Journal of Engineering Mechanics

Cardiac electromechanics is a coupled multiphysics and multiscale problem. Of great interest to medicine and pharmacology is how the heart responds to changes in ion channel dynamics within the myocyte that are either caused by disease or by the administration of drugs. A successful model of cardiac mechanical response must therefore incorporate a first-principles description of electrophysiology of the cardiac myocyte including intracellular calcium dynamics, transmembrane ionic currents and action potential (AP) formation at the cellular level. This article reviews the evolution of electrophysiological models of cardiac ventricular myocytes in terms of coupled differential equations whose state variables include ion channel gating parameters, intracellular ionic concentrations and the membrane voltage. The myocytes are connected through gap junctions forming fibers, which in turn connect to form cardiac tissues. The electromechanical response of cardiac tissues is coupled through intracellular calcium dynamics and stretch induced/ modulated currents, and can be solved using suitable discretization schemes under appropriate initial and boundary conditions. We discuss in detail the single-cell dynamics of the ORd model of human ventricular myocytes and describe the propagation of AP in periodically paced 1D fibers and 2D tissues. The origin of tissue-level diseased conditions in altered subcellular dynamics are discussed.

The kinematic plastic limit, unified shakedown criteria, and reduced kinematic formulation have been utilized to study the plastic collapse modes of truss structures subjected to complex loading cycles. The development from a series of local alternating plastic failures toward the global instantaneous or incremental collapse of the structures with increasing load ranges has been identified. The finite element method and optimization techniques are implemented to effectively solve the resulting mathematical programming problems, with illustrative examples and explanations.

Abstract

The validity of the theoretical Debye–Hückel length (${\kappa }^{-1}$), determined on the basis of the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, to characterize diffuse layer thickness has been experimentally challenged. A series of linear swelling tests using a LVDT apparatus was utilized to measure shale swelling as it interacted with various ionic solutions. A regression technique was employed to develop an empirical equation for an experimental Debye–Hückel length (${\kappa }_E^{-1}$) as a function of ionic strength ($I$) and swelling displacement ($\mathrm{\Delta }L$). Results showed that the measured ${\kappa }_E^{-1}$ is less than the predicted ${\kappa }^{-1}$ due to the physicochemical interactions of shale with the ionic solutions. Such discrepancy had a profound impact on the estimated electric potential ($\psi /{\psi }_0$) and total interaction energy ($V_T$) in the electrical diffuse double layer (EDDL). Moreover, the energy barrier was found to be smaller when ${\kappa }_E^{-1}$ is used as the diffuse layer’s thickness than when $\pm E^{-1}$ is used. Results also showed that increasing the ionic strength of the solution decreases the energy barrier and the distance ($x$) at which the energy barrier occurs (location). The blind reliance on theoretical (${\kappa }^{-1}$) may induce errors in characterizing clay behavior in the presence of ionic solutions, which could compromise the process of design and engineering, especially those related to wellbore stability problems.

Practical Applications

Shale swelling is regarded to be one of the main causes of wellbore stability in shale formations drilled with water-based muds. The unfavorable exchange of water and ions between shale and water-based drilling muds may lead to the expansion or shrinkage of clay platelets. To avoid shale swelling, water extraction out of shale by means of chemical osmosis, through the addition of salts, is often adopted in order to reduce the amount of clay platelets separation between clays that make up shale formations. The separation distance between clay platelets is generally associated with the Debye–Hückel length, diffuse layer thickness. Therefore, many operators rely on theoretical Debye–Hückel length to get a first-hand estimate of the amount of shale swelling prior to the application of certain salt drilling muds. The blind reliance on theoretical Debye–Hückel length may underestimate the diffuse layer thickness and separation distance between clay platelets because it completely ignores the physicochemical interactions of clay with the ionic solutions. Such practice may induce errors in characterizing clay behavior in the presence of ionic solutions, which could compromise the process of design and engineering, especially those related to wellbore stability problems. This may eventually lead to wellbore collapse and loss of resources.

The realistic modeling of vibratory energy harvesters is necessary to ensure their reliable performance when subjected to random excitation. However, the hysteretic behavior of piezoelectric materials and the nonlocality of fractional electrical components make the numerical estimation of their stochastic response computationally challenging. This paper proposes an iterative method based on equivalent linearization and stochastic averaging for estimating the stationary probability density function of the output voltage amplitude of vibratory energy harvesters modeled as a hysteretic oscillator with fractional electrical components subject to a broadband stochastic process. By estimating the average of hysteretic terms, one can find an amplitude-dependent linear governing equation for the output voltage, from which one can determine a stochastic differential equation governing the evolution of the output voltage amplitude. We obtain the stationary solution of the corresponding Fokker–Planck equation in a semianalytical form, and we include comparisons with pertinent Monte Carlo simulation data to show that the estimated probability density functions are accurate and obtained at a minimal computational cost.

