Hydrostatic stress

About: Hydrostatic stress is a research topic. Over the lifetime, 1568 publications have been published within this topic receiving 37773 citations.

Theoretical and numerical modeling of rock hysteresis based on sliding of microcracks

Abstract: Nonlinearity and hysteresis are two key features of elastic rock deformation. This behavior can be attributed to the presence of cracks and crack-like voids. The hysteretic behavior of rocks is related to the concept of unrecovered energy. Two main processes lead to the existence of unrecovered energy in the sliding crack model: (i) the work of frictional forces and (ii) the strain energy trapped in the solid. In this paper, a theoretical and numerical analysis will be presented to extend the work of David et al. [1] to consider 3D penny-shaped cracks. A 3D finite element analysis is used to evaluate the sliding crack model numerically. In this approach, the penalty method is used to simulate the contact behavior of the crack faces. The stick-slip condition of the crack faces is simulated by employing the constitutive frictional law of Amontons. The results show that no residual strain is developed in the body containing randomly oriented cracks if one assumes a uniform stress over all the crack cells. The energy loss is therefore equal to the work of frictional forces on the crack faces. mechanisms and sources. The cracks were generally considered to be initially closed, as well. In addition, no numerical simulation has been carried out to verify the theoretical results. There remains a need for a more precise constitutive model that can capture the nature of the micro-structured materials by considering the frictional contact behavior of initially open interacting cracks in a general loading condition. Table 1. Constitutive models of microstructured materials based on frictional contact of microcracks. Loading condition Crack specifications Frictional constitutive law Walsh [6] Uniaxial compression (loading only) Noninteracting closed 2D cracks Coulomb Kachanov [5] Triaxial asymmetric compression (loading only) Noninteracting closed pennyshaped cracks Coulomb (μ=0.6) Horry and NematNasser [4] Biaxial plane strain (loading only) open pennyshaped cracks interacting based on selfconsistent approach Coulomb (μ=0, ∞) Lawn and Marshall [7] Uniaxial compression (loading and unloading) Noninteracting closed pennyshaped cracks friction coefficient together a cohesion term David et al. [1] Uniaxial compression (loading and unloading) Noninteracting open 2D cracks Coulomb The hysteretic behavior of rocks introduces the concept of unrecovered energy. Two main processes lead to the existence of unrecovered energy in the sliding crack model: (i) the work of frictional forces, and (ii) the strain energy trapped in the solid. Whereas the work of the frictional forces is lost as heat energy, strain energy is available in the solid, and may be recovered at a later loading stage. Given that shear stress plays an important role in frictional sliding, hysteretic behavior under triaxial loading is expected to be different from the uniaxial case. For example, according to the sliding crack model, the hysteresis vanishes for the pure hydrostatic stress state. The classic work of Walsh [6], described the role of microcracks in inducing nonlinear and hysteretic behavior. David et al. [1] extended Walsh’s formulation to consider initially open cracks, and analyzed the behavior of the rock during both loading and unloading, under uniaxial compression. They compared a twodimensional analytical formulation against experimental data on sandstones and thermo-mechanically loaded granite specimens, and concluded that the elastic deformation of the rock subjected to uniaxial compression can be fully characterized by four microstructural parameters: the modulus of the uncracked rock, the crack density, an initial crack aspect ratio, and a friction coefficient. In the present paper, a theoretical and numerical analysis will be presented to extend the work of David et al. [1] to consider 3D penny-shaped cracks. A 3D finite element analysis is also used to evaluate the sliding crack model numerically. 2. THEORETICAL MODELING OF ROCK HYSTERESIS 2.1. Solid Containing a Single Crack Assuming a cube of edge length containing a penny-shaped crack with the orientation of relative to the direction of the uniaxial applied stress σ, the effective modulus in the direction of applied load ( ) is determined by applying Betti’s reciprocal theorem [6]:

Effect of geometry on stress relaxation in InAs∕GaAs rectangular nanomesas: Multimillion-atom molecular dynamics simulations

Abstract: We report the results of multimillion-atom parallel molecular dynamics simulations performed to investigate the lattice-misfit-induced stress relaxation in nanometer-sized rectangular GaAs mesas covered with InAs overlayers of 12-ML thickness. The morphology of atomic planes in the InAs overlayers and the stress distributions in the mesas are studied for varied linear dimensions and aspect ratios. We find that the lattice-mismatch-induced stress relaxation pathways is strongly dependent on the mesa and InAs overlayer geometry. The lattice-misfit-associated stress is accommodated through both the morphology changes of the InAs overlayer planes and the stress accommodation in the GaAs mesa interior. The effects are quantified by computing the atomic displacements in the InAs overlayer atomic planes and the hydrostatic stress distributions. Simulation results reveal that, as the aspect ratio of the rectangular mesa top increases, the morphology of the atomic planes shows a transition from dimple-type morphol...

Plastic zones at the tips of inclined cracks in glassy polymers under small scale yielding

Abstract: A thorough study of the shape and size of plastic zones developed around cracks subjected to combined opening-mode and sliding-mode loading conditions in glassy polymers under small scale yielding was undertaken. Two pressure-modified von Mises yield criteria which take into account the characteristic behavior of glassy polymers expressed by the dependence of their yield locus on the hydrostatic stress component and the difference in their tensile and compressive yield stresses were used. The case of an infinite plate subjected to a uniaxial uniform stress at an arbitrary inclination with respect to the axis of the crack was considered. From the whole study useful results concerning the dependence of the shape and size of plastic zones on the crack inclination angle, the Poisson's ratio, and the ratio of the compressive to tensile yield stress of the plate were derived.