Abstract Accurate prediction of strain localization and postnecking behavior is critical for understanding failure in ductile metals such as copper. Traditional tensile testing methods based on engineering stress–strain curves and extensometer readings often fail to capture localized deformation phenomena, especially beyond the onset of necking. In this study, digital image correlation (DIC) and finite element modeling (FEM) are used to investigate the deformation and damage behavior of pure copper dogbone specimens under quasi-static uniaxial tension. Full-field strain measurements obtained via two-dimensional digital image correlation (2D-DIC) enable detailed visualization of the strain localization process. The finite element (FE) simulations are used to qualitatively and quantitatively validate the experimental results. The FEM framework incorporates isotropic plasticity and a ductile damage model with fracture energy–based regularization to ensure mesh objectivity. We assess the model’s predictive capabilities by comparing force–displacement curves, axial strain fields, and localization zone morphology with the experimental observations. The effect of mesh refinement is examined using multiple element sizes (2, 1, and 0.5 mm), demonstrating convergence in both global and local metrics. Strain map comparisons between DIC and FEM reveal good agreement in the necking position and shape, although peak axial strain values differ due to differences in strain definitions and spatial resolution. This coupled DIC-FEM approach provides an experimentally validated framework for modeling postnecking behavior in copper, with implications for ductile damage calibration and microelectronic reliability applications. The results also serve as a reference dataset for future multiscale and inverse identification efforts in strain-localized regimes.
Abstract Multi-time-step (MTS) methods enable fast, stable, and accurate simulations of multi-scale problems in structural dynamics. This is achieved by decomposing a large computer model into several subdomains and using a small time step in subdomains with high temporal gradients while integrating other subdomains with a large time step to save computational cost. Thus, compared to conventional uniform time-stepping (UTS) schemes that use a small time step for the entire problem domain, MTS methods are significantly faster. Despite the computational efficiency of existing MTS methods, they still require a three-step process: solve the subdomains independently, compute the Lagrange multipliers needed for enforcing continuity of the solution across the interface between subdomains, and finally couple all the subdomains together by updating their solutions to satisfy the continuity constraints. The key to obtaining accurate solutions with MTS methods is to compute the Lagrange multipliers accurately, which necessitates the time-consuming three-step process. To eliminate this three-step process a machine learning approach is used to obtain the Lagrange multipliers needed for coupling the various subdomains at each time step. Data collected from solutions generated using conventional MTS methods are used to train a long short-term memory (LSTM) network that predicts these Lagrange multipliers. Output from the LSTM network, along with other state information, is then used to solve all the subdomains in a single (one-step) process. The resulting algorithm is called the machine learning–assisted MTS (ML-MTS) method and it advances the global solution in a single pass while maintaining continuity of the solution across the subdomain interfaces. Two numerical examples are presented to compare the performance of the proposed ML-MTS approach to existing MTS methods in terms of accuracy and computational cost. Results show that the proposed ML-MTS method achieves additional speedup on top of the computational gains of existing MTS methods while maintaining the accuracy of the solution.
Abstract A new data-driven failure criterion has been developed to improve modeling of orthotropic structural composites. Rather than using an analytical expression traditionally employed to predict failure, a point cloud failure surface is constructed in the stress/strain space using a combination of laboratory testing and virtual testing with multiscale models based on representative volume elements. In the current work, the failure predictions are extended from a three-dimensional stress space that is suitable for use with thin shell finite elements to a six-dimensional stress space, suitable for use with thick shell and solid finite elements. A crucial step in using the material characterization failure data is the ability of a method to correctly predict when failure onset in a finite element takes place. This predictive capability needs to balance efficiency and accuracy. Three predictive methods are compared in this paper: approximate nearest neighbor, neural network, and a new custom exact nearest neighbor that was developed specifically to be accurate and efficient in low-dimensional search space. Point cloud data from a unidirectional composite, the T800-F3900, commonly used for aerospace applications, are used for comparative evaluation of these methods. Results indicate that the custom exact nearest neighbor and neural network implementations are robust, efficient, and accurate.
