### STP405: Matrix-Tensor Mathematics in Orthotropic Elasticity

Jayne, B. A.

*Professor, University of Washington, Seattle, Wash.*

Suddarth, S. K.

*Professor, Purdue University, Lafayette, Ind.*

Pages: 20 Published: Jan 1966

**Abstract**

A description of the Hookean elastic behavior of orthotropic materials is presented through the formalism of matrix algebra and tensor calculus. Stress, strain, and Hooke's law are formulated in cartesian tensor notation. These same quantities also are written in matrix form, and the simple rules of matrix algebra are used for their manipulation. Finally, the tensor forms of stress, strain, and Hooke's law are transformed from one to another cartesian reference frame. The transformation of the elastic tensor serves to demonstrate the special forms of anisotropy which can exist when geometric and orthotropic axes are not coincident.

**Keywords:**

matrix algebra, tensor analysis, anisotropy, orthotropism, fibrous materials, elasticity, Hooke's law, cartesian tensors

**Paper ID:** STP45150S

**Committee/Subcommittee:** D30.07

**DOI:** 10.1520/STP45150S

ASTM International is a member of CrossRef.