Thermo-mechanical Coupling Problems Research Articles

Topology optimization for minimizing the mean compliance under thermo-mechanical loads using element-free Galerkin method

This paper presents a numerical model for addressing thermo-mechanical coupling problems in topology optimization, utilizing the element-free Galerkin (EFG) method. A multi-parameter density-based topology optimization framework is introduced to interpolate the thermal stress coefficient, encompassing thermal conductivity, thermal expansion coefficient, and elastic modulus. Two numerical examples are provided to investigate the model's characteristics and associated considerations, including the impact of EFG node distribution, quantity, calculation points layout, design variables, and filtering techniques on optimized results. Numerical findings indicates that the present model allows for adaptable adjustments in nodes number and distribution, calculation points layout, choice of design variables, and application of various filtering techniques while maintaining consistent background grids. Although these adjustments may affect convergence rates and final objective values, they can promise satisfactory optimization structures. Additionally, the study highlights the critical influence of filtering radius on optimization outcomes and the objective value, recommending a value of approximately 16∼20 calculation points.

Finite element analysis of the thermal and thermo-mechanical coupling problems in the dry friction clutches using functionally graded material

Abstract The friction clutch is an important machine part in the torque transmission system, where it is responsible for gently transmitting the power from the engine to the gearbox and damping the tensional vibration. At the beginning of the engagement between the clutch’s elements, a large amount of heat is released due to frictional sliding between the elements of the clutch system, generating very high temperatures. In this work, the two- and three-dimensional finite element models were developed from scratch to explore the clutch disk’s temperature and contact pressure behaviors using an alternative frictional material such as functionally graded material (FGM). The two assumptions for the thermal loads were considered: uniform wear and uniform pressure assumptions. The thermal–structural problem for the new frictional material was solved numerically and then presented as the temperature distributions and the contact pressure at any instant of sliding time. Also, a comparison was made between the clutch system behaviors when using FGM with different frictional materials. The results showed that the FGM has superior results to the other available frictional materials.

Prediction of thermal contact resistance for reusable heat-pipe cooled thermal protection system based on an inverse thermo-mechanical coupling method

Thermal contact resistance (TCR) is a critical characteristic on increasing or decreasing thermal energy transmission efficiency between two bodies in thermal management systems. However, it is difficult to accurately determine the thermal contact resistance in actual engineering structures, due to the complicated influence factors, such as pressure, temperature, and physical properties. In the work, a new method is presented to estimate the thermal contact resistance for a three-dimensional (3D) reusable heat-pipe cooled thermal protection system based on boundary measurements, by solving transient inverse thermo-mechanical coupling problems. Moreover, the thermal contact resistance varies with interface pressure, temperature, and spatial position, which is more practical and challenging. The thermo-mechanical coupling analysis is conducted by the finite element method, and the inversion is carried out by the gradient-based algorithm. First, the present method is validated by identifying the constant TCR, based on the available experimental data. Then, the thermal contact resistance with the functional form in the 3D reusable thermal protection system is accurately estimated. Finally, the convergence stability and robustness of the proposed method are evaluated, by considering the effects of initial guess value and measurement error, respectively. The accurate determination of thermal contact resistance of the reusable thermal protection system effectively avoids the overweight of aircraft and improves its utilization. The present work provides a novel approach for the determination of thermal contact resistance in actual engineering applications.

Thermo-mechanical coupled peridynamics simulation of concrete failure under fire scenarios

A coupled thermo-mechanical bond-based peridynamical (PD) method is developed to simulate thermal cracking processes in concrete. Based on the bond-based PD heat conduction and motion equations, the PD differential operator (PDDO) is used to express the classical computational fluid dynamics basic equations in a non-local integral form, establishing a PD model for the thermo-mechanical coupling problems. In this model, concrete is considered a heterogeneous material composed of aggregates and mortar, with material parameters assumed to be temperature-dependent. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. The model is applied to simulate the transient heat transfer problem of a homogeneous plate. The results show good agreement with the analytical solution, providing evidence for the correctness and accuracy of the proposed coupled numerical method. The damage behavior of the borehole heated concrete plate is analyzed, followed by the simulation of the damage to the concrete plate under a fire scenario. The numerical results accurately predict the temperature distribution within the heterogeneous concrete and the resulting material damage. This study provides new theoretical basis for the fire resistance design and high-temperature performance improvement of concrete materials and structures.

