According to the generalized Hooke Law, the elastic strain
energy released from the unit rock mass under the triaxial compression test is (Xie et al., 2011):
where e and [eta] are the internal energy and the entropy per unit mass; p = tr([sigma])/3 and s are hydrostatic and deviatoric components of the Cauchy stress [sigma]; [delta]=tr([epsilon]) is the volumetric strain, [[bar.[epsilon]].sub.e] is the deviatoric elastic strain
and [[epsilon].sub.p] is the plastic strain; q is the heat flux vector per unit area and h is the heat source per unit mass; [rho] is the density and [theta] is the temperature.
The elastic strain
energy of the ith beam element is:
For each specimen, three major factors , including energy dissipation ([E.sub.h]), elastic strain
energy ([E.sub.e]), and equivalent viscous damping ratio ([[xi].sub.eq]), were calculated for each hysteric loop with MATLAB.
As a result, some features of ECS response, which are uncorrelated to elastic strain
, become sensitive to plastic strain .
investigated the nonlinear behavior of damaged materials and conducted a large number of calculations and simulations of their elastic strain
The strain-life curve, according to Basquin , Coffin-Manson [8, 9] and Morrow , is a summation of the elastic strain
[[epsilon].sub.a,e] and the plastic strain [[epsilon].sub.a,p], so that the total strain amplitude [[epsilon].sub.a,t] equates to
Here, [[epsilon].sub.kl] are the components of the elastic strain
, [E.sub.1] are the components of the electric field, [[sigma].sub.ij] are the components of the stress tensor, and [D.sub.i] are the components of the electric displacement.
in their study "Stability Analysis of Water-Resistant Strata in Karst Tunnel Based on Releasable Elastic Strain
Energy." In this paper, the energy instability criterion of water-resistant strata and rock mass failure index (RMFI) are proposed based on releasable elastic strain
energy [Ue.sup..] The RMFI is employed to represent the damage extent of water-resistant strata.
where U is the total energy stored in the infinite plate, [U.sub.t] represents the initial total elastic strain
energy, [U.sub.c] is the total elastic strain
energy released by the crack on the upper and lower surfaces of the crack length of 2a, W is the work performed by the external force, and [U.sub.s] is the free surface energy.
Remembering now that the stress can also be thought of as an energy density, we can ask, What is the contribution of the singular stress field near the crack to the total elastic strain
energy in the solid?
As the high elastic strain
energy accumulated in the rock masses is greater than the energy consumed by rock failure, imbalance of the rock mass structure occurs and the excess energy causes the rock to explode and emitted rock debris", he explained.