Shear behavior of intact granite under thermo-mechanical coupling and three-dimensional morphology of shear-formed fractures

The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

A thermo-mechanical damage constitutive model for deep rock considering brittleness-ductility transition characteristics

This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.

Efficient Inverse Analysis for Solving a Coupled Conduction,Convection and Radiation Problem Involving Non⁃gray Participating Media

The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.

Study on inhomogeneous cooling behavior of extruded profile with unequal and large thicknesses during quenching using thermo-mechanical coupling model

The interfacial heat transfer coefficient between hot profile surface and cooling water was determined by using inverse heat conduction model combined with end quenching experiment. Then, a Deform-3 D thermo-mechanical coupling model for simulating the on-line water quenching of extruded profile with unequal and large thicknesses was developed. The temperature field, residual stress field and distortion of profile during quenching were investigated systematically. The results show that heat transfer coefficient increases as water flow rate increases. The peak heat transfer coefficient with higher water flow rates appears at lower interface temperatures. The temperature distribution across the cross-section of profile during quenching is severe nonuniform and the maximum temperature difference is 300 ℃ at quenching time of 3.49 s. The temperature difference through the thickness of different parts of profile first increases sharply to a maximum value, and then gradually decreases. The temperature gradient increases obviously with the increase of thickness of parts. After quenching, there exist large residual stresses on the inner side of joints of profile and the two ends of part with thickness of 10 mm. The profile presents a twisting-type distortion across the cross-section under non-uniform cooling and the maximum twisting angle during quenching is 2.78°.

Formation Mechanism in Alloy Steel Rolling Process Using Thermo-mechanical Coupling Method

Based on the theory of elastic-plastic finite element method, the high-speed hot continuous rolling process of a billet is simulated and analyzed in vertical and horizontal passes. The billet is dragged into the passes by contact friction force between the billet and rollers. The rollers and billet are represented by respectively rigid and deformable bodies, and three-dimensional models are developed for the billet and rollers. The distribution of deformation field, effective strain, rolling force and temperature field are accurately calculated for the whole rolling process （including unstable and stable stages）. In addition, the rolling pressure on the width symmetry center is compared with that in the in-situ experimental measurements. It is revealed that various heat exchange phenomena among the billet, rollers and surroundings can result in unbalanced temperature distribution on the cross section. Rolling force and strain can change significantly when the billet is moved towards or away from the roller gap, and keep almost invariable in the stable stage. It is expected that the simulation results would be useful for practical manufacture and provide the theoretical foundation for improvement of process planning and optimization of process parameters.

Thermo-mechanical coupled particle model for rock

A thermo-mechanical coupled particle model for simulation of thermally-induced rock damage based on the particle simulation method was proposed.The simulation results of three verification examples,for which the analytical solutions are available,demonstrate the correctness and usefulness of the thermo-mechanical coupled particle model.This model is applied to simulating an application example with two cases：one is temperature-independent elastic modulus and strength,while the other is temperature-dependent elastic modulus and strength.The related simulation results demonstrate that microscopic crack initiation and propagation process with consideration of temperature-independent and temperature-dependent elastic modulus and strength are different and therefore,the corresponding macroscopic failure patterns of rock are also different.On the contrary,considering the temperature-dependent elastic modulus and strength has no or little effect on the heating conduction behavior.Numerical results,which are obtained by using the proposed model with temperature-dependent elastic modulus and strength,agree well with the experimental results.This also reveals that the rock subjected to heating experiences much more cracking than the rock subjected to cooling.

Impact of cooling rate on mechanical properties and failure mechanism of sandstone under thermal-mechanical coupling effect