Abstract Chemical reactions in porous media can proceed either entirely within the pore space (nonsolid reaction) or engage with the skeleton (solid reaction), leading to different chemomechanical coupling mechanisms and constitutive behavior. However, current hydromechanical-chemo models do not explicitly distinguish between these reaction types, and many thermodynamic formulations encounter intrinsic difficulties when handling reactions in closed systems or treating reactions involving changes in the solid skeleton. To address these issues, this paper develops a thermodynamically consistent chemomechanical framework that explicitly distinguishes solid and nonsolid reactions. By using nonequilibrium thermodynamics, the entropy production for both closed and open systems are quantified, and the reaction affinity is decomposed into solid and fluid contributed parts, leading to the treatment of chemical reactions in open and closed systems in a unified way and yielding explicit Helmholtz free energy expressions that distinguish the two reaction types. Following that, chemoelastic models for both closed and open systems are derived, with mass density and chemical potential being the chemical variables. The Biot-type reactive poroelastic model is subsequently recovered and reformulated, in which the chemical reaction in the pore fluid is indirectly coupled with stress through pore pressure, whereas reaction with solid is directly coupled with the mechanical process through reaction-induced stress. The governing equations and a numerical model for the hydromechanical-chemical (HMC) coupling are presented to illustrate the differences between nonsolid and solid reaction.
Abstract This paper presents an analytical study of a transient, spherically symmetric thermoelastic response of a multilayer spherical vessel subjected to combined thermal and mechanical loading. The vessel consists of a load-bearing core, an intermediate composite layer, and an external thermal insulation coating. Within the quasi-static approximation, the temperature field is obtained independently by solving the transient heat conduction problem governed by Fourier’s law and is subsequently introduced into the mechanical formulation as a prescribed thermal load. The mechanical problem accounts for internal pressure and thermally induced strains, while the intermediate layer is modeled using a homogenization approach that captures its effective macroscopic properties without explicit representation of the underlying microstructure. An efficient direct integration method is employed to derive closed-form expressions for the stresses and the radial displacement in each layer, allowing for a consistent treatment of material inhomogeneity and multilayer interfaces. The proposed formulation enables a systematic investigation of the effects of the intermediate layer characteristics and the thermal insulation coating parameters on the transient stress–strain state of the vessel. The results demonstrate that appropriate selection of the intermediate layer properties can significantly reduce peak thermal stresses and alter their temporal evolution, while the insulation coating primarily influences the magnitude and location of maximum stresses by modifying the temperature gradients. The developed analytical framework provides a practical tool for designing and optimizing multilayer spherical pressure vessels that operate under transient thermal conditions.
Abstract The lateral–torsional instability of soft-core sandwich beams with intermediate supports and the impact of the sandwich configuration on the evolution of instability are investigated. A nonlinear, high-order, sandwich model that accounts for the nature of the soft-core sandwich construction, its response to flexure and twist, and their interaction with the intermediate supports is adopted for this purpose. The research novelty lies in exploring, for the first time, the combined impact of the sandwich configuration and the supporting scheme on lateral–torsional instability and the roles these features play in the global nonlinear behavior. The numerical part of the investigation validates the model, explores two case studies, quantifies the parametric sensitivity, and reveals the unique physical features of the sandwich structure. In particular, the coupled evolution of global, wrinkling, and lateral instabilities, the distortion of the sandwich cross-sections, and the localization of stresses and deformations are observed and quantified. The paper presents new findings on the complex nonlinear response of sandwich beams to flexure, and the role of the core layer in this response. It shows that the combined effect of the core deformability and the presence of intermediate support can alter the sequence of instabilities. With relatively stiff cores, the lateral instability governs the nonlinear behavior. With more compliant cores, the localized distortion of the cross-section with the intermediate support triggers wrinkling and interactive local–global instability. These observations reveal, for the first time, the combined impact of the sandwich construction on its lateral instability and provide new insight into the nonlinear behavior of soft-core sandwich beams.
