Spherical Elastic-Plastic Waves

Abstract

By examining the micro-mechanical foundation of thermoplasticity and ductile damage, an indica tion of its continuum effects, which are to be considered as material imperfections of the ideal linear elastic background structure, is given. This approach, originally developed for structural vibrations, was recently extended to include uniaxial propagating waves. This method suggests pursuing the initially elastic wave until it produces plastic deformation, which means a distortion and thus a source that emits elastic waves. Since the spherical waves in such a procedure must be derived from nondispersive D'Alembert wave functions, nonlocal sources extending from each of the plastic sources to infinity are ignited as well and contribute to the elastic wave pattern. The contribution of thermal stresses resulting from the rapid changes of temperature that are produced under adiabatic conditions by the dissipated energy are included in the general analysis, but the material parameters are kept constant. In terms of the control theory of distributed parameter time variant systems, a typical feedback mechanism is constructed. By dividing space into sufficiently small cells, the dis tortion may be kept constant during a yielding event, and by superposition of all the waves, the exact solution, including plastic wave fronts, is obtained. By means of the constitutive relations, strength and distribution of the internal sources are updated after each time step. One major aspect of the procedure is the consideration of the constitutive relations at a late stage of the solution routine. Yet all the merits of the elastic dynamic Green's function are taken into account. The nonlinear spherical wave problem resulting from an explosion in a cavity is solved for the special case of an ideal elastic plastic material under isothermal conditions and without any ductile damage to check the resulting wave pattern by comparison with previously published ones.