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Keywords = coupled thermomechanical problem

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18 pages, 2673 KB  
Article
Thermo-Mechanical Approach to Material Extrusion Process During Fused Filament Fabrication of Polymeric Samples
by Mahmoud M. Farh and Viktor Gribniak
Materials 2025, 18(19), 4537; https://doi.org/10.3390/ma18194537 - 29 Sep 2025
Abstract
While material extrusion via fused filament fabrication (FFF) offers design flexibility and rapid prototyping, its practical use in engineering is limited by mechanical challenges, including residual stresses, geometric distortions, and potential interlayer debonding. These issues arise from the dynamic thermal profiles during FFF, [...] Read more.
While material extrusion via fused filament fabrication (FFF) offers design flexibility and rapid prototyping, its practical use in engineering is limited by mechanical challenges, including residual stresses, geometric distortions, and potential interlayer debonding. These issues arise from the dynamic thermal profiles during FFF, including temperature gradients, non-uniform hardening, and rapid thermal cycling, which lead to uneven internal stress development depending on fabrication parameters and object topology. These problems can compromise the structural integrity and mechanical properties of FFF parts, especially when the load-bearing capacity and geometric accuracy are critical. This study focuses on polylactic acid (PLA) due to its widespread application in engineering. It introduces a computational framework for coupled thermo-mechanical simulations of the FFF process using ABAQUS (Version 2020) finite element software. A key innovation is an automated subroutine that converts G-code into a time-resolved event series for finite element activation. The simulation framework explicitly models the sequential stages of printing, cooling, and detachment, enabling prediction of adhesive loss and post-process warpage. A transient thermal model evaluates the temperature distribution during FFF, providing boundary conditions for a mechanical simulation that predicts residual stresses and warping. Uniquely, the proposed model incorporates the detachment stage, enabling a more realistic and experimentally validated prediction of warpage and residual stress release in FFF-fabricated components. Although the average deviation between predicted and measured displacements is about 10.6%, the simulation adequately reflects the spatial distribution and magnitude of warpage, confirming its practical usefulness for process optimization and design validation. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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30 pages, 12280 KB  
Article
A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
by Lin Zhang, D. M. Li, Cen-Ying Liao and Li-Rui Tian
Mathematics 2025, 13(14), 2259; https://doi.org/10.3390/math13142259 - 12 Jul 2025
Viewed by 324
Abstract
A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation [...] Read more.
A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article
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24 pages, 2987 KB  
Article
Optimization of Engine Piston Performance Based on Multi-Method Coupling: Sensitivity Analysis, Response Surface Model, and Application of Genetic Algorithm
by Bin Zheng, Qintao Shui, Zhecheng Luo, Peihao Hu, Yunjin Yang, Jilin Lei and Guofu Yin
Materials 2025, 18(13), 3043; https://doi.org/10.3390/ma18133043 - 26 Jun 2025
Viewed by 542
Abstract
This paper focuses on the use of advanced optimization design strategies to improve the performance and service life of engine pistons, with emphasis on enhancing their stiffness, strength, and dynamic characteristics. As a core component of the engine, the structural design and optimization [...] Read more.