Abstract Postearthquake decisions regarding the repair, retrofit, and safety of damaged infrastructure often rely on accurate estimates of structural response demands. These estimates are highly sensitive to uncertain material parameters whose true values often deviate from those used in the numerical model. This study proposes a Bayesian framework for updating nonlinear structural model parameters using postearthquake visual damage indicators (VDI) as evidence. Observed damage is probabilistically linked to engineering demand parameters (EDPs) through limit-state relationships defined in established literature and standards of practice. Prior parameter distributions are propagated through Monte Carlo nonlinear response history analyses with and without record-to-record ground-motion uncertainty to obtain probabilistic EDPs. These are then used to compute likelihoods and update both marginal and joint parameter distributions. The framework is demonstrated using an experimentally tested reinforced-concrete structural wall. Updated maximum-a-posteriori model parameter estimates are shown to substantially improve predictions of global and local seismic response demands relative to priors and produce fragility curves that differ appreciably. Results also show that incorporating parametric correlations can further enhance these estimates. The proposed methodology provides a practical pathway for leveraging observed damage to improve postearthquake performance assessment and decision support.
Abstract Hysteretic structural systems exhibit highly nonlinear behaviors governed by parameter interactions, creating challenges for traditional sensitivity analysis methods, especially when higher-order effects dominate. This work introduces a β -variational autoencoder ( β -VAE) framework that learns low-dimensional, interpretable latent representations of nonlinear hysteretic responses and reveals the dominant parameter interactions that drive the dynamic response behavior. Using simulated response data from a multistory base-isolated building subjected to nonstationary ground motions, we demonstrate that the β -VAE reliably compresses base displacement trajectories into a small number of (linearly) disentangled latent variables that align with physically meaningful generative factors. A β -annealing strategy is proposed to control latent-space sparsity and sequentially extract salient combinations of generative factors that arise from either structural or excitation parameters. We complement this with multiple linear regression analysis to further identify salient parameter combinations for latent variables and Sobol’ sensitivity analysis to quantitatively rank latent contributions. Through a series of examples that consider uncertainty in the structural and excitation parameters, both separately and jointly, we show that the β -VAE uncovers stiffness–strength axes, duration-frequency controlled excitation modes, and higher-order cross-domain interactions that cannot be easily isolated by conventional Sobol’ indices. These results highlight the potential of VAEs as data-driven yet interpretable tools for nonlinear system analysis, offering a pathway toward model-order reduction, feature discovery, and future physics-integrated learning strategies in structural dynamics.
Abstract The rapid advancement of modern wireless technologies has imposed restrictions on device miniaturization and seamless integration with electronic circuits. Surface acoustic wave (SAW) devices are widely adopted for their strong confinement of acoustic energy near the surface, which imparts exceptional sensitivity to surface configuration. Motivated by reduced surface-to-volume ratios and surface sensitivity, this study investigates antiplane [Love and Bleustein–Gulyaev (B–G)-type] wave propagation in a nonlocal piezomagnetic fiber–reinforced composite (NPMFC) structure. The interface conditions incorporate higher-order strain-gradient effects within a finite neighborhood that accounts for size-dependent interfacial response. Five nonlocal interfacial imperfections, namely, nonlocal welded (NLW), nonlocal magnetically weakly permeable (NMWP), nonlocal magnetically highly permeable (NMHP), nonlocal low magnetic permeable (NLMP), and nonlocal magnetically grounded (NMG), are examined. Size effects are modeled via Eringen’s nonlocal elasticity coupled with the extended Gurtin–Murdoch surface elasticity. Secular equations are obtained for each enforced nonlocal imperfection under magnetically open/short conditions, and the framework is validated against established results. A parametric analysis highlights the influence of the size-dependent surface parameter, nonlocality, fiber volume fraction, and nonlocal–magnetic interfacial imperfections on the normalized velocities of both waves. Omitting surface and nonlocal effects leads to velocity misestimation, whereas their inclusion is crucial to capture confinement and phase delay, leading to the design of high-performance SAW devices.