Base isolation systems (BISs) are used to isolate equipment or structures from vibration sources; however, the reduction in transmitted loads with the BIS can come at the cost of large isolation layer displacements. The clutching inerter damper (CID) is a device proposed to be coupled with the BIS to improve its isolation performance and simultaneously decrease the associated base displacements. The CID acts as a linear inerter when in its engaged state, adding effective mass in the form of rotational inertance to oppose a system’s motion, and, when disengaged, it idles freely and dissipates its rotational energy without directing this energy back into the system. Previous studies on the CID in base-isolated multi-degree-of-freedom (MDOF) structures are limited and focus heavily on the time history analyses of seismic or harmonic loadings. Furthermore, much of the research on this topic considers an ideal CID where all rotation is damped out between engagements, which is not physically realistic in many circumstances. This work numerically investigates the performance of a base-isolated MDOF system with a CID subjected to white noise loading from a frequency domain perspective and employs a more realistic numerical model of the CID’s dynamics. Several indices, such as the ${\mathrm{H}}_2$ and ${\mathrm{H}}_{\infty }$ analog of displacement and acceleration frequency response functions, are analyzed to evaluate the system response. The performance of the BIS with the CID is compared against the BIS with a linear inerter, the BIS without a CID or inerter, and the superstructure without base isolation. Results indicate that the BIS with a CID outperforms the other configurations for several key indices. The analysis also reveals that increases in the CID’s ability to improve system performance slow with higher levels of rotational inertance. The performance of the CID illustrates its potential effectiveness for isolation systems in MDOF structures.

This paper investigates the effect of the horizon size on failure due to strain and damage localization in the case where peridynamics is a nonlocal theory by its own, which corresponds to most bond-based peridynamics models. Two constitutive relationships are discussed: the microelastic brittle model and a progressive damage model. The usual practice with the microelastic brittle model is to fit the microelastic constant for a given horizon size so that elasticity is recovered. At the same time, the fracture energy provides the critical bond stretch. This methodology yields an indirect determination of the tensile strength of the material, that goes to infinity as the horizon size trends to zero. With the damage model, the stretch at the inception of damage can be obtained from the tensile strength. Then, a simple one-dimensional case of wave propagation and interactions in a bar is considered. For fixed values of the horizon, convergence with a refinement of the discretization is checked. The energy dissipated upon fracture is found to be a linear function of the horizon. It is also a function of the softening response. The horizon cannot be chosen arbitrarily, unless the softening parameter is adjusted to fit the fracture energy, like in the crack band model. Surprisingly, such a methodology is very seldom mentioned in the current literature dealing with fracture modeled by peridynamics.

Mass timber has gained increasing focus as a sustainable alternative to concrete structures, and recent innovations have allowed timber buildings as high as 25 stories. However, although critical factors such as fire safety have been studied thoroughly, other facets, such as long-term material performance, have been neglected. Thorough assessments of sustainability must consider the full service life of a building, including its time-dependent behavior. Deformations in timber elements undergoing these time-dependent effects, namely creep, will have notable implications for the serviceability of a building. This study proposes a comprehensive model for predicting moisture-dependent creep in timber, based on the theory of microprestress in partially saturated porous materials. The model is implemented numerically using a Kelvin-chain approximation for basic creep and midpoint integration for mechanosorptive effects, resulting in a computationally efficient approach. Results show the model is able to fully capture the effects of moisture cycling, including effects of hygrothermal gradients. Using both calibrated and estimated parameters the model also predicts with reasonable accuracy the long-term moisture-dependent creep in structural-scale mass timber elements.