Regularized coupling multiscale method for thermomechanical coupled problems

The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In the paper, we develop a regularized coupling multiscale method based on the generalized multiscale finite element method (GMsFEM) to solve coupled thermomechanical problems, and it is referred to as the coupling generalized multiscale finite element method (CGMsFEM). The method consists of defining the coupling multiscale basis functions through local regularized coupling spectral problems in each coarse-grid block, which can be implemented by a novel design of two relaxation parameters. Compared to the standard GMsFEM, the proposed method can not only accurately capture the multiscale coupling correlation effects of multiphysics problems but also greatly improve computational efficiency with fewer multiscale basis functions. In addition, the convergence analysis is also established, and the optimal error estimates are derived, where the upper bound of errors is independent of the magnitude of the relaxation coefficient. Several numerical examples for periodic, random microstructure, and random material coefficients are presented to validate the theoretical analysis. The numerical results show that the CGMsFEM shows better robustness and efficiency than uncoupled GMsFEM.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation, the numerical manifold method (NMM) adopts a double covering system, which can easily deal with discontinuous deformation problems and has a high calculation accuracy. Aiming at the thermo-mechanical (TM) coupling problem of fractured rock masses, this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field, deduces related system equations, and proposes a penalty function method to deal with boundary conditions. Numerical examples are employed to confirm the effectiveness and high accuracy of this method. By the thermal stress analysis of a thick-walled cylinder (TWC), the simulation of cracking in the TWC under heating and cooling conditions, and the simulation of thermal cracking of the Swedish Äspö Pillar Stability Experiment (APSE) rock column, the thermal stress, and TM coupling are obtained. The numerical simulation results are in good agreement with the test data and other numerical results, thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

A reduced-order modeling for thermo-mechanical coupling analyses by using radial integration boundary element method

In order to efficiently solve thermo-mechanical coupling problems, this work combines the radial integration boundary element method (RIBEM) and the proper orthogonal decomposition (POD) to construct a fast reduced-order model. This model transforms high-dimensional systems into low-dimensional ones, enabling faster computation of thermo-mechanical coupling problems under thermal loads. Firstly, RIBEM is employed to solve coupled thermoelastic dynamic problems under thermal shock loads. Domain integrals are converted to boundary integrals using the radial integration method, establishing a purely boundary element algorithm without internal cells. Subsequently, finite difference techniques are applied to calculate the discretized algebraic equations, and the obtained field variables are used as a snapshot matrix to establish POD modes and construct the POD reduced-order model. Numerical examples demonstrate that the results of the reduced-order model are essentially consistent with the full-order model across various physical parameters and boundary conditions. Therefore, this reduced-order model significantly improves computational efficiency while maintaining high accuracy, especially when solving large-scale problems.

Topology optimization for transient thermomechanical coupling problems

Thermal deformation is a cause of damage to mechanical components that operate at high temperatures, requiring structural designs that reduce thermal deformation. Given the changes in temperature and deformation that occur during the operation of devices containing mechanical components, nonstationarity is a key consideration. Therefore, we propose topology optimization for transient thermomechanical coupling problems. We focused on a thermoelastic model consisting of two-phase materials. We treated complete transient thermomechanical coupling problems in which we can consider the time dependence of both temperature and displacement. We applied the step-by-step integration method to deal with the arbitrary profiles of mechanical load and heat flux over time. An interpolation scheme of material properties was discussed as an approach to resolve the grayscale issues involved in the thermal load. We propose a highly accurate sensitivity analysis method for transient thermomechanical coupling problems. Numerical examples are presented to confirm the validity of the proposed method.