Abstract This study introduces a negative stiffness tuned mass damper (NSTMD) and its inerter-assisted variant (NSTMDI) as novel passive devices for bridge deck flutter control. Rational function approximation of the self-excited forces enables time-domain modeling of the aeroelastic system. A genetic algorithm–based multiobjective optimization framework is developed to maximize flutter speed while minimizing auxiliary mass block stroke, leading to Pareto-optimal designs. A combined performance index (CPI), based on weighted min–max normalization of the two objectives, provides a single transparent metric for selecting practically implementable designs from the Pareto set. Tuned mass dampers (TMDs), NSTMD, and NSTMDI achieve maximum flutter speed enhancements of approximately 22%, 30%, and 31%, respectively. The corresponding mass block stroke for NSTMDI is nearly two times lower than that of NSTMD and more than five times lower than that of TMD, underscoring the superior efficiency of the combined negative stiffness and inerter-assisted configuration. Negative stiffness effectively stabilizes the torsional mode, shifting the critical instability to the vertical mode at higher wind speeds, while the inerter enhances energy dissipation and reduces stroke demand. Although the controlled divergence speed is slightly lower than that of the uncontrolled system for NSTMD and NSTMDI, the overall stability margin improves appreciably because flutter, which governs the onset of instability, occurs at higher wind speeds. For a common target flutter speed, both NSTMD and NSTMDI yield lower RMS responses, shorter settling times, and smaller mass block strokes than TMD at preflutter conditions. The effective control moment acts predominantly out of phase with torsional velocity, providing enhanced damping, while NSTMD and NSTMDI generate significantly higher peak control moments than TMD, resulting in stronger and faster stabilization. Robustness analyses under structural and aeroelastic uncertainties, together with detuning of the optimal control parameters, confirm the superior efficacy of the NSTMDI for bridge deck flutter control.
Reliable estimation of full-field structural displacements and internal forces from limited sensor data remains a key challenge in Structural Health Monitoring (SHM), particularly during strong dynamic events. This study proposes the Modal Structural Stress Mapping (MSSM) method, a real-time reconstruction technique for structural displacements and internal forces using sparse sensor measurements and modal superposition. Unlike traditional SHM approaches that detect damage through modal parameter shifts, MSSM provides direct physical response estimations that can support rapid damage localization and performance evaluation. The method has been implemented in a structural analysis software platform, integrated with an IoT-based SHM workflow, and validated through both numerical simulations and the instrumented Van Nuys hotel testbed. The results demonstrate that MSSM can reconstruct structural response with high accuracy, showing displacement errors below 0.12% compared to full time history analyses. The method extends beyond seismic applications and is suitable for various structural typologies, including fatigue assessment under wind and vehicular loads. It provides a robust framework for evaluating long-term structural integrity and identifying potential damage in both structural and non-structural elements based on observed deformation patterns.
This study presents fast Fourier transform (FFT) based spectral analysis of acoustic emission (AE) waveforms to assess damage and fractal stick-slip processes in fiber reinforced composites. Mode I fracture experiments were conducted on plain concrete (PC) and steel fiber reinforced concrete (SFRC). The study aims to enhance real-time nondestructive evaluation of SFRC. The fracture behavior of the SFRC was modeled by analyzing the fiber induced stick-slip behavior using singular fractal functions. The frequencies of all AE waveforms were correlated with the frequency centroid spectrum (FCS) to analyze different fracture mechanisms, such as the initiation of microcracking, coalescence, macrocracking, and fiber bridging. At the initial peak load, the distributed crack growth in PC was found to be about five times higher than SFRC with 2% fiber content, as indicated by the steeper slope of FCS. Based on the experimental results and damage parameter, an optimal steel fiber content of about 1.5% appears to provide a balance between ultimate peak load (Pu) and the damage progression in SFRC.
Phononic crystals offer new insights for reducing vibration and noise. The bandgaps of traditional phononic crystals are challenging to balance between low frequency and broadband. Achieving subwavelength vibration suppression has always been a challenge, in particular, tunability without introducing additional weight has attracted great attention. Here, we utilized oblique springs to construct a quasi-zero stiffness (QZS) mechanism, which harnesses geometric nonlinearity to achieve tunability of the bandgap within the ultralow-frequency range. We have evaluated the dispersion relations of this system using both linearized model and perturbation methods. The results indicate that the introduction of the QZS mechanism can generate zero-frequency bandgap and critical wavenumber. The proposed structure offers two types of band gap tunability-variation amplitude and changes in the length of the oblique springs. To support these findings, numerical simulation was carried out, and provides strong support for our theoretical results. We expect that this research offers a new perspective for low-frequency vibration reduction.