High geo-temperature is one of the inevitable geological disasters in deep engineering such as resource extraction,space development,and energy utilization.One of the key issues is to understand the mechanical properties and failure mechanism of high-temperature rock disturbed by low-temperature airflow after excavation.Therefore,.the experimental and numerical investigation were carried out to study the impact of cooling rate on mechanical properties and failure mechanism of high temperature sandstone.First,uniaxial compression experiments of high temperature sandstone at different real-time cooling rates were carried out to study the mechanical properties and failure modes.The experimental results indicate that the cooling rate has a significant effect on the mechanical properties and failure modes of sandstone.The peak strain,peak stress,and elastic modulus decrease with an increase in cooling rate,and the fragmentation degree after failure increases gradually.Moreover,the equivalent numerical model of heterogeneous sandstone was established using particle flow code(PFC)to reveal the failure mechanism.The results indicate that the sandstone is dominated by intragrain failure in the cooling stage,the number of microcracks is exponentially related to the cooling rate,and the higher the cooling rate,the more cracks are concentrated in the exterior region.Under axial loading,the tensile stress is mostly distributed along the radial direction,and the damage in the cooling stage is mostly due to the fracture of the radial bond.In addition,axial loading,temperature gradient and thermal stress mismatch between adjacent minerals are the main reasons for the damage of sandstone in the cooling stage.Moreover,the excessive temperature gradient in the exterior region of the sandstone is the main reason for the damage concentration in this region.

Spudcan Penetration Simulation Using the Coupled Eulerian-Lagrangian Method with Thermo-Mechanical Coupled Analysis

A novel modeling technique based on the coupled Eulerian-Lagrangian(CEL) method is provided to solve the geotechnical problems with large deformations. The technique is intended to solve the update problem of soil mechanical properties during spudcan penetration in normally consolidated clay soil. In the CEL model, the normal method of assigning an increasing shear strength profile with depth(NA) is defective due to its Eulerian framework. In this paper, a new technique is proposed to update soil material properties by introducing thermo-mechanical coupled analysis(TMCA) to the CEL models. During establishment of the CEL models, the optimal penetration velocity and minimum mesh size are determined through parametric studies. Reasonability and accuracy are then verified through comparison of the preliminary results with the soil flow configuration and penetration resistance(Fv) of a centrifuge test, and the results of the proposed method are compared with those of the remeshing and interpolation technique with small strain(RITSS) method. To achieve a CEL model with satisfactory accuracy, the NA and TMCA methods implemented in the CEL models and the RITSS method are first adopted in weightless soil. Comparison of the findings with those obtained in previous studies shows that the TMCA method can update material properties and predict Fv. The TMCA method is then applied to soils with self-weight and different shear strength profiles. Results show that the proposed method is capable of accurately modeling the large deformation problem of spudcan penetration in non-homogeneous clay.

Numerical modeling of coupled thermo-mechanical response of a rock pillar

Understanding the rock mass response to excavation and thermal loading and improving the capability of the numerical models for simulating the progressive failure process of brittle rocks are important for safety assessment and optimization design of nuclear waste repositories.The international cooperative DECOVALEX-2011 project provides a platform for development,validation and comparison of numerical models,in which the sp pillar stability experiment（APSE） was selected as the modeling target for Task B.This paper presents the modeling results of Wuhan University（WHU） team for stages 1 and 2 of Task B by using a coupled thermo-mechanical model within the framework of continuum mechanics.The rock mass response to excavation is modeled with linear elastic,elastoplastic and brittle-plastic models,while the response to heating is modeled with a coupled thermo-elastic model.The capabilities and limitations of the model for representation of the thermo-mechanical responses of the rock pillar are discussed by comparing the modeling results with experimental observations.The results may provide a helpful reference for the stability and safety assessment of the hard granite host rock in China＇s Beishan preselected area for high-level radioactive waste disposal.

Numerical study on coupled thermo-mechanical processes in sp Pillar Stability Experiment

This paper presents a study of the full three-dimensional thermo-mechanical （TM） behavior of rock pillar in,Aspo Pillar Stability Experiment （APSE） using a self-developed numerical code TM-EPCA3D. The transient thermal conduction function was descritized on space and time scales, and was solved by using cellular automaton （CA） method on space scale and finite difference method on time scale, respectively. The advantage of this approach is that no global, but local matrix is used so that it avoids the need to develop and solve large-scale linear equations and the complexity therein. A thermal conductivity versus stress function was proposed to reflect the effect of stress on thermal field. The temperature evolution and induced thermal stress in the pillar part during the heating and cooling processes were well simulated by the developed code. The factors that affect the modeling results were discussed. It is concluded that, the complex TM behavior of Aspo rock pillar is significantly influenced by the complex boundary and initial conditions.

