## Category / Strength of Materials

## Failure Theories

For part stresses that are multi-axial, failure theories relate the failure in a part subjected to arbitrary multi-axial loads to that of a uni-axially loaded test specimen. The general form of these…

## Principal Stresses in 3D

Here we will determine the normal principal stresses and planes on an arbitrary 3D element using numerical tools. When a stress element is characterized by its six stress components and these components…

## Principal Stresses in 2D

Here we will derive the principal stresses in a two-dimensional system. Starting with a unit cube subjected to combined tensile and shear stresses, take a cut at an arbitrary angle to make…

## Modulus of Rigidity

Analogous to Young’s Modulus, the modulus of rigidity is the proportionality constant in the elastic range for shear.

## Axial Stress and Strain

Normal Stress Stress characterizes the internal forces within a body, where forces act between one particle and the next within the material microstructure. A stressed body can be studied by visualizing the…

## Generalized Hooke’s Law

Take a unit cube subjected to multiaxial loading and having an isotropic material. The strain produced by one load consists of the normal strain from the load in its direction, plus lateral…

## Bulk Modulus

Also the modulus of compression, refers to a body under uniform hydrostatic pressure. For a unit cube all stress components are the same and equal to the pressure p. The change per…

## Poisson’s Ratio

Represents the ratio between strains in orthogonal directions, where the lateral strains are some factor of the axial strain. For an isotropic material with an axial load in the x direction: \begin{equation}…