Mechanical Boundary Conditions Research Articles

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

An analysis is performed in this research to examine the thermally induced vibrations in skew cylindrical shells. It is assumed that shell is made from a composite laminated material where each layer is reinforced with graphene platelets (GPLs). The amount of GPLs in the layers may be different which results in a piecewise functionally graded media. The one-dimensional transient heat conduction equation is established through the thickness of the shell. Heat conduction equation is solved using the finite difference method for each layer and continuity of temperature and heat flux is applied between the layers. Crank Nicolson algorithm is implemented to obtain the temperature profile at each time step and after that thermally induced force and moment are evaluated. The kinematics of the shell are estimated following the first order shear deformation shell theory. Also it should be noted that an oblique coordinates system in addition to orthogonal system is defined which make it easier to apply the boundary conditions. The definition of strain and kinetic energies are constructed and Following the Ritz method whose shape functions are estimated by Chebyshev polynomials, energies are provided in discrete form of the governing equations. Results of this study are provided to explore the effects of thermal and mechanical boundary conditions, geometry of the shell, weight fraction and distribution patterns of GPLs. It is highlighted that thermally induced vibrations indeed exist especially in thin class of shells.

Biomechanics of Macrophages on Disordered Surface Nanotopography.

Macrophages are involved in every stage of the innate/inflammatory immune responses in the body tissues, including the resolution of the reaction, and they do so in close collaboration with the extracellular matrix (ECM). Simplified substrates with nanotopographical features attempt to mimic the structural properties of the ECM to clarify the functional features of the interaction of the ECM with macrophages. We still have a limited understanding of the macrophage behavior upon interaction with disordered nanotopography, especially with features smaller than 10 nm. Here, we combine atomic force microscopy (AFM), finite element modeling (FEM), and quantitative biochemical approaches in order to understand the mechanotransduction from the nanostructured surface into cellular responses. AFM experiments show a decrease of macrophage stiffness, measured with the Young's modulus, as a biomechanical response to a nanostructured (ns-) ZrOx surface. FEM experiments suggest that ZrOx surfaces with increasing roughness represent weaker mechanical boundary conditions. The mechanical cues from the substrate are transduced into the cell through the formation of integrin-regulated focal adhesions and cytoskeletal reorganization, which, in turn, modulate cell biomechanics by downregulating cell stiffness. Surface nanotopography and consequent biomechanical response impact the overall behavior of macrophages by increasing movement and phagocytic ability without significantly influencing their inflammatory behavior. Our study suggests a strong potential of surface nanotopography for the regulation of macrophage functions, which implies a prospective application relative to coating technology for biomedical devices.

Revealing the three-dimensional arrangement of polar topology in nanoparticles

In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

Incorporation of self-heating effect into a thermo-mechanical coupled constitutive modelling for elastomeric polyurethane

Elastomeric polyurethane (EPU) is characterised by distinctive mechanical properties, including high toughness, low glass transition temperature, and high impact resistance, that render it indispensable in diverse engineering applications from soft robotics to anti-collision devices. This study presents a thermo-mechanically coupled constitutive model for EPU, systematically incorporating hyperelasticity, viscoelasticity, thermal expansion, and self-heating effect in a thermodynamically consistent manner. Experimental data, obtained from previous studies, are then used for parameter identification and model validation, including iterative updates for temperature parameters considering the self-heating effect. Subsequently, the validated model is integrated into finite element codes, i.e., user subroutine to define a material’s mechanical behaviour (UMAT) based on the commercial finite element software ABAQUS, for the computation of three-dimensional stress-strain states, facilitating the analysis of the structural response to various mechanical loads and boundary conditions. The results obtained from simulations are compared with analytical solutions to confirm the precision of Finite Element Method (FEM) implementation. The self-heating effect is further analysed under different strain rates and temperatures. To validate the engineering significance of the FEM implementation, a plate with a hole structure is also simulated. In conclusion, this research provides a robust tool for engineers and researchers working with soft materials, enhancing their understanding and predictive capabilities, notably addressing the self-heating effect in thermo-mechanical behaviours.

Локализованные акустические волны в одномерных периодически модулированных структурах

A number of one-dimensional phononic crystals, which are periodic thin-film structures of various geometries, consisting of sets of columns and metal inclusions located on a piezoelectric half-space, have been proposed and studied. The features of propagation in such structures of acoustic waves localized near the free surface and inhomogeneous inclusions have been studied. An unusual behavior of the dispersion curves for the studied localized modes was discovered. Particular attention is drawn to the so-called forbidden zones, i.e. frequency ranges in which there are no propagating localized modes. The influence of mechanical and electrical boundary conditions on the spectrum of the waves under study is discussed in detail.