Numerical modeling for the coupled thermo-mechanical processes and spalling phenomena in sp Pillar Stability Experiment (APSE)

In this paper, the coupled thermo-mechanical （TM） processes in the AEspoe Pillar Stability Experiment （APSE） carried out by the Swedish Nuclear Fuel and Waste Management Company （SKB） were simulated using both continuum and discontinuum based numerical methods. Two-dimensional （2D） and three- dimensional （3D） finite element method （FEM） and 2D distinct element method （DEM） with particles were used. The main objective for the large scale in situ experiment is to investigate the yielding strength of crystalline rock and the formation of the excavation disturbed/damaged zone （EDZ） during excavation of two boreholes, pressurizing of one of the boreholes and heating. For the DEM simulations, the heat flow algorithm was newly introduced into the original code. The calculated stress, displacement and temperature distributions were compared with the ones obtained from in situ measurements and FEM simulations. A parametric study for initial microcracks was also performed to reproduce the spalling phenomena observed in the APSE.

Coupling Study on the Problem Chain Teaching Mode and Moral Education Construction in Primary and Secondary Schools

The construction of moral education in primary and secondary schools is facingmany dilemmas,such as formalism,passivity,task-type,Tacitus trap and new media interaction.There is a high degree of coupling between the progressive,stepped and interlocking supply of Problem Chain mode and the demand of moral education construction in primary and secondary schools.Problem Chain mode is helpful to solve the problems of teaching content,teaching effects and educational object in moral education construction in primary and secondary schools.

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Numerical Simulation of Coupled Thermo-mechanical Behavior of a Cylinder Billet during Hot-forging Process

A finite volume method is applied to simulate a closed die hot forging process of a cylinder billet. Since variation and distribution of temperature play very important role in hot forging, the code involves a methodology of a coupled system of mechanical and thermal equations. The simulated results are compared with the experimental ones. The distribution of temperature in the billet obtained from the simulation is also discussed.

Design and Coupled Thermo-Mechanical Analysis of Silicon Carbide Primary Mirror Assembly

Based on the principle that the thermal expansion coefficient of the support structure should match that of the mirror, three schemes of primary mirror assembly were designed. Of them, the first is fused silica mirror plus 4J32 flexible support plus ZTC4 support back plate, the second K9 mirror plus 4J45 flexible support plus ZTC4 support back plate, and the third SiC mirror plus SiC rigid support back plate. A coupled thermo-mechanical analysis of the three primary mirror assemblies was made with finite element method. The results show that the SiC assembly is the best of all schemes in terms of their combination properties due to its elimination of the thermal expansion mismatch between the materials. The analytical results on the cryogenic property of the SiC primary mirror assembly show a higher surface finish of the SiC mirror even under the cryogenic condition.

Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale （SSOTS） analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro- characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.

Transfer Matrix Approach for Two-State Scattering Problem with Arbitrary Coupling

The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.

Multi-objective Topology Optimization of Thermo-mechanical Compliant Mechanisms

The material characteristics of a structure will change with temperature variation,and will induce stress within the structure.Currently,the optimal design for the topology of compliant mechanisms is mainly performed in single physical field.However,when compliant mechanisms work in high temperature environments,their displacement outputs are generated not only by mechanical load,but also by the temperature variation which may become the prominent factor.Therefore,the influence of temperature must be considered in the design.In this paper,a novel optimization method for multi-objective topology of thermo-mechanical compliant mechanisms is presented.First,the thermal field is analyzed with finite-element method,where the thermal strain is taken into account in the constitutive relation,and the equivalent nodal thermal load is derived with the principle of virtual work.Then the thermal load is converted into physical loads in elastic field,and the control equation of the thermo-mechanical compliant mechanism is obtained.Second,the mathematical model of the multi-objective topology optimization is built by incorporating both the flexibility and stiffness.Meanwhile,the coupling sensitivity function and the sensitivity analysis equations of thermal steady-state response are derived.Finally,optimality criteria algorithm is employed to obtain numerical solution of the multi-objective topology optimization.Numerical examples show that the compliant mechanisms have better performance and are more applicable if the temperature effect is taken into account in the design process.The presented modeling and analysis methods provide a new idea and an effective approach to topology optimization of compliant mechanisms in electrothermic coupling field and multiphysics fields.