This paper focuses on the use of advanced optimization design strategies to improve the performance and service life of engine pistons, with emphasis on enhancing their stiffness, strength, and dynamic characteristics. As a core component of the engine, the structural design and optimization of the piston are of great significance to its efficiency and reliability. First, a three-dimensional (3D) model of the piston was constructed and imported into ANSYS Workbench for finite element modeling and high-quality meshing. Based on the empirical formula, the actual working environment temperature and heat transfer coefficient of the piston were accurately determined and used as boundary conditions for thermomechanical coupling analysis to accurately simulate the thermal and deformation state under complex working conditions. Dynamic characteristic analysis was used to obtain the displacement–frequency curve, providing key data support for predicting resonance behavior, evaluating structural strength, and optimizing the design. In the optimization stage, five geometric dimensions are selected as design variables. The deformation, mass, temperature, and the first to third natural frequencies are considered as optimization goals. The response surface model is constructed by means of the design of the experiments method, and the fitted model is evaluated in detail. The results show that the models are all significant. The adequacy of the model fitting is verified by the “Residuals vs. Run” plot, and potential data problems are identified. The “Predicted vs. Actual” plot is used to evaluate the fitting accuracy and prediction ability of the model for the experimental data, avoiding over-fitting or under-fitting problems, and guiding the optimization direction. Subsequently, the sensitivity analysis was carried out to reveal the variables that have a significant impact on the objective function, and in-depth analysis was conducted in combination with the response surface. The multi-objective genetic algorithm (MOGA), screening, and response surface methodology (RSM) were, respectively, used to comprehensively optimize the objective function. Through experiments and analysis, the optimal solution of the MOGA algorithm was selected for implementation. After optimization, the piston mass and deformation remained relatively stable, and the working temperature dropped from 312.75 °C to 308.07 °C, which is conducive to extending the component life and improving the thermal efficiency. The first to third natural frequencies increased from 1651.60 Hz to 1671.80 Hz, 1656.70 Hz to 1665.70 Hz, and 1752.90 Hz to 1776.50 Hz, respectively, significantly enhancing the dynamic stability and vibration resistance. This study integrates sensitivity analysis, response surface models, and genetic algorithms to solve multi-objective optimization problems, successfully improving piston performance. Full article
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27 pages, 3647 KB  
Article
A Hybrid RBF-PSO Framework for Real-Time Temperature Field Prediction and Hydration Heat Parameter Inversion in Mass Concrete Structures
by Shi Zheng, Lifen Lin, Wufeng Mao, Yanhong Wang, Jinsong Liu and Yili Yuan
Buildings 2025, 15(13), 2236; https://doi.org/10.3390/buildings15132236 - 26 Jun 2025
Viewed by 443
Abstract
This study proposes an RBF-PSO hybrid framework for efficient inversion analysis of hydration heat parameters in mass concrete temperature fields, addressing the computational inefficiency and accuracy limitations of traditional methods. By integrating a Radial Basis Function (RBF) surrogate model with Particle Swarm Optimization [...] Read more.
This study proposes an RBF-PSO hybrid framework for efficient inversion analysis of hydration heat parameters in mass concrete temperature fields, addressing the computational inefficiency and accuracy limitations of traditional methods. By integrating a Radial Basis Function (RBF) surrogate model with Particle Swarm Optimization (PSO), the method reduces reliance on costly finite element simulations while maintaining global search capabilities. Three objective functions—integral-type (F1), feature-driven (F2), and hybrid (F3)—were systematically compared using experimental data from a C40 concrete specimen under controlled curing. The hybrid F3, incorporating Dynamic Time Warping (DTW) for elastic time alignment and feature penalties for engineering-critical metrics, achieved superior performance with a 74% reduction in the prediction error (mean MAE = 1.0 °C) and <2% parameter identification errors, resolving the phase mismatches inherent in F2 and avoiding F1’s prohibitive computational costs (498 FEM calls). Comparative benchmarking against non-surrogate optimizers (PSO, CMA-ES) confirmed a 2.8–4.6× acceleration while maintaining accuracy. Sensitivity analysis identified the ultimate adiabatic temperature rise as the dominant parameter (78% variance contribution), followed by synergistic interactions between hydration rate parameters, and indirect coupling effects of boundary correction coefficients. These findings guided a phased optimization strategy, as follows: prioritizing high-precision calibration of dominant parameters while relaxing constraints on low-sensitivity variables, thereby balancing accuracy and computational efficiency. The framework establishes a closed-loop “monitoring-simulation-optimization” system, enabling real-time temperature prediction and dynamic curing strategy adjustments for heat stress mitigation. Robustness analysis under simulated sensor noise (σ ≤ 2.0 °C) validated operational reliability in field conditions. Validated through multi-sensor field data, this work advances computational intelligence applications in thermomechanical systems, offering a robust paradigm for parameter inversion in large-scale concrete structures and multi-physics coupling problems. Full article
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20 pages, 10342 KB  
Article
Investigation of the Thermo-Mechanical Modeling of the Manufacturing of Large-Scale Wire Arc Additive Manufacturing Components with an Outlook Towards Industrial Applications
by Tim Fritschle, Moritz Kaess, Stefan Weihe and Martin Werz
J. Manuf. Mater. Process. 2025, 9(5), 166; https://doi.org/10.3390/jmmp9050166 - 20 May 2025
Cited by 2 | Viewed by 1466
Abstract
The simulation of additive manufacturing processes, such as Wire Arc Additive Manufacturing (WAAM), is becoming increasingly important to predict material and component properties in advance of the real-life manufacturing. In contrast to prior work focusing on the simulation of simplified WAAM parts, this [...] Read more.