Quantifying the mechanical degradation of solid oxide cells based on 3D reconstructions of the real microstructure using a unified multiphysics coupling numerical framework

In this work, a multiphysics coupling numerical framework is developed to quantitatively investigate the initial performances of solid oxide cells (SOCs) based on the thermodynamically consistent integration of the finite element method (FEM) and the phase field method (PFM) to reveal the interaction between species-defect transport, electrochemical reaction kinetics, stress and mechanical damage in SOC electrodes. The modeling framework is validated by comparing the simulation results based on real 3D microstructure reconstructions of specific SOCs with the experimental measurements in electrolysis and fuel cell modes. The phenomena of internal microstructure fracture and delamination observed in the experiment thus can be numerically modeled to quantify the effects of thermal and chemical stresses on the mechanical degradation of heterogeneous electrodes. The framework is also applied in the cross-scale quantification of the possible mechanical damage in SOCs subjected to different mechanical boundary conditions. The framework proposed in this work is flexible, can be superimposed with other fields, and incorporates input from cross-scale simulations. It provides a great potential platform for the optimization of future energy devices considering actual operating conditions and fills the gap in theoretical multiphysics modeling in the field of SOCs.

Macroscopic Polarization from Nonlinear Gradient Couplings.

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

Coherent Phase Change in Interstitial Solutions: A Hierarchy of Instabilities.

Metal hydrides or lithium ion battery electrodes can take the form of interstitial solid solutions with a miscibility gap. This work discusses theory approaches for locating, in temperature-composition space, coherent phase transformations during the charging/discharging of such systems and for identifying the associated transformation mechanisms. The focus is on the simplest scenario, where instabilities derive from the thermodynamics of the bulk phase alone, considering strain energy as the foremost consequence of coherency and admitting for stress relaxation at free surfaces. The extension of the approach to include capillarity is demonstrated by an example. The analysis rests on constrained equilibrium phase diagrams that are informed by geometry- and dimensionality-specific mechanical boundary conditions and on elastic instabilities-again geometry-specific-as implied by the theory of open-system elasticity. It is demonstrated that some scenarios afford the analysis of chemical stability to be based entirely on a linear stability analysis of the mechanical equilibrium, which provides closed-form solutions in a straightforward manner. Attention is on the impact of the system geometry (infinitely extended or of finite size) and on the chemical (closed or open system) and mechanical (incoherent or coherent) boundary conditions. Transformation mechanism maps are suggested for documenting the findings. The maps reveal a hierarchy of instabilities, which depend strongly on each of the above characteristics. Specifically, realistic, finite-sized systems differ qualitatively from idealized systems of infinite extension. Among the transformation mechanisms exposed by the analysis are a uniform switchover to the other phase when the open system reaches its chemical spinodal, practical coherent nucleation, as well as chemo-elastically coupled spontaneous buckling modes, which may take the form of either, single-phase or dual-phasestates.

Efficient finite strain elasticity solver for phase-field simulations

We present an effective mechanical equilibrium solution algorithm suitable for finite strain consideration within the phase-field method. The proposed algorithm utilizes a Fourier space solution in its core. The performance of the proposed algorithm is demonstrated using the St. Venant–Kirchhoff hyperelastic model, but the algorithm is also applicable to other hyperelastic models. The use of the fast Fourier transformation routines and fast convergence within several iterations for most common simulation scenarios makes the proposed algorithm suitable for phase-field simulations of rapidly evolving microstructures. Additionally, the proposed algorithm allows using different strain measures depending on the requirements of the underlying problem. The algorithm is implemented in the OpenPhase phase-field simulation library. A set of example simulations ranging from simple geometries to complex microstructures is presented. The effect of different externally applied mechanical boundary conditions and internal forces is also demonstrated. The proposed algorithm can be considered a straightforward update to already existing small strain solvers based on Fourier space solutions.

