The non-uniform motion of a thin smooth rigid inclusion through an elastic solid

Author:
L. M. Brock

Journal:
Quart. Appl. Math. **36** (1978), 269-277

MSC:
Primary 73.35; Secondary 35C99

DOI:
https://doi.org/10.1090/qam/521409

MathSciNet review:
521409

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Abstract: A two-dimensional example of non-uniform motion by a smooth, relatively thin, symmetric rigid inclusion through an elastic solid is analyzed. Integral solutions to the related boundary-initial value problem are obtained for the case of edge speeds bounded by the dilatational wave speed at large times. The wavefront patterns, including the possibility of Mach waves, are noted. Some attention is focused on the case of the straight wedge, and logarithmic singularities are found at its edge for subsonic speeds.

**[1]**N. I. Muskhelishvili,*Some basic problems of the mathematical theory of elasticity*, Noordhoff International Publishing, Leyden, 1975. Fundamental equations, plane theory of elasticity, torsion and bending; Translated from the fourth corrected and augmented Russian edition by J. R. M. Radok; Reprint of the second English edition of 1963. MR**0363078****[2]**A. T. deHoop, Appl. Sci. Res.**B8**, 349 (1960)**[3]**I. N. Sneddon,*The use of integral transforms*, McGraw-Hill, New York, 1972, pp. 495-503**[4]**Ivar Stakgold,*Boundary value problems of mathematical physics. Vol. I*, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1967. MR**0205776****[5]**K. Bertram Broberg,*The propagation of a brittle crack*, Ark. Fys.**18**(1960), 159–192 (1960). MR**0115409****[6]**L. B. Freund, J. Appl. Mech.**40**, 699 (1973)

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DOI:
https://doi.org/10.1090/qam/521409

Article copyright:
© Copyright 1978
American Mathematical Society