The simulation of additive manufacturing processes, such as Wire Arc Additive Manufacturing (WAAM), is becoming increasingly important to predict material and component properties in advance of the real-life manufacturing. In contrast to prior work focusing on the simulation of simplified WAAM parts, this paper presents an investigation into the thermo-mechanical finite element (FE) simulation of the manufacturing of large-scale WAAM components. The investigation focuses on various problems within the individual steps of the FE workflow wherein ABAQUS influences the modeling of large-scale components. The investigations are founded upon a thermo-mechanically coupled FE model in ABAQUS 2020. For this purpose, several thermo-mechanical simulation models are set up with the target of investigating the meshing, element activation and variation of process parameters. Appropriate discretization of WAAM components is found to be a major problem when setting up a simulation. The meshing of the component is limited by the element type and size and the meshing routines used. Also, differences in the axes of motion for the simulation and the real process cause the simulation to differ from reality. High element start temperatures are found to be beneficial for simulation stability and performance. An integrated parameter variation was made possible with the modeling techniques used. Full article
(This article belongs to the Special Issue Large-Scale Metal Additive Manufacturing)
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33 pages, 669 KB  
Article
On Anisothermal Electromagnetic Elastic Deformations in Flight in Fair Weather and Lightning Storms
by Luiz M. B. C. Campos and Manuel J. S. Silva
Appl. Sci. 2025, 15(7), 3605; https://doi.org/10.3390/app15073605 - 25 Mar 2025
Viewed by 318
Abstract
The thermomechanical effects on aircraft structures in flight are compared between fair weather and a lightning storm based on a model problem, namely, equations of anisothermal unsteady piezoelectromagnetism are solved in the particular case of a parallel-sided slab assuming (i) steady conditions and [...] Read more.
The thermomechanical effects on aircraft structures in flight are compared between fair weather and a lightning storm based on a model problem, namely, equations of anisothermal unsteady piezoelectromagnetism are solved in the particular case of a parallel-sided slab assuming (i) steady conditions and spatial dependence only on the coordinate orthogonal to the slab; (ii) the displacement vector orthogonal to the slab; (iii) the magnetic field orthogonal to the electric field, with both in the plane parallel to the sides of the slab. The exact analytical solution is obtained in the linear approximation for the displacement vector, electric and magnetic fields and temperature as function of the coordinate normal to the slab, taking into account heating by the Joule effect of Ohmic electric currents and Fourier thermal conduction. These specify the strain and stress tensors, the electric current and the heat flux. The material properties involved include the mass density, dielectric permittivity, magnetic permeability, elastic stiffness tensor, electromagnetic coupling and thermal stress tensors, pyroelectric and pyromagnetic vectors and piezoelectric and piezomagnetic tensors. The analytic results of the theory are simplified assuming (i) isotropic material properties; (ii) a steady state independent of time. The profiles as a function of the coordinate normal to the slab of the electric and magnetic fields, temperature and heat flux and displacement, strain and stress are obtained in these conditions. Full article
(This article belongs to the Special Issue Novel Applications of Electromagnetic Energy Systems)
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17 pages, 2985 KB  
Article
Buckling Analysis of Functionally Graded GPL-Reinforced Composite Plates Under Combined Thermal and Mechanical Loads
by Jin-Rae Cho
Materials 2025, 18(3), 567; https://doi.org/10.3390/ma18030567 - 26 Jan 2025
Cited by 2 | Viewed by 973
Abstract
The buckling-like mechanical behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) structures is increasingly attracting research attention. However, buckling behavior has previously been studied separately as thermal buckling and mechanical buckling. In this context, this study investigates the buckling behavior of FG-GPLRC plates [...] Read more.
