Micromechanics model of gas saturated coal weakened by elliptical microcracks

Based on the analysis of the deformation and growth of a representative elliptical microcrack with arbitrary orientation and geometrical size embedded in a representative volume element subjected to triaxial stress and pore pressure, the additional compliance tensor induced by an embedded opening/closed elliptical microcrack is derived. Assuming numerous elliptical microcracks, and introducing an appropriate probability density function to describe the distribution of orientation and geometrical size of microcracks, the additional compliance tensor induced by microcracks system is analyzed in Taylor’s scheme, and a three-dimensional micromechanics model for gas saturated coal materials is obtained. The validity of the proposed micromechanics model is verified by the agreement between the theoretical and experimental results of gas saturated coal under triaxial compression. The effect of pore pressure and confining pressure on the damage behavior induced by microcracks is investigated. The calculations show microcracks of coal under higher pore pressure will be more inclined to slide and grow, and induce larger additional strain in the last deformation stage.

A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow

A coupled plastic damage model with two damage scalars is proposed to describe the nonlinear features of concrete. The constitutive formulations are developed by assuming that damage can be represented effectively in the material compliance tensor. Damage evolution law and plastic damage coupling are described using the framework of irreversible thermodynamics. The plasticity part is developed without using the effective stress concept. A plastic yield function based on the true stress is adopted with two hardening functions, one for tensile loading history and the other for compressive loading history. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction of the plastic hardening rate. The specific reduction factor is then deduced from the compliance tensor of the damaged material. Finally, the proposed model is applied to plain concrete. Comparison between the experimental data and the numerical simulations shows that the proposed model is able to describe the main features of the mechanical performances observed in concrete material under uniaxial, biaxial, and cyclic loadings.

A Meso-Mechanical Constitutive Model of Particle Reinforced Titanium Matrix Composites Subjected to Impact Loading

A meso-mechanical constitutive model of TiC particle reinforced titanium matrix composites (TiC/TMCs) under impact loading is established to investigate the mechanical behavior of TiC/TMCs. Based on Eshelbys equivalent inclusion theory and Mori-Tanakas concept of average stress in the matrix, the compliance tensor is formulated. By adding nucleation and growth crack models, the influences of micro-cracks on compliance tensor and damage evolution are examined. Finally, a one-dimensional dynamic constitutive model subjected to impact loading is presented to explore the mechanical behavior of TiC/TMCs.

Stress-dependent anisotropy in transversely isotropic rocks: Comparison between theory and laboratory experiment on shale

Understanding the effect of stress and pore pressure on seismic velocities is important for overpressure prediction and for 4D reflection seismic interpretation. A porosity-deformation approach (originally called the piezosensitivity theory) and its anisotropic extension describe elastic moduli of rocks as nonlinear functions of the effective stress. This theory assumes a presence of stiff and compliant parts of the pore space. The stress-dependent geometry of the compliant pore space predominantly controls stress-induced changes in elastic moduli. We show how to apply this theory to a shale that is transversely isotropic (TI) under unloaded conditions. The porosity-deformation approach shows that components of the compliance tensor depend on exponential functions of the principal components of the effective stress tensor. In the case of a hydrostatic loading of a TI rock, only the diagonal elements of this tensor, expressed in contracted notation, are significantly stress dependent. Two equal shear components of the compliance will depend on a combination of two stress exponentials. Exponents of the stress exponentials are controlled by components of the stress-sensitivity tensor. This tensor is an important physical characteristic directly related to the elastic nonlinearity of the porous rock. We simplify the porosity-deformation theory for TI rocks and provide corresponding explicit equations. We apply this theory to ultrasonic measurements on saturated shale samples from the North Sea. We show that the theory explains the compliance tensor, anellipticity, and three anisotropic parameters under a broad range of loads.