Development of the four-dimensional lattice spring model for thermo-mechanical fracturing and large deformation of solids

Thermo-mechanical coupling is a key issue in the fields of engineering structure security, geothermal energy exploitation, metal hot working, crustal evolution, etc. This work aims to further develop the four-dimensional lattice spring model (4D-LSM) to address thermo-mechanical coupling problems involving fracturing and large deformations. To reproduce the thermal governing equations, a thermal pipe network partially or completely duplicates the corresponding mechanical lattice, where Fourier's law is solved at the pipe level. Furthermore, two different time steps are adopted in the calculations of the equations of force and heat to enable the coupled model to address both transient and steady-state thermo-mechanical coupling problems. The influence of the thermal field on the mechanical responses is addressed through the thermal expansion equation, and the influence of fracturing and recontacting on the thermal connections of the pipe is considered. By introducing thermal damage functions, the influence of temperature on material properties has been considered in the coupled model. A series of examples are evaluated to verify the correctness and accuracy of the coupled thermo-mechanical 4D-LSM. Next, several application examples are analysed to show the ability of the coupled model to simulate the thermal fracturing of heterogeneous materials and the large deformation behaviours of solids.

Simulation of cryogenic fracturing of rock-like materials using material point method

Cryogenic fracturing is a relatively new technique used in gas and oil extraction. The material point method (MPM) combines the advantages of the Lagrangian and Eulerian methods and effectively solves problems involving fracture propagation and thermomechanical coupling. Hence, in this study, this method was applied to the simulation of cryogenic fracturing in rocks to reveal the mechanism of the process. First, the heat-conduction equation was discretized using the MPM. Subsequently, the thermomechanical-coupling problem was solved under the unified framework of the MPM. The discontinuous fields around the fracture were described, and fracture propagation was predicted using the phantom node method and interaction integral methods in the MPM. The results were then compared with finite-element simulation results to verify the feasibility of these methods. Finally, cryogenic fracturing simulations in the literature were examined, and the simulation results agreed well with the experimental results. Moreover, the distribution characteristics of thermal fractures were explained using the inhibitory interactions between fractures. The simulation results indicated that increasing the convective heat transfer coefficient results in a significant increase in the number of fractures.

Calculation accuracy of mathematical homogenization method for thermo-mechanical coupling problems

The paper analyzes the thermo-mechanical couplinag phenomenon under the condition of sliding contact, establishes the finite element analysis continuous model of thermo-mechanical coupling, and proposes the system dynamic equilibrium equation and thermodynamic equilibrium equation. The article analyzes the contact conditions between the objects in the system and obtains the objects? contact conditions? mathematical expression. On this basis, the constraint function is used to express the mathematical homogenization. We apply the variation principle to the constraint function and form a non-linear equation group with the system balance equation solve the thermal-mechanical coupling problem. The example shows that we use the constraint function method to solve the thermo-mechanical coupling problem, which has good convergence, stable algorithm, and the calculation result can reflect the actual situation.

A refined thermo-mechanical fully coupled peridynamics with application to concrete cracking

The accurate numerical prediction of concrete cracking under thermal or thermo-mechanical loads is essential and urgent due to the requirement of structure reliability and durability. In the present paper, a refined bond-based peridynamic approach for thermo-mechanical coupling problems is developed and applied to the thermal diffusion, thermal-induced deformation, and fracture of mesoscale concrete structures. Specifically, the classical differential thermo-mechanical equations are reformulated by applying the peridynamic differential operator on and thus converted to a novel nonlocal integral formulation, which is called a refined thermo-mechanical fully coupled peridynamics. It gets rid of the micro-conductivity and does not require any calibration procedure, and the temperature-deformation term is expressed in terms of the integral of displacement difference directly. Besides, A multi-rate explicit time integration scheme is applied to overcome different time-scale problems in multi-physical systems as well. Meanwhile, a new micro-conduction model is developed for the broken bonds, and the cracks are not assumed to be adiabatical herein. And, the fracture energy release rate is considered to be temperature-dependent. Moreover, three benchmark examples for thermal diffusion and fully coupled thermo-mechanical problems are analyzed to illustrate the correctness and accuracy of the proposed peridynamic approach. At last, the simulations of a thick-walled heterogeneous concrete cylinder geometrically modeled in two- and three-dimension suffering heating load are performed, whose cracking results agree well with corresponding experimental results.

