Energetic Formulation of Large-Deformation Poroelasticity

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.

A Nonlinear Constitutive Model for Disintegrated Carbonaceous Mudstone Based on Logarithmic Functions

To study the mechanical characteristics of the disintegrated carbonaceous mudstone (DCM), consolidated drained triaxial tests were conducted on the DCM with three degrees of compaction (i.e., 90%, 93%, and 96%). Then, the nonlinear constitutive model suitable for the DCM was established based on test results using a logarithmic function. The stress-strain characteristics of the DCM were analyzed. The results revealed that the axial strain of the DCM was positively correlated with the deviatoric stress and lateral strain. The slopes of deviatoric stress-axial strain curves decreased with the increase of axial strain and so did the slopes of the axial strain-volumetric strain curves. The strength of the DCM increased with the increase of the confining pressure and the degree of compaction. In addition, the axial strain induced by dilatancy was also positively correlated with the degree of compaction and the confining pressure. Furthermore, under triaxial loading conditions, the relationship between the stress and strain of the DCM can be expressed by a logarithmic function; based on this, a nonlinear constitutive model with ten material parameters was derived. In addition, the results of numerical tests using the model showed similar stress-strain characteristics of the DCM comparing with the triaxial tests. Hence, it indicated that the nonlinear constitutive model based on the logarithmic function can reflect the nonlinear stress-strain characteristics of the DCM.

Tunnel Behaviour Caused by Basement Excavation in Clay

Many researchers have investigated the effect of basement excavation on tunnel deformation. However, the influence of consolidation on the interaction of basement-tunnel-soil is rarely considered or systematically studied in clay. In this study, three-dimensional coupled-consolidation finite element analyses were conducted to investigate the effect of consolidation on the tunnel response to excavation. An advanced nonlinear constitutive model was adopted, and numerical parametric investigations were conducted to study the effect of the excavation depth, tunnel stiffness, soil permeability coefficient, and consolidation time on the tunnel response. The results revealed that the basement excavation led to stress release, which caused tunnel heave. Owing to the dissipation of excess negative pore water pressure, the tunnel heave further increased to become approximately twice as large compared with that observed when the foundation pit excavation had just been completed. As the consolidation time increased, the longitudinal tunnel heave and tunnel diameter change caused by the foundation pit excavation gradually increased, but the growth rate was slower down. When the consolidation time changed from 50 days to 150 days, the maximum tunnel heave at the crown and the maximum tunnel diameter change increased by 1.18 and 1.48 times, respectively. The soil’s permeability coefficient did not have a significant effect on the tunnel heave at the crown nor on the tunnel diameter change. The results obtained by this study are expected to be useful as an engineering reference for the analysis of soil structure problems in clay.

Constitutive Model of Isotropic Magneto-Sensitive Rubber with Amplitude, Frequency, Magnetic and Temperature Dependence under a Continuum Mechanics Basis

A three-dimensional nonlinear constitutive model of the amplitude, frequency, magnetic and temperature dependent mechanical property of isotropic magneto-sensitive (MS) rubber is developed. The main components of MS rubber are an elastomer matrix and magnetizable particles. When a magnetic field is applied, the modulus of MS rubber increases, which is known as the magnetic dependence of MS rubber. In addition to the magnetic dependence, there are frequency, amplitude and temperature dependencies of the dynamic modulus of MS rubber. A continuum mechanical framework-based constitutive model consisting of a fractional standard linear solid (SLS) element, an elastoplastic element and a magnetic stress term of MS rubber is developed to depict the mechanical behavior of MS rubber. The novelty is that the amplitude, frequency, magnetic and temperature dependent mechancial properties of MS rubber are integrated into a whole constitutive model under the continuum mechanics frame. Comparison between the simulation and measurement results shows that the fitting effect of the developed model is very good. Therefore, the constitutive model proposed enables the prediction of the mechanical properties of MS rubber under various operating conditions with a high accuracy, which will drive MS rubber’s application in engineering problems, especially in the area of MS rubber-based anti-vibration devices.

A nonlinear strain-rate dependent constitutive model for uncured rubber materials under large deformation

Uncured rubber possesses remarkable hyperelastic and viscoelastic properties while it undergoes large deformation; therefore, it has wide application prospects and attracts great research interests from academia and industry. In this paper, a nonlinear constitutive model with two parallel networks is developed to describe the mechanical response of uncured rubber. The constitutive model is incorporated with the Eying model to describe the hysteresis phenomenon and viscous flow criterion, and the hyperelastic properties under large deformation are captured by a non-Gaussian chain molecular network model. Based on the model, the mechanical behaviors of hyperelasticity, viscoelasticity and hysteresis under different strain rates are investigated. Furthermore, the constitutive model is employed to estimate uniaxial tensile, cyclic loading–unloading and multistep tensile relaxation mechanical behaviors of uncured rubber, and the prediction results show good agreement with the test data. The nonlinear mechanical constitutive model provides an efficient method for predicting the mechanical response of uncured rubber materials.

High-Temperature Mechanical Behaviors of SiO2-Based Ceramic Core for Directional Solidification of Turbine Blades

The high-temperature mechanical behaviors of SiO2-based ceramic cores for the directional solidification of turbine hollow blades were investigated. Isothermal uniaxial compression tests of ceramic core samples were conducted on a Gleeble-1500D mechanical simulator with an innovative auxiliary thermal system. The stress–strain results and macro- and micro- structures of SiO2-based ceramic cores were investigated experimentally. The microstructures were characterized by the scanning electron microscope (SEM). Based on the experimental data, a nonlinear constitutive model for high temperature compressive damage was established. The statistical results of Weibull moduli show that the stability of hot deformation increases with the increase of temperature. The fracture type of the SiO2-based core samples is brittle fracture, but when the temperature exceeds 1400 °C, the mechanical behavior exhibits thermo-viscoelastic and viscoplastic property. Under high-temperature (>1400 °C) and stress conditions, the strength of the ceramic core is weakened owing to the viscous slip of SiO2, which is initially melted at the temperature of 1400 °C. The comparison results between the predictions of nonlinear model and experimental values indicate that the model is applicable.

Nonlinear Constitutive Model of Soil-bentonite Based on Triaxial Tests along Different Stress Paths

To investigate the constitutive behavior of soil-bentonite, which is commonly used as the backfill of cutoff walls, a series of triaxial tests were conducted along different stress paths. The tested soil-bentonite comprises 5% Wyoming bentonite and 95% silty clay excavated from a landfill site located in Jiangsu Province, China. Some mechanical properties of the soil-bentonite, including the compression characteristic, shearing characteristic, and coupled deformation of mean and deviatoric stress, were discussed based on the test data. Then, a nonlinear constitutive model was developed under the axisymmetric condition based on a modified hypoelastic model framework. All six independent parameters included in the model were calibrated according to the test data. The mechanical behaviors that the triaxial tests revealed can be fully reflected by the nonlinear model; therefore, it can reasonably describe the stress-strain behaviors of the soil-bentonite in triaxial tests of this study and another literature. Compared with the Modified Cam-Clay model, the prediction effect for the shear strain of the nonlinear model is better. According to a large-scale in-situ test employing a soil-bentonite cutoff wall, the actual stress paths of soil-bentonite are basically included in the application scope of the nonlinear model, preliminarily indicating its applicability for practical engineering projects.