Based on Crack the Second Expansion the Variation and Generalized Variation Problem of Fractured Rock Mass under Unloading
Firstly, in the paper based on the constitutive equation and the basic equations of the unloading fractured rock mass on the second expansion phase at the crack, the two types of variables of the energy functional about the variation problem was constructed the,as the independent variables at that stage. In order to identify the undetermined function G,the energy functional variational the independent variables ,,the variational function was satisfied the principle of minimum potential then can obtain the function G. Second, Secondly on this basis, two undetermined Lagrange multipliers were introduced to the new functional in order to absorb the balance equation and stress boundary conditions into the new functional .As the same, variational the independent variables,, then obtained the . To simplify the using the Green formula and then can be identified the undetermined Lagrange multipliers.Finally,the unloading the fractured rock mass at the crack of secondary expansion phase of the unconstrained variational energy functional can be obtained which is the generalized variational principle.
Chunliang Zhang and Paul P. Lin
L. Yu et al., "Based on Crack the Second Expansion the Variation and Generalized Variation Problem of Fractured Rock Mass under Unloading", Applied Mechanics and Materials, Vols. 226-228, pp. 1348-1352, 2012