Mechanical Problems Research Articles

Novel techniques to analyze dynamical properties of quantum chaos with peculiar evidence of hybrid systems confinement

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

Recognition of local fiber orientation state in prepreg platelet molded composites via deep learning

This paper presents a novel deep learning approach for reconstruction of local through-the-thickness fiber orientation distribution (FOD) in discontinuous long-fiber, prepreg-platelet molded composites (PPMC). The thermal-residual strains on composite surfaces are used as inputs to train a fully convolutional neural network, named U-Net, to predict spatially varying, local FOD. High fidelity synthetic data was generated via computational simulation of PPMC with stochastic material orientation state and was used for training the deep learning model. The proposed U-Net model allowed for rapid recognition of PPMC morphology by solving the inverse structural mechanics problem of determining the average fiber orientation through the composite thickness based on the provided surface strain measurements. Upon training and validation, the U-Net deep learning model was deployed to rapidly predict complex distributions of the local through-the-thickness FOD in PPMC.

Convergence Results for History-Dependent Variational Inequalities

We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove that solving these problems is equivalent to solving the original history-dependent variational inequality. Next, we state and prove a convergence criterion, i.e., we provide necessary and sufficient conditions which guarantee the convergence of a sequence of functions to the solution of the considered inequality. Based on the equivalence above, we deduce various consequences that present some interest on their own, and, moreover, we obtain convergence results for the two additional problems considered. Finally, we apply our abstract results to the study of an inequality problem in solid mechanics. It concerns the study of a viscoelastic constitutive law with long memory and unilateral constraints, for which we deduce a convergence result and provide the corresponding mechanical interpretations.

Minimization principle for hemivariational–variational inequality driven by uniformly monotone operators with application to problems in contact mechanics

In this paper, we consider hemivariational–variational inequalities driven by uniformly monotone or d-monotone operators in Banach spaces. We establish related minimization principles leading to the existence and uniqueness of solutions to the inequality considered as well as we suggest the Ritz type numerical approximations. The theoretical results obtained are next applied to some problems inspired by models from contact mechanics.

PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation

The aim of this paper is to introduce the PLEIADES framework offering a set of services and numerical tools to model and simulate the behavior of nuclear fuels of different concepts of reactors. The framework provides in particular the following features: interfaces to manipulate meshes and fields, services to deal with different physical solvers, setup of coupling trees to realize multiphysics partitioned (accelerated) fixed point couplings, automated time-marching algorithm, checkpoint/restart strategies, capability to realize on-the-fly multiscale couplings. It is built with a permanent concern for sustainability, scalability and maintainability. PLEIADES framework supports multidimensional simulations, typically 1D, 2D and 3D, possibly multilayered. To date, this framework relies on the generic thermomechanical finite elements solver Cast3M to deal with partial derivative problems (mechanical, thermal or diffusion problems) at the scale of the structure or the (heterogeneous) microstructure. It also makes use of so-called point models (mainly based on ODE — ordinary differential equations) to describe the local (mesoscale) evolution of the material through the physics of irradiation. Several software applications are built on the PLEIADES framework, they can use its parallel features to use multiple processors. The multilayered calculation scheme provides a way to loosen the computations and access to a good parallel performance up to hundred cores. It is also possible to achieve efficient scalable concurrent multiscale simulations through finite element square (FE2) computational homogenization algorithms.

Design a cross-linked film based on cellulose nanocrystals doping for enhancing the interfacial performance and desensitization of CL-20

Despite the extensive researches on CL-20 crystals, the mechanical safety issues and process problems of CL-20 applications have not been studied in-depth. Herein, the cellulose nanocrystals (CNC) was doped in microcrystalline wax (MW), oxidized microcrystalline wax (OMW) and hydrogel (PPC) to design and fabricate the cross-linked CL-20 composites by simple water-suspension melting and freeze-drying methods. The composites were characterized by SEM, XPS, TG-DSC, XRD, mechanical sensitivity device and inclined chute tester. It is found that the CNC@OMW composite film exhibits excellent coating effect (99.96%) on CL-20 due to the cross-linking results. The Ea of CL-20 is increased from 190.92 to 388.71 kJ/mol under the synergistic effect of the excellent compatibility between components and the compact coating structure of CNC@OMW. Additionally, the film enhances the Tp0 of CL-20 from 218.15 to 222.66 ℃ and Tb from 220.27 to 223.73 ℃, respectively. While, the PPC@CNC only promoted Ea, Tp0 and Tb of CL-20–292.89.71 kJ/mol, 224.22 ℃ and 225.66 ℃, respectively. Besides, the XRD results confirms that three composite films dose not cause a transformation of the ε-CL-20 crystal phase. Most importantly, the cross-linked film brings mechanical sensitivity of CL-20 from 60 N and 3.5 J to a level of over 360 N and 10.4 J, comparable to WO3/Al nanothermite with 5 wt% polyaniline (360 N) and composite with 95 wt% LLM-105 and 5 wt% ternary (11–12 J). This improvement enables the composite explosives to be handled using standard procedures. Furthermore, the ability of the particles to accumulate electrostatic charge after cross-linking coating is significantly reduced, and PVC is more suitable as the contact material of CL-20 and composite particles than copper for use in the transportation and packaging. These findings can serve as a reference for wide application of CL-20.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials

Abstract Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This paper also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pre-trained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pre-training.