The buckling-like mechanical behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) structures is increasingly attracting research attention. However, buckling behavior has previously been studied separately as thermal buckling and mechanical buckling. In this context, this study investigates the buckling behavior of FG-GPLRC plates under combined thermal and mechanical loads. The coupled buckling problem is formulated according to the minimum potential energy theorem using first-order shear deformation theory (FSDT). In addition, the problem is approximated by the 2-D natural element method (NEM), and the resulting coupled eigen matrix equations are derived to compute the critical buckling temperature rise (CBTR) and the mechanical buckling load. The developed numerical method can solve thermal, mechanical, and coupled thermo-mechanical buckling problems, and its reliability is examined through convergence and benchmark tests. Using the developed numerical method, the buckling behavior of FG-GPLRC plates under thermal and mechanical buckling loads is examined in depth with respect to the key parameters. In addition, a comparison with functionally graded CNT-reinforced composite (FG-CNTRC) plates is also presented. Full article
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18 pages, 7292 KB  
Article
Part-Scale Thermomechanical and Grain Structure Modeling for Additive Manufacturing: Status and Perspectives
by Yancheng Zhang, Gildas Guillemot, Théophile Camus, Oriane Senninger, Michel Bellet and Charles-André Gandin
Metals 2024, 14(10), 1173; https://doi.org/10.3390/met14101173 - 16 Oct 2024
Cited by 2 | Viewed by 1316
Abstract
Thermomechanical modeling of additively manufactured parts made by laser powder bed fusion aims to control stresses and distortions built during processing. This is, by nature, a multiscale metallurgical and mechanical problem, notably due to the strong texture of the grain structure that results [...] Read more.
Thermomechanical modeling of additively manufactured parts made by laser powder bed fusion aims to control stresses and distortions built during processing. This is, by nature, a multiscale metallurgical and mechanical problem, notably due to the strong texture of the grain structure that results from the process and may locally dictate the thermomechanical behavior law. Similarly, stresses and distortions are directly influenced by the heat transfer process at the system scale, including the consequences of the link between the part and the substrate and the weaker interactions with the powder bed and the gas environment. To achieve relevant modeling, we first demonstrate capabilities to assess at part scale, both i- the prediction of the grain structure and ii- the thermomechanical analyses. A discussion follows that summarizes the foreseen directions to achieve coupling and/or chaining between grain structure simulations and mechanical analyses at part scale. Full article
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19 pages, 32780 KB  
Article
Coupled Non-Ordinary State-Based Peridynamics Model for Ductile and Brittle Solids Subjected to Thermal Shocks
by Hui Li, Hanbo Zhang, Yixiong Zhang, Xiaoming Bai, Xuejiao Shao and Bingyang Wu
Appl. Sci. 2024, 14(16), 6927; https://doi.org/10.3390/app14166927 - 7 Aug 2024
Cited by 2 | Viewed by 1426
Abstract
A coupled thermomechanical non-ordinary state-based peridynamics (NOSB-PD) model is developed to simulate the dynamic response arising from temperature and to predict the crack propagation with thermal shocks in brittle and ductile solids. A unified multiaxial constitutive model with damage growth is proposed to [...] Read more.