Validated, high-resolution, non-linear, explicit finite element models for simulating screw - bone interaction

Background and ObjectivePrimary stability evaluation of screw implants through pull-out or push-in experiments is commonly used to investigate the mechanism of screw loosening. Numerical models simulating these testing methods could provide an enhanced understanding of the underlying attachment mechanisms as well as save time and cost in the development of new screws. However, previous numerical models have been limited by compromises between modelling the trabecular structure at high resolution versus incorporating sophisticated mechanical properties and boundary conditions, leading to overestimated mechanical performance. The aim of this study was to overcome these limitations. MethodsWe developed explicit models incorporating the microstructure of trabecular bone, with frictional contact, and a non-linear material model incorporating damage. One model digitally inserted the screw into the trabecular bone structure using Boolean operations, while another model simulated the screw's rotational insertion. ResultsThe results showed a strong correlation between numerical and experimental results (R2: 0.54–0.93) for force-displacement response in terms of stiffness and strength. We found that the damage induced by the screw insertion process is an important factor to be considered, as the absence of modelling it led to an overestimated stiffness in previous studies. ConclusionsThe study highlights the importance of including frictional contact and also identified screw insertion damage as an important part of the simulating screw-bone interaction. Our findings demonstrate the potential of explicit finite element models for accurately replicating experimental push-in results and optimizing orthopaedic screws. The code is available at https://github.com/zhou436/Bone-Screw-Constructs-eFEM.

A 2D ferroelectric vortex pattern in twisted BaTiO3 freestanding layers

The wealth of complex polar topologies1–10 recently found in nanoscale ferroelectrics results from a delicate balance between the intrinsic tendency of the materials to develop a homogeneous polarization and the electric and mechanical boundary conditions imposed on them. Ferroelectric–dielectric interfaces are model systems in which polarization curling originates from open circuit-like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux-closure11–14 domains that evolve into vortex-like structures at the nanoscale15–17 level. Although ferroelectricity is known to couple strongly with strain (both homogeneous18 and inhomogeneous19,20), the effect of mechanical constraints21 on thin-film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles provides an opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated with the twisting. Furthermore, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding provides opportunities to create two-dimensional high-density vortex crystals that would enable us to explore previously unknown physical effects and functionalities.

Reconfigurable Growth of Engineered Living Materials.

The growth of multicellular organisms is a process akin to additive manufacturing where cellular proliferation and mechanical boundary conditions, amongst other factors, drive morphogenesis. Engineers have limited ability to engineer morphogenesis to manufacture goods or to reconfigure materials comprised of biomass. Herein, a method that uses biological processes to grow and regrow magnetic engineered living materials (mELMs) into desired geometries is reported. These composites contain Saccharomyces cerevisiae and magnetic particles within a hydrogel matrix. The reconfigurable manufacturing process relies on the growth of living cells, magnetic forces, and elastic recovery of the hydrogel. The mELM then adopts a form in an external magnetic field. Yeast within the material proliferate, resulting in 259 ± 14% volume expansion. Yeast proliferation fixes the magnetic deformation, even when the magnetic field is removed. The shape fixity can be up to 99.3 ± 0.3%. The grown mELM can recover up to 73.9 ± 1.9% of the original form by removing yeast cell walls. The directed growth and recovery process can be repeated at least five times. This work enables ELMs to be processed and reprocessed into user-defined geometries without external material deposition. This article is protected by copyright. All rights reserved.

Arbitrary-Order Sensitivity Analysis in Wave Propagation Problems Using Hypercomplex Spectral Finite Element Method

Many modern structural health monitoring (SHM) systems use piezoelectric transducers to induce and measure guided waves propagating in structures for structural damage detection. To increase the detection capabilities of SHM systems, gradient-based optimization of sensor placement is frequently necessary. However, available numerical differentiation methods for mechanical wave propagation problems suffer from truncation and subtraction errors and are difficult to extend to high-order sensitivities. This paper addresses these issues by introducing an approach to obtain highly accurate numerical sensitivities of arbitrary order in mechanical wave propagation problems. The hypercomplex time-domain spectral finite element method (ZSFEM) couples the hypercomplex Taylor series expansion method with the time-domain spectral finite element method. We show how ZSFEM can be implemented within the commercial finite element package ABAQUS/Explicit. For verification, we compared the numerical and analytical results of the displacement and its sensitivities with respect to mechanical parameters, geometry, and boundary conditions for a rod subjected to a sudden, distributed axial load. First- and second-order sensitivities were obtained with normalized root mean square deviations below 4×10−3. Mesh convergence analyses revealed that p-refinement offered better convergence rates than h-refinement for the outputs and their sensitivities. Also, the sensitivities obtained with ZSFEM were compared with finite differences showing higher accuracy and step-size independence (e.g., no iteration is needed to determine the step size that minimizes the error). For simplicity, ZSFEM was presented only for one-dimensional truss elements, but the method is general and can be applied to other elements.