Triaxial Load Cell for Ergonomic Risk Assessment: A Study Case of Applied Force of Thumb

To assess the ergonomic risk level in work systems involving tasks performed with hands or fingers, it is necessary to know the exerted triaxial forces. To address this need, a prototype of a triaxial load cell based on principles of linear elasticity theory and mechanical problems of torsion, bending and axial load is presented. This work includes an analytical strain model for each instrumented point and its solution regarding the applied force to a triaxial load cell. The proposed load cell was calibrated and validated by performing different static experimental tests. As a case study, the applied force in three directions while the thumb activates a cigarette lighter was measured. Triaxial forces and resultant forces were obtained and compared with the parameter of 10 N established by the ergonomic standards as reference values for pressing down with the thumb, finding that the applied forces in eight tests were 23.73 N, 43.51 N, 12.69 N, 14.50 N 20.35 N, 21.67 N, 39.74 N and 46.02 N, exceeding the reference values and establishing a direct relationship with Quervain syndrome. In conclusion, the developed load cell is a valid and reliable alternative to measure many forces that cannot be obtained with commercial devices, allowing the level of ergonomic risk to be determined with great precision.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.

Axisymmetric virtual elements for problems of elasticity and plasticity

AbstractThe virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.

A new unified arc-length method for damage mechanics problems

A new unified arc-length method for damage mechanics problems

Solving forward and inverse problems of contact mechanics using physics-informed neural networks

This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush–Kuhn–Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer–Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.

Stabilization‐free virtual element method for 2D elastoplastic problems

AbstractIn this paper, a novel first‐ and second‐order stabilization‐free virtual element method is proposed for two‐dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher‐order projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization‐free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization‐free virtual element method.

An Ultra-soft Thermal Diode

The controlling of heat flow direction stands as a prominent methodological approach within the domain of thermal management, and this can be accomplished through the utilization of thermal diodes. However, if the thermal diode lacks mechanical compliance, hindering its intimate contact with heat source/sink surfaces, the thermal rectification performance is limited. In this work, we propose a method to solve the mechanical compliance problem that is introducing phase change material (PCM) consisting of dual alkanes (hexadecane and paraffine wax) and polyurethane to fabricate the heterojunction thermal diode. The fabricated thermal diode exhibits an ultra-soft mechanical feature, with a low elastic modulus of 0.4 KPa and >300 % elongation until failure – the best values reported to date for thermal diodes. The measured thermal rectification factor is as high as 1.42 – in line with the theoretical model prediction. Molecular dynamic simulations reveal that the thermal rectification mechanism of the PCM-based thermal diode originates from the crystal-amorphous phase transition of the hexadecane terminal as the temperature bias flips. Therefore, the heat flow in the forward direction is greater than the flux in the reverse direction. A series of experiments and finite element analyses are employed to verify the feasibility of thermal diodes for applications in real contexts like the civil engineering.

Fracture prediction on hydrogen-charge notched samples using a stress-state-dependent phenomenological model

There is a consensus for transitioning to clean energy sources to meet the world’s energy demands. Hydrogen is a candidate to supply green energy. However, hydrogen embrittlement (HE) in materials is an issue that needs to be assessed. Based on the damage concept, a straightforward and robust computational framework is presented to predict the harmful effects on material resistance caused by the HE phenomenon. The adopted model framework builds upon dealing with the coupled mechanical diffusion problem in a simplified approach by considering the local equilibrium between hydrogen concentration at interstitial sites and Cauchy stresses. A modified version of the Mohr–Coulomb criterion dependent on the stress triaxiality and Lode angle introduces a damage indicator parameter. The proposed model is applied to study the brittle intergranular fracture of a high-strength AISI 4135 steel. A detailed description of the stress state and hydrogen-driven failure parameters are presented for two specimens with different notch radii. The proposed model is implemented in a VUMAT subroutine and made available for download to the technical community for research and educational use. After calibrating the model parameters, the numerical results yield good agreements of the predicted fracture strength of notched hydrogen-charged samples compared to the experimental ones. Maximum differences of around 10% among experimental and numerical tests are observed.

Mathematics-Informed Neural Network for Acoustic Scattering by Parallel Plates

This paper proposes a mathematics-informed neural network (MINN) approach for resolving the long-term challenge in wave scattering modeling. The central innovation lies in integrating Cauchy–Riemann equations into machine learning architectures. By incorporating Cauchy integrals and boundary conditions, the neural network successfully learns to numerically produce matrix kernel factorization for Wiener–Hopf analytical models. To validate and demonstrate the approach, a benchmark case of wave scattering from parallel hard–soft plates is studied by comparing the machine learning results with the available analytical solutions. The proposed MINN approach could provide a new route to extensively enhance the theoretical modeling capability for several wave scattering and fluid mechanics problems. The code can be found at https://github.com/lscapku/MINN.

