Vectors_Tensors_12_HigherOrderTensors

# Vectors_Tensors_12_HigherOrderTensors - Section 1.12 Solid...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 1.12 Solid Mechanics Part III Kelly 107 1.12 Higher Order Tensors In this section are discussed some important higher (third and fourth) order tensors. 1.12.1 Fourth Order Tensors After second-order tensors, the most commonly encountered tensors are the fourth order tensors A , which have 81 components. Some properties and relations involving these tensors are listed here. Transpose The transpose of a fourth-order tensor A , denoted by T A , by analogy with the definition for the transpose of a second order tensor 1.10.4, is defined by B C C B : : : : T A A = (1.12.1) for all second-order tensors B and C . It has the property ( ) A A = T T and its components are klij ijkl ) ( ) ( T A A = . It also follows that ( ) A B B A ⊗ = ⊗ T (1.12.2) Identity Tensors There are two fourth-order identity tensors . They are defined as follows: T : : A A A A = = I I (1.12.3) and, from 1.9.7, they have components i j j i l k j i jk il j i j i l k j i jl ik e e e e e e e e e e e e e e e e ⊗...
View Full Document

## This note was uploaded on 01/20/2012 for the course ENGINEERIN 3 taught by Professor Staff during the Fall '11 term at Auckland.

### Page1 / 3

Vectors_Tensors_12_HigherOrderTensors - Section 1.12 Solid...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online