Thermal analysis for laminated plates with arbitrary supports under non-uniform temperature boundary conditions

This paper aims to investigate thermal behaviors of composite laminated plates with different supports under non-uniform temperature boundary conditions. The thermo-elastic solutions of temperature, displacements, and stresses for the laminated plate with arbitrary layer numbers and thickness are obtained based on the three-dimensional theory of thermoelasticity. By applying the Fourier law of heat conduction and the thermoelastic equations, the state-space equations are established by employing the temperature, heat flux, displacements, and stresses as state variables without the hypothesis of displacement form. The differential quadrature method is introduced to discretize the in-plane state variables. On the basis of the continuities of state variables at the interfaces in the laminated plate, the relationships of temperature, heat flux, displacements, and stresses between the top and bottom surfaces can be derived. By simultaneously considering temperature and mechanical boundary conditions applied to the surfaces of the laminated plate, the initial state variables for temperature, displacements, and stresses can be determined uniquely. The errors in the temperature, displacements and stresses resulting from the differential quadrature method can be eliminated by incrementally augmenting the number of sampling points in the convergence study. The accuracy of the present method is thoroughly verified by comparing the current results with both the finite element solutions and the findings reported in previous literature. Finally, the influences of surface temperature, length-to-thickness ratios, material properties, layer numbers, and support types for the distributions of the temperature field, displacements, and stresses in the laminated plate are discussed in detail.

The possible influence of third-order shim coils on gradient–magnet interactions: an inter-field and inter-site study

ObjectiveTo assess the possible influence of third-order shim coils on the behavior of the gradient field and in gradient–magnet interactions at 7 T and above.Materials and methodsGradient impulse response function measurements were performed at 5 sites spanning field strengths from 7 to 11.7 T, all of them sharing the same exact whole-body gradient coil design. Mechanical fixation and boundary conditions of the gradient coil were altered in several ways at one site to study the impact of mechanical coupling with the magnet on the field perturbations. Vibrations, power deposition in the He bath, and field dynamics were characterized at 11.7 T with the third-order shim coils connected and disconnected inside the Faraday cage.ResultsFor the same whole-body gradient coil design, all measurements differed greatly based on the third-order shim coil configuration (connected or not). Vibrations and gradient transfer function peaks could be affected by a factor of 2 or more, depending on the resonances. Disconnecting the third-order shim coils at 11.7 T also suppressed almost completely power deposition peaks at some frequencies.DiscussionThird-order shim coil configurations can have major impact in gradient–magnet interactions with consequences on potential hardware damage, magnet heating, and image quality going beyond EPI acquisitions.

Force relaxation response in the poroelastic axisymmetric Boussinesq problem for an indenter of arbitrary profiles I: Permeable and impermeable surface drainage conditions

In this study, we have derived a theoretical solution for the poroelastic axisymmetric Boussinesq problem when an indenter with arbitrary profiles is subjected to step displacement loading. The analysis is conducted within the framework of Biot’s theory, employing the McNamee–Gibson displacement function method. We explore two distinct scenarios for surface drainage boundary conditions: one where the surface allows full permeability and another where it is fully impermeable. The formulation of the mechanical boundary condition at the surface relies on an equation that establishes the relationship between the depth of indentation and the contact radius. Our solution encompasses two aspects: force asymptotes at the undrained and drained limits, and a normalized force relaxation that accounts for transient responses. Specific findings are presented for three indenter shapes: paraboloidal, conical, and cylindrical. Of particular significance, we demonstrate that for these specific indenter shapes, the normalized force relaxation at ω=0 can be expressed in closed form in the Laplace domain. In addition to this analytical breakthrough, we conducted numerical simulations employing actual indenters. Remarkably, the normalized force relaxation curves from actual indenters show negligible dependence on material properties and closely align with our closed-form solution at ω=0. This finding suggests that the closed-form solution could act as a universal master curve capable of characterizing the normalized force relaxation response in instances of a real indenter, irrespective of material properties.

A graph model to describe the network connectivity of trabecular plates and rods.