A coupled thermomechanical non-ordinary state-based peridynamics (NOSB-PD) model is developed to simulate the dynamic response arising from temperature and to predict the crack propagation with thermal shocks in brittle and ductile solids. A unified multiaxial constitutive model with damage growth is proposed to simultaneously describe the ductile and brittle fracture mechanisms. The main idea is the use of Lemaitre’s model to describe ductile damage behavior and the use of tensile strength instead of yield stress in Lemaitre’s model to describe brittle damage behavior. A damage-related fracture criterion is presented in the PD framework to predict crack propagation, which avoids numerical oscillations when using the traditional bond stretch criterion. To capture the dynamic plastic response induced by thermal shocks, the time and stress integration are achieved by an alternating solving strategy and implicit return-mapping algorithm. Several numerical examples are presented to show the performance of the proposed model. Firstly, a thermomechanical problem simulation based on both the proposed model and the FEM illustrate the accuracy of the proposed model in studying the thermal deformation. Moreover, a benchmark brittle fracture example of the Kalthoff–Winkler impact test is simulated, and the crack path and angle are similar to the experimental observations. In addition, the simulation of ductile fracture under different loads illustrates the effect of temperature on crack propagation. Finally, the simulation of the 2D quenching test shows the ability of the proposed model in predicting crack propagation under thermal shocks. Full article
(This article belongs to the Section Applied Thermal Engineering)
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36 pages, 8255 KB  
Article
Feasible Actuator Range Modifier (FARM), a Tool Aiding the Solution of Unit Dispatch Problems for Advanced Energy Systems
by Haoyu Wang, Roberto Ponciroli, Andrea Alfonsi, Paul W. Talbot, Thomas W. Elmer, Aaron S. Epiney and Richard B. Vilim
Energies 2024, 17(12), 2945; https://doi.org/10.3390/en17122945 - 14 Jun 2024
Cited by 1 | Viewed by 1647
Abstract
Integrated energy systems (IESs) seek to minimize power generating costs in future power grids through the coupling of different energy technologies. To accommodate fluctuations in load demand due to the penetration of renewable energy sources, flexible operation capabilities must be fully exploited, and [...] Read more.
Integrated energy systems (IESs) seek to minimize power generating costs in future power grids through the coupling of different energy technologies. To accommodate fluctuations in load demand due to the penetration of renewable energy sources, flexible operation capabilities must be fully exploited, and even power plants that are traditionally considered as base-load units need to be operated according to unconventional paradigms. Thermomechanical loads induced by frequent power adjustments can accelerate the wear and tear. If a unit is flexibly operated without respecting limits on materials, the risk of failures of expensive components will eventually increase, nullifying the additional profits ensured by flexible operation. In addition to the bounds on power variations (explicit constraints),the solution of the unit dispatch problem needs to meet the limits on the variation of key process variables, including temperature, pressure and flow rate (implicit constraints).The FARM (Feasible Actuator Range Modifier) module was developed to enable existing optimization algorithms to identify solutions to the unit dispatch problem that are both economically favorable and technologically sustainable. Thanks to the iterative dispatcher–validator scheme, FARM permits addressing all the imposed constraints without excessively increasing the computational costs. In this work, the algorithms constituting the module are described, and the performance was assessed by solving the unit dispatch problem for an IES composed of three units, i.e., balance of plant, gas turbine, and high-temperature steam electrolysis. Finally, the FARM module provides dedicated tools for visualizing the response of the constrained variables of interest during operational transients and a tool aiding the operator at making decisions. These techniques might represent the first step towards the deployment of an ecological interface design (EID) for IES units. Full article
(This article belongs to the Section F: Electrical Engineering)
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16 pages, 8680 KB  
Article
Determination of Laser Parameters in Thermomechanical Treatment of Skin Based on Response Surface Methodology
by Hasan Mhd Nazha, Mhd Ayham Darwich, Basem Ammar, Hala Dakkak and Daniel Juhre
Appl. Sci. 2024, 14(6), 2619; https://doi.org/10.3390/app14062619 - 21 Mar 2024
Cited by 1 | Viewed by 1790
Abstract
An investigation was conducted to examine the photothermal and thermomechanical effects of short-pulse laser irradiation on normal tissues. This study analyzed the impact of short-pulse laser radiation on the heat-affected region within tissues, taking into consideration a set of laser variables, namely wavelength, [...] Read more.
