Under applied stresses, elastic strain energy
(UE) will be generated and stored in materials.
The first approach is the introduction of some specific nonlinear elastic strain energy
functions, which are functions of the irreducible invariants of strain tensor and structure tensor [13-20]; in particular, Merodio and the coworkers [21, 22] use this approach to deal with different invariants, anisotropic materials, residual stress, and structural instabilities.
However, the question still remains as to how to deal with the singularity problem and the answer lies in dealing with the elastic strain energy
as opposed to focusing on the stress level.
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.
The conditions for this mechanical instability depend on the strength to break the fibril and the intensity of the elastic strain energy
that is the potential energy accumulated in the structure until the fibril is broken.
Storage of elastic strain energy
in muscle and other tissues.
This numerical approach involves minimizing the elastic strain energy
for a frictionless interfacial contact subject to the condition of all contact pressures being compressive and therefore greater than zero, other than for regions of no-contact.
However, the presented here approach does not allow for the influence of changes in the geological structure of bed on the distribution of stresses and elastic strain energy
predicted in rockmass.
Elastic strain energy
takes an important role in a solid-state phase transformation.
The internal energy E comprises elastic strain energy
This was termed the tearing energy by Rivlin and Thomas (see reference 1), and it is defined by [Mathematical Expression Omitted] where U is the total elastic strain energy
stored in the sample, A is the area of one fracture surface of the crack (in the unstrained state), and the partial derivative indicates that the sample is considered at a fixed deformation so the external forces do no work (strain controlled rather than load controlled deformation).
The latter point leads to substantial simplifications when large deformations, including large rotations especially, are considered, with negligible differences obtained with respect to significantly more complex hyperelastic laws (where an elastic strain energy
function is defined) when elastic strains keep small, as is the case in the applications considered here.