Entropic Limit Analysis Applied to Radial Cavity Expansion Problems

Abstract

Analytical solutions of limit analysis design for the simple problem of plane strain expansion of a cylindrical cavity are derived and generalized into entropic extremum principles that allow a fundamental assessment of coupled thermal/hydro/mechanical/chemical (THMC) material instabilities and their effect on the upper and lower bounds of dissipation. The proposed approach integrates a thermodynamically based estimation of uncertainties in coupled deformation processes and an identification of the intrinsic material length/time scales that appear as energy eigenstates of the localization problem. Analytical limit analysis design solutions of the cavity expansion are obtained and upper and lower bound estimates are shown to coincide. This provides a robust framework for adding multiphysics feedbacks. Isothermal conditions are first relaxed and the feedback between shear heating, thermal weakening and thermal diffusion is analyzed. Then the analysis is extended to a full range of THMC localization phenomena which are described with a cascade of characteristic time/length scales derived from instabilities in the governing reaction-diffusion equations. Entropic uncertainties are estimated by alternating system constraints between thermodynamic flux and thermodynamic force on the boundaries.