Microcontinuum derivation of Goodman�Cowin theory for granular materials

Chen, Kuo-Ching; Lan, Jeng-Yin
December 2008
Continuum Mechanics & Thermodynamics;Dec2008, Vol. 20 Issue 6, p331
Academic Journal
This study presents a derivation of the Goodman�Cowin (GC) equation using the microcontinuum field theory. Through the decomposition of various microcontinuum field quantities into the straining, dilatant, and rotational parts, a microcontinuum can be classified into seven subclasses. One of the subclasses, called a microdilatation continuum, is introduced when only the dilatant motion in a macroelement is taken into account. The balance equation of equilibrated force in the GC theory can be derived while introducing the equilibrated intrinsic body force in the energy balance equation of the microdilatation continuum. The internal length of granular materials, appearing in the modified GC equation, is interpreted as the gyration radius of a macroelement. This study also obtains the evolution equation of the internal length from the microcontinuum point of view.


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