A novel second-order reduced homogenization approach for nonlinear thermo-mechanical problems of axisymmetric structures with periodic micro-configurations

A novel second-order reduced homogenization (SORH) approach is introduced for analyzing dynamic thermo-mechanical coupling problems in axisymmetric inelastic structures with periodic micro-configuration. The axisymmetric heterogeneous structures are periodically distributed in radial and axial directions and homogeneous distribution in circumferential directions. Firstly, the nonlinear coupled thermo-mechanical model is proposed, and the high-order nonlinear local problems, effective material parameters and the nonlinear homogenization equations are derived successively by the multiscale asymptotic expansion. Further, in order to reduce the large computational amount evaluated by the classical multiscale homogenization approach, the reduced-order nonlinear multiscale models and the corresponding finite-element algorithms are established in detail. The key features of the proposed approach are that an efficient reduced-model form based on transformation field analysis (TFA) to analyze nonlinear local cell problems is proposed and a nonlinear thermo-mechanical problem which considers the mutual coupling for the temperature and displacement fields is computed. In particular, a new SORH algorithm is proposed for investigating the axisymmetric inelastic structures. Finally, three typical numerical experiments are carried out, and the effectiveness and correctness of our presented algorithms in simulating and predicting the macroscopic behavior of the heterogeneous structures are confirmed.

Thermal rectification enhancement of bi-segment thermal rectifier based on stress induced interface thermal contact resistance

Thermal rectification is the phenomenon that heat flows much easier from forward direction than reverse direction across the structure. Materials with temperature-dependent thermal conductivity and/or variable cross section area segments are always adopted to utilize obvious thermal rectification effect. Previous studies often ignored the effect of thermal contact resistance between the two segments of traditional bi-segment thermal rectifier. Since interface thermal contact resistance also contributes significantly to the total effective thermal conductivity of the rectifier, the present paper proposed a finite element scheme to simulate the thermomechanical coupling problem caused by the stress-dependent thermal contact resistance. The proposed method is verified and validated with analytical and experimental examples respectively, and numerical results show the effect of thermal contact resistance on the optimization of thermal rectification ratio. Several key parameters such as the initial gap between the two segments and the thermal contact resistance model parameters are investigated numerically, and the present paper provide a novel approach and design guidance to manipulate heat flux through stress-dependent thermal contact resistance.

The Rigid-Flexible-Thermal Coupled Analysis for Spacecraft Carrying Large-Aperture Paraboloid Antenna

Abstract Since the thermal load would adversely introduce degradation to the normal operation of spacecraft, resulting in unpredictable thermal-dynamic behavior, thermomechanical coupling problems are important and have been investigated extensively. Based on the absolute nodal coordinate formulation (ANCF), a thermal integrated ANCF thin plate element based on the unified description is constructed, which could depict the displacement and the temperature field integratedly. By means of the proposed element, the heat transfer and continuum mechanics are integrated in the unified finite element method (FEM) mesh of revolving paraboloid antenna. Additionally, the ANCF reference node is introduced for describing the rigid central hub where the antenna is mounted on to make the rigid-flexible-thermal coupled response being captured in a unified analysis procedure. The solar radiation input and the surface emitting radiation are included in the heat transfer equations. Furthermore, the influence of the rigid body motion and the deformation on the radiant absorption are also considered with the self-shadowing. The established rigid-flexible-thermal coupled simulation is performed on a modified generalized-α integrator which solves the set of multidisciplinary governing equations synchronously. For revealing the nonlinear behavior of the rigid-flexible-thermal coupled system, the observed thermally induced vibration and perturbation on the pointing accuracy of the spacecraft are given in the results, and the feasibility of the presented method is proved.

