THE PROPAGATION OF SHOCK WAVES IN SEMILINEAR VISCOELASTIC MATERIALS.
Interim technical rept.,
CALIFORNIA UNIV BERKELEY STRUCTURAL ENGINEERING LAB
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A nonlinear viscoelastic material whose constitutive functional is represented by a multiple integral expansion, with the characteristic property that the instantaneous response is linear, is called semilinear. It is shown that, in a longitudinal impact on the end of a long bar of such a material, the velocity or stress is governed by a nonlinear integro-differential equation. If the velocity or stress is prescribed at the end of the bar, then the solution may be obtained in the form of a traveling wave, with the state variables behind the wave front expressed in the form of power series whose coefficients are obtainable by quadratures. A sample calculation exhibits the quantitative effects of nonlinear memory on wave propagation. The method used in the paper is also shown to be extendable to certain problems of three dimensional wave propagation. Author
- Metallurgy and Metallography