The glass transition as a boundary layer problem of the energy landscape kinetic master equations and its relationship with quantum path integrals

The glass transition is a process in which a non-periodic solid is obtained by fast cooling a melt. In this work, an analysis is made of the energy landscape kinetic equations that allow to describe such phenomena. In particular, it is shown that the glass transition occurs at the boundary layer of the energy landscape kinetic master equations, as solutions always have steep gradients and are very sensitive to the initial conditions. Moreover, it is discussed that the evolution operator is given by a path integral where the cooling rate plays a role akin to the Planck constant in a quantum mechanical problem. As an example, the kinetic equation properties of a two-level fully connected energy landscape system, capable of exhibiting both a glass and a thermodynamic phase transition, both of which are analytically solvable, are analysed in detail.

Risk Factors for Unplanned Early Implantable Port Catheter Removal in Adult Hematology Cancer Patients Receiving Chemotherapy: A Propensity Score Matching Study.

Implantable port catheter is a reliable vascular access for chemotherapy infusion in cancer patients. However, patients with hematology malignancies usually present with a myriad of blood cell abnormalities that put them at risk of infection and mechanical problems requiring catheter removal. This study aims to determine the risk factors associated with unplanned (catheter removal other than completion of treatment plan) early (within 90 days of catheter implantation) implantable port catheter removal. A retrospective, propensity score-matched study of 386 patients with hematology malignancies who received implantable venous access ports between January 2015 and December 2022. We conducted a univariate analysis to select the variables for propensity score matching. Patients with unplanned early implantable port catheter removal (early group) were matched 1:1 to patients without unplanned early removal (non-early group). Univariate analysis demonstrated a statistically significant difference between early and non-early groups for age (p = 0.048), hemoglobin level (p = 0.028), thrombocytopenia (p = 0.025), and PG-SGA (p < 0.001). Thrombocytopenia was the only independent risk factor with a statistically significant difference in Cox proportional hazard analysis, HR 2.823, 95 CI 1.050-7.589, p = 0.040. The median catheter survival for patients with thrombocytopenia was 61 days (95% CI 28.58-93.42) compared to 150 days (95% CI 9.81-290.19) for patients without thrombocytopenia, p = 0.015. Patient survival is not affected by early catheter removal. The median survival for patients in the early group was 28.28 months (95% CI 27.43-29.15) compared to 32.39 months (95% CI 24.11-40.68), for the non-early group, p = 0.709. Hematology malignancy patients with thrombocytopenia are at high risk for unplanned early port catheter removal without survival difference.

A Study on Power Transmission Control for Applying MR Fluid Multi-Plate Clutch to Automobile Power Distribution Device

The aim of this study is to design and manufacture a multi-plate clutch system that uses magnetorheological (MR) fluid control to allow for a variable power transmission ratio in power distribution systems. MR fluid is a smart material that enables presenting a solution to the shocks and power loss that occur due to mechanical problems in power distribution systems. As such, the longitudinal and lateral dynamic properties of 4WD (four-wheel drive) vehicles were examined and analyzed to develop an algorithm to control the front/rear power distribution according to the road surface state and driving conditions. To verify the algorithm, the CarSim vehicle dynamics simulation program was adopted to perform experiments to understand the vehicle’s dynamic performance improvements and turning stability via a HILS (Hardware in the Loop) system. In this study, an MR fluid, multi-plate clutch was used that combines a dry clutch and a wet clutch using the characteristics of the MR fluid. Such a clutch was designed to enable continuous and smooth torque transmission by utilizing the strengths of each of the dry and wet clutches. The CarSim vehicle dynamics program was used to conduct the experiments, which were conducted by linking to the manufactured MR fluid clutch experimental device. The experiments investigated the dynamic performance based on the power distribution ratio by performing longitudinal flat, inclined driving and lateral DLC (double lane change) driving. In summary, this study found that it is possible to perform power transmission by applying a current to an MR fluid and forming a magnetic field to change the flow properties of the fluid to control the torque transmission ratio that occurs in an MR fluid clutch.

Inverse design from the catenary problem

Inverse problems in science normally involve the challenge of obtaining from a set of observations the causal factors that generated them in the first place. However, physics students are seldom exposed to such problems as part of their training. Here we revisit the mechanics problem of finding the shape of a hanging cable, but this time in reverse, i.e. by asking what mass density a cable must have to follow a specific shape. This concept is then generalised into the possibility of identifying a cable whose hanging shape follows any form we wish to design. This inverted design strategy is experimentally verified with an inexpensive setup that is suitable for classroom activities.