Mechanical Boundary Conditions Research Articles

Effects of Glacial Isostatic Adjustment on Fault Reactivation and Its Consequences on Radionuclide Migration in Crystalline Host Rocks

AbstractTo assess the robustness of a safety case for a deep geological repository (DGR), it is necessary to analyze a range of scenarios covering likely, less likely, and hypothetical future developments. Crystalline rock can, under ideal conditions, provide a suitable hydrogeologic barrier due to its extremely low matrix permeability. However, this host rock is often fractured, which can compromise its hydro-mechanical (HM) barrier function. We quantify how faults that are prone to reactivation during glacial events can affect radionuclide migration around a DGR in a crystalline host rock. We extend a previously developed finite element model of coupled fluid flow and radionuclide transport to numerically solve the component transport problem before and after fault reactivation. Assuming that fault reactivation is triggered by changes in mechanical boundary conditions, we derive heterogeneous permeability distributions in the reactivated faults by evaluating the Coulomb failure stress criterion of finite element solutions of a complementary hydro-mechanical problem. Specifically, we evaluate the consequences of glacial isostatic adjustment (GIA) during a glacial cycle. We find that the increased permeability in the reactivated faults accelerates the migration of radionuclides along the fault by channeling the flow, while it is reduced in the direction perpendicular to the fault. The channeling observed is also a result of heterogeneous permeability enhancement, and the flow fields differ from those of the previous model which postulated a homogeneous permeability enhancement. Although the proposed numerical workflow has been applied to the case of GIA, it is adaptable to study hydro-mechanical processes induced by seismic events or by hydrofracking in enhanced geothermal systems.

Diffraction correction in high-precision pulse-echo and multiple-reflection ultrasonic measurement systems for fluids.

In high-precision ultrasonic measurement systems, diffraction correction models accounting for electrical and mechanical boundary conditions may be needed, as shown in prior work using a finite element diffraction correction (FEDC) model for one-way transmit-receive systems. Such descriptions may also be needed for pulse-echo and multiple-reflection ultrasonic measurement applications. The FEDC model is here generalized to n-way measurement systems (n = 1, 2, 3,…) using coaxially aligned piezoelectric transducers in a fluid medium. Comparisons are made with existing diffraction correction models, based on baffled-piston theory combined with (i) specular reflection or (ii) reflection modeled as radiation from a "new source." Numerical results are given for an example system with two identical cylindrical piezoelectric disks, operating in a fluid medium at ambient conditions. The piston-type diffraction correction models deviate notably from the FEDC model both in the near- and far-fields, and also from each other. The deviations are expected to be application-specific and depend, e.g., on the reflector-to-sound-beam diameter ratio, distance, frequency, and the transducers' vibration patterns. The results show that accurate description of the diffraction effects, such as the one provided by the FEDC model, may be needed in high-precision ultrasonic measurement systems.

Mechanical boundary conditions for motor protein dictate geometric pattern and dynamics of actin gel contraction

Mechanical boundary conditions for motor protein dictate geometric pattern and dynamics of actin gel contraction

Approximate Bayesian Computation for structural identification of ancient tie-rods using noisy modal data

Masonry arches and vaults are common historic structural elements that frequently experience asymmetric loading due to seismic action or abutment settlements. Over the past few decades, numerous studies have sought to enhance our understanding of the structural behavior of these elements for the purpose of preventive conservation. The assessment of the structural performance of existing constructions typically relies on effective numerical models guided by a set of unknown input parameters, including geometry, mechanical characteristics, physical properties, and boundary conditions. These parameters can be estimated through deterministic optimization functions aimed at minimizing the discrepancy between the output of a numerical model and the measured dynamic and/or static structural response. However, deterministic approaches overlook uncertainties associated with both input parameters and measurements. In this context, the Bayesian approach proves valuable for estimating unknown numerical model parameters and their associated uncertainties (posterior distributions). This involves updating prior knowledge of model parameters (prior distributions) based on current measurements and explicitly considering all sources of uncertainties affecting observed quantities through likelihood functions. However, two significant challenges arise: the likelihood function may be unknown or too complex to evaluate, and the computational costs for approximating the posterior distribution can be prohibitive. This study addresses these challenges by employing Approximate Bayesian Computation (ABC) to handle the intractable likelihood function. Additionally, the computational burden is mitigated through the use of accurate surrogate models such as Polynomial Chaos Expansions (PCE) and Artificial Neural Networks (ANN). The research focuses on setting up numerical models for simple structural systems (tie-rods) and inferring unknown input parameters, such as mechanical properties and boundary conditions, through Bayesian updating based on observed structural responses (modal data, strains, displacements). The main novelties of this research regard, on the one hand, the proposal of a methodology for obtaining a reliable estimate of the axial force in ancient tie-rods accounting for different sources of uncertainty and, on the other hand, the application of ABC to obtain the structural identification inverse problem solution.