The drying-free preparation of coated magnetic particles has been proven to significantly improve the comprehensive performance and preparation efficiency of magnetorheological (MR) fluid. Due to the magnetic separation technique in the drying-free process, the residual anhydrous ethanol and silicone oil form a Pickering emulsion, whose influence on the properties of MR fluid is ignored in existing mechanical models. In this study, in order to improve the application accuracy of MR fluid and provide methods for further improvement of MR fluid performance, with consideration of the influence of the Pickering emulsion caused by the drying-free process, the tight simple cubic (TSC) structure model and the body-centered cubic (BCC) structure model of MR fluid were proposed based on the mechanism of chain formation of MR fluid and the magnetic dipole theory. To reflect the coexistence and transformation mechanism of these two structures, a distribution probability function was introduced and a hybrid spatial structure model comprised of both TSC and BCC structures was established. The validity and accuracy of the models were verified by the comparison with the experimental data. The proposed hybrid spatial structure micromechanical model considers the influence of Pickering emulsion on the microstructure of MR fluid and can accurately describe the properties of MR fluid prepared by the drying-free process.

The triply periodic minimal surface (TPMS) is being potentially considered in innovative applications, including robotics, biomedical engineering, impact energy absorption, and so on, so that the information on mechanical property and energy absorption of TPMS components under the damage loading is significant to understand, with a considerably reduced cost before being put into use. For the first time, a deep artificial neural network (ANN)-powered prediction method for TPMS lattices, including sheet gyroid, sheet primitive, sheet I-graph-wrapped package curved surface (I-WP) and solid I-WP subjected to damage loading, with an extremely low cost is introduced in this work where a loop with multiple conditions (LMC) inserted to improve its accuracy. It is a low-cost model due to the fact that it only requires a training experimental data set from 9 TPMS samples with relative density ranging from 0.1 to 0.55, subjected to the damage test to train and then generates the mechanical information and energy absorption at almost any point of the relative density (Rd). Impressively, the ANN prediction method can well comprehend and learn from experimental samples, and then accurately provide the information of mechanical behavior of TPMS architectures, including the stress-strain response, Young’s modulus, and yield strength at almost any relative density in the range, under the damage load. Specifically, Young’s modulus and yield strength obtained from ANN model agree well with that from the experimental damage test data, which does not belong to the training samples, with maximum percent differences found approximately 1%, and 2%, respectively. Surprisingly, ANN approach demonstrates an ability to predict the mechanical response of TPMSs, with thousands of times faster and significantly lower financial cost than that of the experiment. Thus, we move forward, by using the approach, to map 2-dimensionally the energy absorption of lattices with respect to varying relative density and deformation, and plot the energy dissipation density versus the relative density under damage loadings.

The COVID-19 pandemic has evidenced that reliable model-based epidemiological predictions have remained an open challenge, and this concerns in particular the identification of model parameters that may change throughout the course of the pandemic. This aging characteristic of an epidemic is our present focus, by example of predicting fatality trends from infection histories. Regarding the challenge as a mechanobiological problem, we employ a hereditary mechanics-rooted Boltzmann-Volterra-type integro-differential equation, so that the fatality rate is obtained as a time integral over the rate of confirmed cases (i.e., the so-called incidence), multiplied with a kernel depending on evolving, i.e., time-dependent, fatality fractions and time lags between infection and death. This novel convolution approach, including its degeneration to an aging infection-to-death-rate delay rule, is superior to the traditional kinetics approach in as many as 93% of the tested cases associated with 228 countries, territories, and US states. The corresponding country-, territory-, and US state-specific fatality fractions appear as exponentially decaying quantities with characteristic decay times ranging from around 100 days to several years; with a world median of some 480 days, and with 100 to 200 days being typical for Western Europe and several Eastern US states. These parameters show periods of fair stability over one to several hundred days, indicating midterm prediction capabilities of our novel approach.

Geotechnical site characterization using multivariate, limited (sparse), and missing (incomplete) data is an important but challenging task, particularly in high dimensions. Toward this problem, this study proposes a Bayesian vine algorithm. In the proposed algorithm, the task of Bayesian update in higher dimensions is translated into a series of lower-dimensional (usually $\le 2$) update tasks using conditional correlation vine. This feature of the proposed algorithm makes it scalable and computationally efficient in higher dimensions. Multiple examples using two-dimensional (2D), five-dimensional (5D), 10-dimensional (10D), 20-dimensional (20D), 50-dimensional (50D), and 100-dimensional (100D) data are shown to demonstrate the capability of the proposed algorithm. The results suggest that the proposed algorithm can be used successfully for geotechnical site characterization. Even an ultrahigh 50D joint distribution with $>\mathrm{1,000}$ parameters (1,325) can be estimated in around 20 min. The proposed algorithm can handle multivariate data sets with limited and missing values and can also handle non-Gaussian multivariate joint distributions. The proposed algorithm only considers cross-correlation in the site data and doesn’t take into account spatial correlation.