An investigation was conducted to examine the photothermal and thermomechanical effects of short-pulse laser irradiation on normal tissues. This study analyzed the impact of short-pulse laser radiation on the heat-affected region within tissues, taking into consideration a set of laser variables, namely wavelength, intensity, beam size, and exposure time. The beam size ranged between 0.5 and 3 mm, and the intensity of the laser radiation ranged from 1 to 5 W/mm2 at wavelengths of 532 and 800 nm. A three-layered, three-dimensional model was implemented and studied in a polar coordinate system (r = 10 mm, z = 12 mm) in COMSOL Multiphysics (version 5.4, COMSOL Inc., Stockholm, Sweden) to perform numerical simulations. The Pennes bioheat transfer model, Beer-Lambert, and Hooke’s law are integrated to simulate the coupled biophysics problem. Temperature and stress distributions resulting from laser radiation were produced and analyzed. The accuracy of the developed model was qualitatively verified by comparing temperature and mechanical variations following the variations of laser parameters with relevant studies. The results of Box-Behnken analysis showed that beam size (S) had no significant impact on the response variables, with p-values exceeding 0.05. Temperature (Tmax) demonstrates sensitivity to both beam intensity (I) and exposure time (T), jointly contributing to 89.6% of the observed variation. Conversely, while beam size (S) has no significant effect on stress value (Smax), wavelength (W), beam intensity (I), and exposure time (T) collectively account for 71.6% of the observed variation in Smax. It is recommended to use this model to obtain the optimal values of the laser treatment corresponding to tissue with specified dimensions and properties. Full article
(This article belongs to the Section Optics and Lasers)
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33 pages, 1042 KB  
Article
Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model
by Christoph Hartmann and Michael Obermeyer
Materials 2024, 17(5), 1078; https://doi.org/10.3390/ma17051078 - 26 Feb 2024
Viewed by 1550
Abstract
Temperature evolution during plastic deformation is of great importance for the design of manufacturing processes, as well as for the analysis and prediction of tool wear. However, the results from experimental- and numerical-type research are still often contradictory. In this paper, we analyze [...] Read more.
Temperature evolution during plastic deformation is of great importance for the design of manufacturing processes, as well as for the analysis and prediction of tool wear. However, the results from experimental- and numerical-type research are still often contradictory. In this paper, we analyze methods for estimating plasticity-induced heating directly from displacement fields that can be recorded during experiments or extracted from simulation results. In terms of computational methodology, the thermodynamically motivated energy-based variational formulation of the coupled thermo-mechanical boundary-value problem is adapted to the problem at hand. Since an analysis of this variational formulation exhibits challenges and distinct inconsistencies with respect to the problem at hand, an alternative approach is proposed. This alternative approach is essentially a purely thermal finite element simulation, and it is conducted using a heat source term that is empirically based on the fraction of irreversible deformation work converted to heat. Our approach estimates plasticity-induced heating based on the strain and strain rate data derived from displacement fields. We therefore incorporate thermo-visco-plastic constitutive behavior (Johnson–Cook) with a thermodynamically motivated model that specifies the fraction of plastic work converted to heat (the Taylor–Quinney coefficient). Full article
(This article belongs to the Section Mechanics of Materials)
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21 pages, 1007 KB  
Article
Symmetry Properties of Models for Reversible and Irreversible Thermodynamic Processes
by S. A. Lurie, P. A. Belov and H. A. Matevossian
Symmetry 2023, 15(12), 2173; https://doi.org/10.3390/sym15122173 - 7 Dec 2023
Cited by 2 | Viewed by 1434
Abstract
The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible [...] Read more.