The modified physics-informed neural network (PINN) method for the thermoelastic wave propagation analysis based on the Moore-Gibson-Thompson theory in porous materials

This paper presents novel contributions to both theory and solution methodology in AI-based analysis of solid mechanics. The physics-informed neural network (PINN) method is developed for thermoelastic wave propagation and Moore-Gibson-Thompson (MGT) coupled thermoelasticity analysis of porous media, a first in the field. The coupled thermoelasticity governing equations, based on the MGT heat conduction model, are derived for a porous half-space, with the thermal relaxation coefficient and strain relaxation factor being considered. Mechanical and thermal shock loading boundary conditions are imposed. The behavior of a magnesium-made porous body is analyzed using the PINN method, with highly accurate results being achieved for the system of coupled PDEs. An adaptive hyperparameter tuning approach, integrating a generalized subset design (GSD) and Bayesian optimization algorithm, is used to automatically select the optimal structure based on the L2 relative error. This hybrid methodology eliminates manual adjustment concerns. The proposed method is verified through a thorough comparison with the Lord-Shulman theory of coupled thermoelasticity. The strength of the methodology lies in its ability to operate without domain data, with only boundary and initial points being required. Four example sets are examined to demonstrate the capabilities of the modified PINN, and high-quality predictions of dimensionless fields’ variables over an extended time interval are obtained, confirming its extrapolation abilities.

Impact of cardiac patch alignment on restoring post-infarct ventricular function.

Acute myocardial infarction (MI) leads to a loss of cardiac function which, following adverse ventricular remodeling (AVR), can ultimately result in heart failure. Tissue-engineered contractile patches placed over the infarct offer potential for restoring cardiac function and reducing AVR. In this computational study, we investigate how improvement of pump function depends on the orientation of the cardiac patch and the fibers therein relative to the left ventricle (LV). Additionally, we examine how model outcome depends on the choice of material properties for healthy and infarct tissue. In a finite element model of LV mechanics, an infarction was induced by eliminating active stress generation and increasing passive tissue stiffness in a region comprising 15% of the LV wall volume. The cardiac patch was modeled as a rectangular piece of healthy myocardium with a volume of 25% of the infarcted tissue. The orientation of the patch was varied from 0 to relative to the circumferential plane. The infarct reduced stroke work by 34% compared to the healthy heart. Optimal patch support was achieved when the patch was oriented parallel to the subepicardial fiber direction, restoring 9% of lost functionality. Typically, about one-third of the total recovery was attributed to the patch, while the remainder resulted from restored functionality in native myocardium adjacent to the infarct. The patch contributes to cardiac function through two mechanisms. A contribution of tissue in the patch and an increased contribution of native tissue, due to favorable changes in mechanical boundary conditions.

Rate-dependent cochlear outer hair cell force generation: Models and parameter estimation

The outer hair cells (OHCs) of the mammalian cochlea are the mediators of an active, nonlinear electromechanical process necessary for sensitive, frequency-specific hearing. The membrane protein prestin conveys to the OHC a piezoelectric-like behavior hypothesized to actuate a high frequency, cycle-by-cycle conversion of electrical to mechanical energy to boost cochlear responses to low-level sound. This hypothesis has been debated for decades, with two key remaining issues: the influence of the rate dependence of conformal changes in prestin and the OHC transmembrane impedance. In this paper, we mainly focus on the rate dependence of the conformal change in prestin. A theoretical electromechanical model of the OHC that explicitly includes rate dependence of conformal transitions, viscoelasticity, and piezoelectricity. Using this theory, we show the influence of rate dependence and viscoelasticity on electromechanical force generation and transmembrane impedance. Furthermore, we stress the importance of using the correct mechanical boundary conditions when estimating the transmembrane capacitance. Finally, a set of experiments is described to uniquely estimate the constitutive properties of the OHC from whole-cell measurements.

