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- W2000817303 abstract "The displacement field of a straight dislocation along the direction t = m {times} n where m and n are two mutually orthogonal vectors perpendicular to the dislocation, is described in terms of six partial solutions u{sub {alpha}} = A{sub {alpha}}f(m{center_dot}r + p{sub {alpha}}n{center_dot}r), {alpha} = 1, {hor_ellipsis}6, where, in the dislocation case, the function f is the logarithm, f(m{center_dot}r + p{sub {alpha}}n{center_dot}r) = log(m{center_dot}r + p{sub {alpha}}n{center_dot}r). Stroh extended the theory by introducing a second vector L{sub {alpha}} besides A{sub {alpha}} which is such that f{sub {alpha}} = {minus}L{sub {alpha}}f{prime} (m{center_dot} + p{sub {alpha}}n{center_dot}) is the force per unit area exerted by the displacement field on a plane with a unit normal n. Note that the vector system A{sub {alpha}} and the associated vector system L{sub {alpha}} do not depend on the particular form of the function f. The same vectors as in the dislocation case are obtained if one instead considers static wavy displacement fields with f(m{center_dot}r + p{sub {alpha}}n{center_dot}r) = exp[ik(m{center_dot}r + p{sub {alpha}}n{center_dot}r)]. Partial solutions are: U{sub {alpha}} = A{sub {alpha}} exp[ik(m{center_dot}r + p{sub {alpha}}n{center_dot})]; f{sub {alpha}} = {minus}ikL{sub {alpha}} exp[ik(m{center_dot}r + p{sub {alpha}}n{center_dot}r)]. One more variance: It has been shown that rotation of the vectormore » system (m,n), about t leaves the six-dimensional vector (A{sub {alpha}}, L{sub {alpha}}) unchanged. Thus (A{sub {alpha}},L{sub {alpha}}) is a definite vector relative to the crystal, depending only on the direction t in the crystal (but p{sub {alpha}} changes according to a definite rule). This invariance is the basis for the so-called integral formalism, and in the present context it means that any halfspace n{center_dot} > 0 with n perpendicular to t can be used in the considerations on partial Stroh wave solutions.« less" @default.
- W2000817303 created "2016-06-24" @default.
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- W2000817303 date "1998-08-01" @default.
- W2000817303 modified "2023-09-26" @default.
- W2000817303 title "Linear relations in the dislocation Stroh vector system, derived by energy considerations" @default.
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- W2000817303 doi "https://doi.org/10.1016/s1359-6462(98)00213-9" @default.
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