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>ARL-RP-0626 - Generalized Pseudo-Finsler Geometry Applied to Nonlinear Mechanics of Torsion of Crystalline Solids | U.S. Army Research Laboratory
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ARL-RP-0626 - Generalized Pseudo-Finsler Geometry Applied to Nonlinear Mechanics of Torsion of Crystalline Solids | U.S. Army Research Laboratory
A continuum theory of the mechanical behavior of solid materials is presented wherein fundamental geometric quantities suchas the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors.This theory, referred to as generalized pseudo-Finsler geometric continuum mechanics, enables depiction of a very broad classof physical phenomena in deformable solid bodies. The general nonlinear theory is reported first, primarily summarizing priorwork by the author. Next, a new application of the theory to torsional deformation of solids is presented, whereby a cylindricalsample of material may be simultaneously subjected to twisting, extension or compression along its axis, as well as possibleradial confinement or contraction. The internal state variable, when normalized by a regularization length, is identified with anorder parameter associated with inelastic deformation that may include slippage, fracture, and/or structural collapse. Evolutionof the internal state follows a generalized Ginzburgâ??Landau type of kinetic equation. For axially homogeneous fields, acoupled system of nonlinear partial differential equations is obtained that can be integrated numerically. Results are firstdocumented for generic solids representative of many crystals that exist in nature. Then solutions corresponding to realisticproperties of crystals of boron carbide ceramic and ice are reported. Results for boron carbide predict a dominant effect ofshearing over compression on the structural transformation process, in agreement with observations from atomisticsimulations. Results for ice demonstrate periods of steady plastic flow under constant applied average shear stress as well astorsional rigidity varying with sample size. Existence of both phenomena agrees with experimental observations.
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