Detrimental Increase of Spin-Phonon Coupling in Molecular Qubits on Substrates.

Molecular qubits are a promising platform for quantum information systems. Although single molecule and ensemble studies have assessed the performance of S = 1/2 molecules, it is understood that to function in devices, regular arrays of addressable qubits supported by a substrate are needed. The substrate imposes mechanical and electronic boundary conditions on the molecule; however, the impact of these effects on spin-lattice relaxation times is not well understood. Here we perform electronic structure calculations to assess the effects of a graphene (Cgr) substrate on the molecular qubit copper phthalocyanine (CuPc). We use a progressive Hessian approach to efficiently calculate and separate the substrate contributions. We also use a simple thermal model to predict the impact of these changes on the spin-phonon coupling from 0 to 200 K. Further analysis of the individual vibrational modes with and without Cgr shows that an overall increase in SPC between the vibrations modes of CuPc with the surface reduces the spin-lattice relaxation time T1. We explain these changes by examining how the substrate lifts symmetries of CuPc in the absorbed configuration. Our work shows that a surface can have a large unintentional impact on SPC and that ways to reduce this coupling need to be found to fully exploit arrays of molecular qubits in device architectures.

Generalized magneto-thermoelasticity problem in an orthotropic hollow sphere under thermal shock

This article addresses the magneto-thermoelasticity problem within an orthotropic hollow sphere. The governing equations are formulated based on the Lord-Shulman coupled theory of thermoelasticity. Time-dependent thermal and mechanical boundary conditions are imposed on the inner and outer surfaces of the hollow sphere. The analytical solution is obtained using the finite Hankel transform. A thermal shock in the form of heat flux is prescribed on the sphere’s inner surface, and subsequently, the transient thermal response of the sphere, along with radial displacement and radial, tangential, and circumferential stresses, are derived. The influence of different magnetic field values, orthotropic material properties, and relaxation time is investigated and presented graphically. The obtained results exhibit excellent agreement with existing literature, validating the robustness of the proposed model. The findings not only contribute to the fundamental understanding of magneto-thermoelasticity but also offer practical insights for engineering applications involving orthotropic materials in complex thermal and magnetic environments. The availability of an exact solution facilitates the validation of numerical models, ensuring their accuracy and reliability in capturing the intricate behavior of orthotropic materials under coupled fields.

Onset of thermal convection in a solid spherical shell with melting at either or both boundaries

SUMMARY Thermal convection in planetary solid (rocky or icy) mantles sometimes occurs adjacent to liquid layers with a phase equilibrium at the boundary. The possibility of a solid–liquid phase change at the boundary has been shown to greatly help convection in the solid layer in spheres and plane layers and a similar study is performed here for a spherical shell with a radius-independent central gravity subject to a destabilizing temperature difference. The solid–liquid phase change is considered as a mechanical boundary condition and applies at either or both horizontal boundaries. The boundary condition is controlled by a phase change number, Φ, that compares the timescale for latent heat exchange in the liquid side to that necessary to build a topography at the boundary. We introduce a numerical tool, available at https://github.com/amorison/stablinrb, to carry out the linear stability analysis of the studied setup as well as other similar situations (Cartesian geometry, arbitrary temperature and viscosity depth-dependent profiles). Decreasing Φ makes the phase change more efficient, which reduces the importance of viscous resistance associated to the boundary and makes the critical Rayleigh number for the onset of convection smaller and the wavelength of the critical mode larger, for all values of the radii ratio, γ. In particular, for a phase change boundary condition at the top or at both boundaries, the mode with a spherical harmonics degree of 1 is always favoured for Φ ≲ 10−1. Such a mode is also favoured for a phase change at the bottom boundary for small (γ ≲ 0.45) or large (γ ≳ 0.75) radii ratio. Such dynamics could help explaining the hemispherical dichotomy observed in the structure of many planetary objects.

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.