= Slip-line field theory
= Slip-line theory
{synonym}
<Slip-line field theory> solves certain two-dimensional problems of <plastic deformation> by constructing two orthogonal families of <characteristic curves>, called <slip lines>. Its classical assumptions include <plane strain>, negligible <inertia> and <body force>, and a rigid, perfectly plastic material. The curves are aligned with the directions of maximum in-plane <shear stress>, rather than the <principal stress> directions.<Applied Mechanics of Solids by A. F. Bower>[§6.2, assumptions 1–5; §6.2.1, interpreting a slip-line field and stress state]{ref}
The curve network encodes both the <stress> field and constraints on admissible <velocity>. Indentation of a thick workpiece by a rigid flat punch provides a motivating application: the construction predicts a plastic flow region and the load needed to sustain that flow. It is useful because geometry can turn coupled field equations into relations integrated along curves. A <slip line> is a continuum characteristic, however, not necessarily a microscopic crystal <slip system> or the actual path of a moving material particle.
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