. The two elastic constants are usually expressed as the Young's modulus E and the Poisson's ratio n. However, the alternative elastic constants K (bulk modulus) and/or G (shear modulus) can also be used. For isotropic materials, G and K can be found from E and n by a set of equations, and vice-versa. Hooke's Law in Compliance Form Hooke's law for isotropic materials in compliance matrix form is given by, Some literatures may have a factor 2 multiplying the shear modulii in the compliance matrix resulting from the difference between shear strain and engineering shear strain, where , etc. Hooke's Law in Stiffness Form The stiffness matrix is equal to the inverse of the compliance matrix, and is given by, Some literatures may have a factor 1/2 multiplying the shear modulii in the stiffness matrix resulting from the difference between shear strain and engineering shear strain, where , etc. Visit the elastic constant calculator to see the interplay amongst the 4 elastic constants (E, n, G, K).
Glossary
STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste.

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

3D Scanners

A white paper to assist in the evaluation of 3D scanning hardware solutions.