Effect of inherent microcrack populations on rock tensile fracture behaviour: numerical study based on embedded discontinuity finite elements

Inherent microcrack populations have a significant effect on the fracture behaviour of natural rocks. The present study addresses this topic in numerical simulations of uniaxial tension and three-point bending tests. For this end, a rock fracture model based on multiple intersecting embedded discontinuity finite elements is developed. The inherent (pre-existing) microcrack populations are represented by pre-embedded randomly oriented discontinuity populations. Crack shielding (through spurious locking) is prevented by allowing a new crack to be introduced, upon violation of the Rankine criterion, in an element with an initial crack unfavourably oriented to the loading direction. Rock heterogeneity is accounted for by random clusters of triangular finite elements representing different minerals of granitic numerical rock. Numerical simulations demonstrate the strength lowering effect of initial microcrack populations. This effect is substantially stronger under uniaxial tension, due to the uniform stress state, than in semicircular three-point bending having a non-uniform stress state with a clear local maximum of tensile stress.

Implementation of Incremental Yield Condition for Continual Problems with Singularity

The limit elastic state of an infinitely large half-plane under the action of concentrated vertical and horizontal forces has been considered. The gradient yield condition specifying the elasto-plastic material yielding initial moment at non-uniform stress state is used as the limit state criterion. The analytical expressions allowing to interpret the result in the singular point have been derived.

ULTIMATE ELONGATION OF CONCRETE

It is shown the results of experimental studies of the deformation and concrete fracture process under the axial tension and under the conditions of non-homogeneous state of stress when changing the deformation gradient over the cross section. The test samples were loaded by the short duration load to the point of structural and with load alleviation under the stresses close to destruction. The basic influencing factors on the ultimate elongation of studied types of concrete are found out and the analytical dependences for their description are proposed. The experiments have shown that under the non-uniform stress state the ultimate elongation is not constant; it varies within a wide range and depends on the critical strain gradient. For solving applied problems, the suitable, for practical use, universal form of connection load – deformation was offered, which truly reflects the unity of the relation between stress and deformation of concrete, which is in the condition of homogeneous and non-homogeneous stress states.

Uniform Stress State in Bone Structure With Residual Stress

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.