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Curvilinear Coordinate Condition for Antiplane Strain Deformation in Power Law Plastic Solid

Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA, Department of Earth and Planetary Sciences, Northwestern University, Evanston, IL 60208, USA

A desirable curvilinear coordinate system for problems in antiplane strain is one in which the shear stress acting across orthogonal trajectories is either zero or has the maximum value. In elastic isotropic solid problems any coordinate system given by z x+iy = f (w) f (u + iv) satisfies this condition. This paper examines some requirements for curvilinear coordinate systems with a power law plastic solid (of power m). In particular, if the curvilinear trajectories are given by x = x (u, v) and y = y (u, v) the trajectories must satisfy the equation

where 7 represents either x or y.

Key Words: antiplane strain • curvilinear coordinates • power law deformation

Mathematics and Mechanics of Solids, Vol. 14, No. 1-2, 258-269 (2009)
DOI: 10.1177/1081286508092614


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