The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible processes, an algorithm based on the principle of stationarity of the functional is incorrect. In this paper, to formulate a variational model of irreversible deformation processes with an expanded range of coupled effects, an approach is developed based on the idea of the introduction of the non-integrable variational forms that clearly separate dissipative processes from reversible deformation processes. The fundamental nature of the properties of symmetry and anti-symmetry of tensors of physical properties in relation to multi-indices characterizing independent arguments of bilinear forms in the variational formulation of models of thermomechanical processes has been established. For reversible processes, physical property tensors must necessarily be symmetric with respect to multi-indices. On the contrary, for irreversible thermomechanical processes, the tensors of physical properties that determine non-integrable variational forms must be antisymmetric with respect to the permutation of multi-indices. As a result, an algorithm for obtaining variational models of dissipative irreversible processes is proposed. This algorithm is based on determining the required number of dissipative channels and adding them to the known model of a reversible process. Dissipation channels are introduced as non-integrable variational forms that are linear in the variations of the arguments. The hydrodynamic models of Darcy, Navier–Stokes, and Brinkman are considered, each of which is determined by a different set of dissipation channels. As another example, a variational model of heat transfer processes is presented. The equations of heat conduction laws are obtained as compatibility equations by excluding the introduced thermal potential from the constitutive equations for temperature and heat flux. The Fourier and Maxwell–Cattaneo equations and the generalized heat conduction laws of Gaer–Krumhansl and Jeffrey are formulated. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos II)
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15 pages, 683 KB  
Article
Finite Element Error Analysis of a Viscoelastic Timoshenko Beam with Thermodiffusion Effects
by Jacobo G. Baldonedo, José R. Fernández, Abraham Segade and Sofía Suárez
Mathematics 2023, 11(13), 2900; https://doi.org/10.3390/math11132900 - 28 Jun 2023
Viewed by 1401
Abstract
In this paper, a thermomechanical problem involving a viscoelastic Timoshenko beam is analyzed from a numerical point of view. The so-called thermodiffusion effects are also included in the model. The problem is written as a linear system composed of two second-order-in-time partial differential [...] Read more.
In this paper, a thermomechanical problem involving a viscoelastic Timoshenko beam is analyzed from a numerical point of view. The so-called thermodiffusion effects are also included in the model. The problem is written as a linear system composed of two second-order-in-time partial differential equations for the transverse displacement and the rotational movement, and two first-order-in-time partial differential equations for the temperature and the chemical potential. The corresponding variational formulation leads to a coupled system of first-order linear variational equations written in terms of the transverse velocity, the rotation speed, the temperature and the chemical potential. The existence and uniqueness of solutions, as well as the energy decay property, are stated. Then, we focus on the numerical approximation of this weak problem by using the implicit Euler scheme to discretize the time derivatives and the classical finite element method to approximate the spatial variable. A discrete stability property and some a priori error estimates are shown, from which we can conclude the linear convergence of the approximations under suitable additional regularity conditions. Finally, some numerical simulations are performed to demonstrate the accuracy of the scheme, the behavior of the discrete energy decay and the dependence of the solution with respect to some parameters. Full article
(This article belongs to the Topic Numerical Methods for Partial Differential Equations)
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16 pages, 15240 KB  
Article
Instantaneous Ablation Behavior of Laminated CFRP by High-Power Continuous-Wave Laser Irradiation in Supersonic Wind Tunnel
by Te Ma, Jiangtao Wang, Hongwei Song, Ruixing Wang and Wu Yuan
Materials 2023, 16(2), 790; https://doi.org/10.3390/ma16020790 - 13 Jan 2023
Cited by 3 | Viewed by 2574
Abstract
Experimental and numerical investigations of the instantaneous ablation behavior of laminated carbon fiber-reinforced polymer (CFRP) exposed to an intense continuous-wave (CW) laser in a supersonic wind tunnel are reported. We establish an in situ observation measurement in the experiments to examine the instantaneous [...] Read more.
Experimental and numerical investigations of the instantaneous ablation behavior of laminated carbon fiber-reinforced polymer (CFRP) exposed to an intense continuous-wave (CW) laser in a supersonic wind tunnel are reported. We establish an in situ observation measurement in the experiments to examine the instantaneous ablation behavior. The surface recession depth is calculated by using the Particle Image Velocimetry (PIV) method, taking the ply angle of laminated CFRP as a reference. A coupled thermal-fluid-ablation numerical model incorporating mechanisms of oxidation, sublimation, and thermomechanical erosion is developed to solve the ablation-through problem of multilayer materials. The results show that the laser ablation depth is related to the laser power density, airflow velocity and airflow mode. Thermomechanical erosion is the primary ablation mechanism when the surface temperature is relatively low and the cavity flow mode is a closed cavity flow. When the surface temperature reaches the sublimation of carbon and the airflow mode is transformed to open cavity flow, sublimation plays a dominant role and the ablation rate of thermomechanical erosion gradually decreases. Full article
(This article belongs to the Special Issue Advanced Laser Ablation and Damage in Materials)
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