Thermo-mechanical analysis of nonlinear heterogeneous materials by second-order reduced asymptotic expansion approach

An effective second-order reduced asymptotic expansion (SRAE) approach is proposed to analyze the thermo-mechanical coupling problems of nonlinear periodic heterogeneous materials. The first-order and second-order nonlinear unit cell solutions at a microscale obtained by calculating the different multiscale cell functions are given at first. Then, the homogenization coefficients are evaluated, and the nonlinear homogenized equations defined on whole structure are solved, successively. Also, the temperature and displacement fields are constructed as second-order multiscale approximate solutions by assembling the distinct local cell solutions and homogenized solutions. The main features of the proposed approach are: (i) an effective model reduction scheme for computing high-order nonlinear unit cell problems and (ii) an asymptotic high-order homogenization solution that does not need high-order continuity of the macroscale solutions. Further, the corresponding finite element-difference algorithms based on the SRAE approach are given in detail. Finally, by some typical numerical examples, the availability and correctness of the proposed algorithms are confirmed. The computational results clearly demonstrate that the SRAE approach reported in this work are efficient and valid to predict the macroscopic thermo-mechanical properties, and can catch the microscale information of the heterogenous materials accurately.

Temperature-constrained topology optimization of thermo-mechanical coupled problems

ABSTRACTTemperature-constrained topology optimization for thermo-mechanical coupled problems under a design-dependent temperature field considering the thermal expansion effect remains an open problem. A temperature-constrained topology optimization method is proposed for thermo-mechanical coupled problems. In this article, the temperature values at the heat sources are constrained. The numerical results reveal that the temperature constraints play an important role in topology optimization of thermo-mechanical coupled problems. The optimized structure obtained by the presented method not only has certain strength but also decreases the temperature significantly compared with structures obtained by other methods without considering temperature constraints. The proposed method is applied to the design of the cooling system of a battery package. Numerical examples verify the efficiency of the presented method.

A Second-Order Two-Scale Algorithm for Thermo-Mechanical Coupling Problems in Quasi-Periodic Porous Materials

A Second-Order Two-Scale Algorithm for Thermo-Mechanical Coupling Problems in Quasi-Periodic Porous Materials

Mechanical Behavior and Damage Constitutive Model of Granite Under Coupling of Temperature and Dynamic Loading

Dynamic compression tests of Huashan granite were conducted using an improved split–Hopkinson pressure bar. The effects of the treatment temperature and strain rate on the mechanical behaviors (for example, the stress–strain curve, dynamic strength, elastic modulus, energy absorption, and failure mode) of the granite samples were explored. In addition, a statistical damage constitutive model for the rock was developed based on a Weibull distribution, and the influencing factors of the model parameters were analyzed. The results show that the enhancement effect of the strain rate on dynamic compressive strength under high temperatures still exists. However, the strain rate has no significant effect on the elastic modulus. The influences of the treatment temperature on the dynamic strength and elastic modulus are complex. There is a positive linear correlation between the energy absorbed by the sample and the incident energy. As the strain rate or incident energy increases, the failure modes of heat-treated samples change from axial splitting to pulverization. Under the same dynamic loading, an increase in the temperature can exacerbate the fragmentation degree of the sample. The proposed statistical damage constitutive model can accurately describe the effects of the treatment temperature and strain rate on the stress–strain responses of rock, and its parameters have definite physical meanings. Thus, the model is a very good tool for the analysis of thermo-mechanical coupling problems involved in deep rock mass engineering.

Transient Thermal Response of a Multilayered Geomaterial Subjected to a Heat Source

The analysis of layered geomaterials thermo-mechanical coupling response is important in design and analysis of a nuclear waste repository. Conventional analytical approaches usually have some intrinsic faults of ill-conditioned matrices for thick layers or accumulative numerical errors for a great quantity of layers for containing positive exponential functions. This paper presents a stable computational approach with no positive exponential functions to study the transient thermal responses of a layered geomaterial subjected to a heat source. Based on the governing equations of thermo-mechanical coupling problems, the analytical layer elements for a finite layer and a half–space are derived by utilizing Laplace and Hankel transforms. The analytical layer elements are then assembled into the total stiffness matrix and solved in the transformed domain. Finally, the Laplace–Hankel transform inversion is employed to obtain an actual solution in the physical domain. Numerical computations indicate that the difference of geomaterial mass properties between layers shows obvious effects on thermal response of the layered system, and these results can be served as a benchmark solution for future analyses of stratified material.