Introduction: The trabecular network is perceived as a collection of interconnected plate- (P) and rod-like (R) elements. Previous research has highlighted how these elements and their connectivity influence the mechanical properties of bone, yet further work is required to elucidate better the deeply interconnected nature of the trabecular network with distinct element formations conducting forces per their mechanical boundary conditions. Within this network, forces act through elements: a rod or plate with force applied to one end will transmit this force to a component connected to the other end, defining the boundary conditions for the loading of each element. To that end, this study has two aims: First, to investigate the connectivity of individually segmented elements of trabecular bone with respect to their local boundary conditions as defined by the surrounding trabecular network and linking them directly to the bone's overall mechanical response during loading using a mathematical graph model of the plate and rod (PR) Network. Second, we use this model to quantify side artifacts, a known artifact when testing an excised specimen of trabecular bone, where vertical trabeculae lose their load-bearing capacity due to a loss of connectivity, ultimately resulting in a change of the trabecular network topology. Resuts: Connected elements derived from our model predicted apparent elastic modulus by fitting a linear regression (R 2 = 0.81). In comparison, prediction using conventional bone volume fraction results in a lower accuracy (R 2 = 0.72), demonstrating the ability of the PR Network to estimate compressive elastic modulus independent of specimen size or loading boundary condition. Discussion: PR Network models are a novel approach to describing connectivity within the trabecular network and incorporating mechanical boundary conditions within the morphological analysis, thus enabling the study of intrinsic material properties of trabecular bone. Ultimately, PR Network models may be an early predictor or provide further insights into osteo-degenerative diseases.

Exploring the mechanical response of functionally graded hollow disks: insights from rotation, gravity and variable heat generation

PurposeThe purpose of the study is to perform elastic stress and deformation analysis of a functionally graded hollow disk under different conditions (rotation, gravity, internal pressure, temperature with variable heat generation) and their combinations.Design/methodology/approachThe classical method of solution, Navier's equation, is used to solve the governing equation. The analysis considers thermal and mechanical boundary conditions and takes into account the variation of material properties according to a power law function of the radius of the disk and grading parameter.FindingsThe findings of the study reveal distinct trends and behaviors based on different grading parameters. The influence of gravity is found to be negligible, resulting in similar patterns to the pure rotation case. Variable heat generation introduces non-linear temperature profiles and higher displacements, with stress values influenced by grading parameters.Practical implicationsThe study provides valuable insights into the behavior of displacement and stresses in hollow disks, offering a deeper understanding of their mechanical response under varying conditions. These insights can be useful in the design and analysis of functionally graded hollow disks in various engineering applications.Originality/valueThe originality and value of this study lies in the consideration of various loading combinations of rotation, gravity, internal pressure and temperature with variable heat generation. Furthermore, the study of effect of various angular rotations, temperatures and pressures expands the understanding of the mechanical behavior of such structures, contributing to the existing body of knowledge in the field.

Vibrational analysis of size-dependent thermo-piezo-photo-electric semiconductor medium under memory-dependent Moore–Gibson–Thompson photo-thermoelasticity theory

This study presents a comprehensive approach to vibrational analysis in a size-dependent, orthotropic thermo-piezo-photo-electric semiconductor half-space under Moore–Gibson–Thompson (MGT) photo-thermoelasticity theory with memory-dependent derivatives. Following Eringen’s nonlocal elasticity theory, the governing equations for the considered material are derived. The normal mode technique is applied to investigate the photothermal excitation process. Focusing on the interface adjacent to the vacuum, the study considers plasma, thermal, and mechanical stress boundary conditions to determine fundamental physical quantities. Through a detailed exploration, this research examines the impact of various thermo-piezo-photo-electric models, time, nonlocal parameters, and spatial coordinates on different physical quantities. The effects are meticulously analyzed and visually represented through graphical illustrations. While the literature survey reveals numerous studies on vibrational analysis in thermo-piezo-photo-electric semiconductor mediums under different thermoelasticity theories, to the best of the authors’ knowledge, no research emphasizing vibrational analysis in a size-dependent thermo-piezo-photo-electric semiconductor medium has been conducted. Moreover, the effect of memory-dependent MGT photo-thermoelasticity theory on a size-dependent thermo-piezo-photo-electric semiconductor half-space has not been illuminated until now, significantly defining the novelty of the conducted research.

On the Impact of Mechanics on Electrochemistry of Lithium-Ion Battery Anodes

Models exploring electrochemistry-mechanics coupling in liquid electrolyte lithium-ion battery anodes have traditionally incorporated stress impact on thermodynamics, bulk diffusive transport, and fracture, while stress-kinetics coupling is more explored in the context of all solid-state batteries. Here, we showcase the existence of strong link between active particle surface pressure and reaction kinetics affecting performance even in liquid electrolyte systems. Traction-free and immobile particle surface mechanical boundary conditions are used to delineate the varying pressure magnitudes in graphite host during cycling. Both tensile and compressive stresses are generated in traction-free case, while a fixed surface subjects the entire particle to a compression state. Pressure magnitudes are nearly two to three orders of magnitude higher for the latter resulting in significant depression of open circuit potential and improvement of exchange current densities compared to stress-free state. The results demonstrate the need for incorporating stress-kinetics linkage in models and provide a rationale for putting battery electrodes under compression to improve kinetics.