A linear algebra approach to stress and strain at a point and theories of yield

摘要

A straightforward method is described whereby the magnitudes and directions of the principal stresses and strains in two or three dimensions may be derived using the matrix methods of elementary linear ulgebra. The ideas are extended to simplify the classical derivation of the extreme values of shear stress and of the octahedral stresses. After a description of several visual aids, the work concludes with a definition of the von Mises yield surface consistent with the foregoing procedures.