In this paper, the nonstationary stochastic response of fractional structural systems subjected to fractional excitations is examined. Fractional operators provide an effective mathematical construct to model energy dissipation and stiffness-damping coupling mechanisms that cannot be modeled by integer operators. In particular, the memory property of fractional operators makes them suitable for treating the non-Markovian features exhibited by systems with path-dependent responses, such as the damping and stiffness mechanisms in structural systems and soils under dynamic loading. In this paper, particular attention is devoted to fractional structural systems excited by a proposed stochastic ground motion model consisting of a nonstationary filtered fractional Kanai-Tajimi process, thus accounting for path-dependent energy dissipation in both the structure and the seismic waves' propagating medium. The work attempts to elucidate the sensitivity and effects on probabilistic structural response predictions due to non-Markovian features in the excitation when both the system and the excitation are modeled using fractional operators. To analyze the fractional operators describing the structure and soil, the operators are discretized and approximated as the superposition of the solutions of a system of linear first-order ordinary differential equations, which, together with the system dynamics equations, are transformed into an equivalent first-order linear state-space model. The stochastic response evaluation for the system is conducted in closed form by solving the associated Lyapunov covariance equation. The analytical results from stochastic analyses are juxtaposed with pertinent Monte Carlo simulations to demonstrate the accuracy of the proposed method. Validation results using measured data from the 2023 Turkey-Syria earthquake demonstrated that the recorded ground motions exhibit fractional features with an energy rate of decay in the spectral density that is captured more accurately by the proposed fractional model than the traditional integer Kanai-Tajimi model.
The upcrossing method is advantageous in extreme value analysis because it leads to a more efficient use of the available data. In its typical applications in extreme wind prediction, conventional analysis often adopts the assumption of statistical independence between wind speed and its time derivative. This assumption leads to a constant cycling rate, which, however, is inconsistent with observations. To address this limitation, wind speed is here modeled as a memoryless transformation of an underlying stationary process. This approach captures the statistical dependence between wind speed and its time derivative, and it explains the observed increase in cycling rate with wind speed. Validation using surface wind records from six meteorological stations showed the relation between cycling rate and wind speed predicted by the translation method aligns well with observations. The comparison of the extreme wind speed demonstrates ignoring the wind-speed-derivative dependence would systematically underestimates design wind speeds by approximately 10%.
Porous shallow-water equations (PSWEs) predict the depth and velocity of urban flooding without resolving individual buildings in the grid, which can reduce computational costs by a factor of 10 or more and thereby streamline large-scale modeling of urban flood hazards. However, PSWEs require a drag coefficient to account for building form drag and bottom shear, and its estimation has been challenging and a source of significant uncertainty in previous studies. Here, we use statistical mechanics, dimensional analysis, and classical shallow-water equations (CSWEs) to develop a new, closed-form equation for the drag coefficient that can be computed using globally available building footprints and topographic slope data. Considering both idealized building configurations and the layouts of numerous cities, and using the new equation for the drag coefficient, we show that coarse-grid PSWE predictions are consistent with fine-grid CSWE predictions at street width and larger scales. This work thus offers a pathway for full closure of the PSWEs for accurate and efficient urban flood prediction.
To study the effect of water-cement (w / c) ratio and pore water on the mesomechanical properties of recycled aggregate concrete (RAC), a computational model of RAC that takes into account various w / c ratios (0.3, 0.36, 0.4, 0.41, 0.49, 0.5, 0.6, 0.7) and porosities (3%, 6%, 8%, 10%, 12%) is established using the Monte Carlo approach. The base face element method (BFEM), an innovative finite element approach derived from complementary energy principle, is applied to calculate the stress and flexibility matrix of each element in a precise description while avoiding the Gauss calculus. The effects of w / c ratio and pore water on stress-strain curves, compressive strength, tensile strength, elastic modulus, and damage modes are investigated. The simulation results show that the compressive strength, tensile strength, and compressive modulus of elasticity gradually decreased while the w / c ratio increased from 0.3 to 0.7. The extended path of damage cracks gradually shifts from the old interfacial transition zone (ITZ) and interior of the old cement mortar to the new ITZ and new cement mortar between the localized cracks. Damage cracks are mainly found in the new cement mortar surrounding the dense area of aggregates. Pore water must be taken into account in the analysis because it significantly affects the tensile mechanical properties of RAC.
