Journal of Engineering Mechanics

The ever-growing reliance on probabilistic performance-based frameworks in assessing and designing structural systems is creating a need for efficient tools for propagating uncertainty through general nonlinear and dynamic structural systems. This research is focused on the development of metamodeling strategies for rapid response evaluation of a class of nonlinear multi-degree-of-freedom (MDOF) structural systems driven by stochastic excitations. In particular, the nonlinear autoregressive with exogenous input (NARX) model has been demonstrated to be versatile and effective in this respect. However, significant difficulties in NARX model calibration and execution have been encountered when directly applying this approach to practical MDOF systems with large numbers of degrees of freedoms. To overcome this limitation, a new metamodeling approach is proposed in this work through combining projection-based model order reduction with multi-input multioutput NARX models. The effectiveness and accuracy of the proposed approach are illustrated on a 40-story nonlinear steel-frame subject to stochastic earthquake excitation.

A numerical model was developed for studying the performance of a rectangular tuned liquid damper (TLD) and fluid–structure interaction. A TLD is a structure which dissipates excitation energy through the sloshing behavior of fluid inside a tank. To design this structure as an effective device, it should be investigated by considering different parameters such as frequency ratio, mass ratio, and structural damping ratio. For numerical modeling of the fluid, the finite-element method with nonlinear boundary conditions was developed. In this method, two types of shape functions are used: classic Lagrange shape functions, and new spherical Hankel shape functions. It was demonstrated that using the new functions with fewer elements than the classic method, the solution accuracy can be improved. After the numerical modeling of the fluid in the tank, the response of the structure, namely the displacement and acceleration, was calculated. The values of the parameters that produced the most effective TLD were obtained. To examine the accuracy and applicability of the algorithm, the numerical results were compared with available experimental data. The results indicated that the proposed model has the capability to study TLD performance with good accuracy.

The mechanical responses of steel fiber–reinforced concrete (SFRC) thermally damaged at high temperature needs a deeper evaluation via a mesoscopic model that explicitly treats the fibers. For this demand, the lattice discrete particle model for SFRC after high temperature (LDPM-F-HT) is formulated. A series of experimental tests for SFRC with 0%, 1%, and 2% of steel fiber volume fraction with different heating treatments are performed to calibrate and validate the LDPM-F-HT. It is found that the nonmonotone decreasing of the macroscopic compressive strength up to 400°C is caused by the slower thermal degradation of shear strength than that of tensile strength at the mesoscale. The good matches between the experimental and numerical results demonstrate that LDPM-F-HT can capture also this phenomenon. In the numerical simulation of three-point bending tests, it is observed that the dimension of the fracture process zone (FPZ) at load peak increases with the increase of fiber content and heating temperatures. However, the FPZ width in SFRC reaches its maximum value after the thermal treatment of 450°C rather than 600°C.

This paper presents an element-by-element-based interval finite-element method (EBE-IFEM) for the uncertain interior acoustic field prediction with uncertain-but-bounded parameters. The interval dynamic matrices and loads vectors are assembled with the element-by-element (EBE) strategy, and decomposed into diagonalization forms additionally. Then the interval dynamic equation can be rewritten as iterative enclosure form, and finally are analyzed by both Rump’s method and the Neumaier-Pownuk method in the comparative discussion. Meanwhile, numerical examples are calculated with the interval perturbation finite-element method (IPFEM), modified interval finite-element method (MIPFEM), and Monte Carlo simulation. The numerical results demonstrate that the solution by the EBE-IFEM shows more accurate and more stable than other cross-references, when evaluating the intervals of sound pressure response in interior acoustic field.

Real-time hybrid simulation (RTHS) is an emerging high-efficiency and low-cost structural test method. Stability analysis is a very important part of RTHS to ensure the stability of the experimental system. Currently, there are two different types of analysis methods: discrete and continuous methods. However, these two methods obtain different stability results when the time step of the numerical substructure (NS) is large. To investigate this difference, a stability analysis strategy based on asynchronous multi-rate hybrid simulation is proposed. These two different types of stability analysis methods were introduced and the fact that the two methods may get different stability results was discussed. The proposed strategy verified that, compared with the continuous method, the discrete method is more suitable for the stability analysis of RTHS. Due to the limitation of the discrete method, it is not suitable to take the critical stability points obtained by the discrete method directly as the whole stability boundary of RTHS when the time step of the NS is large. The proposed strategy can handle cases in which the time step of the NS is large to obtain a more accurate stability result.

Discrete response of structures often is a key probabilistic quantity of interest. For example, one may need to identify the probability of a binary event, such as whether a structure has buckled. This study used an adaptive domain-based decomposition and classification method, combined with sparse grid sampling, to develop an efficient classification surrogate modeling algorithm for such discrete outputs. An assumption of monotonic behavior of the output with respect to all model parameters, based on the physics of the problem, helps to reduce the number of model evaluations and makes the algorithm more efficient. As an application problem, this paper developed a computational framework for generation of a probabilistic penetration response of S-$2\mathrm{glass}/\mathrm{SC}$-15 epoxy composite plates under ballistic impact. This enables the computationally feasible generation of the probabilistic velocity response (PVR) curve, or the $V_0-V_{100}$ curve, as a function of the impact velocity, and prediction of the ballistic limit velocity as a function of the model parameters. The PVR curve incorporates the variability of the model input parameters and describes the probability of penetration of the plate as a function of impact velocity.

Masonry panels consisting of piers and spandrels in buildings are vulnerable to in-plane actions caused by seismicity and soil subsidence. Tectonic seismicity is a safety hazard for masonry structures, whereas low-magnitude induced seismicity can be detrimental to their durability due to the accumulation of light damage. This is particularly true in the case of unreinforced masonry. Therefore, the development of models for the accurate prediction of both damage initiation and force capacity for masonry elements and structures is necessary. In this study, a method was developed based on analytical modeling for the prediction of the damage initiation mode and capacity of stand-alone masonry piers; the model was then expanded through a modular approach to masonry walls with asymmetric openings. The models account for all potential damage and failure modes for in-plane loaded walls. The stand-alone piers model is applicable to all types of masonry construction. The model for walls with openings can be applied as is to simple buildings but can also be extended to more complex structures with simple modifications. Model results were compared with numerous experimental cases and exhibited very good accuracy.

Unreinforced masonry structures, particularly façade walls, are seismically vulnerable due to their weak connections with adjacent walls, floors, and/or roofs. During an earthquake, such walls formulate local mechanisms prone to out-of-plane collapse. This behavior has been largely investigated using classical rocking theory, which assumes the structure responds as a rigid body undergoing rocking motion, with energy dissipation at impact. Due to the complexity of the problem, however, e.g., number of degrees of freedom or boundary conditions, numerical block-based modeling is gaining momentum. However, numerical models lack a consistent and reliable treatment of the energy loss at impact. This paper bridges the gap between the well-established energy loss of classical rocking theory and the treatment of damping in numerical modeling. Specifically, it proposes an equivalent viscous damping model through novel ready-to-use predictive equations that capture the dissipative phenomena during both one-sided and two-sided planar rocking motion. The results reveal a satisfactory performance of the proposed model through comparisons with experimental results from literature and highlight its universality and robustness through applications of the model in fundamentally different block-based numerical modeling software.

For granular materials, the kinematic degrees of freedom at the microscale of particles are the particles’ displacements and rotations. In classical continuum mechanics, the kinematic degree of freedom at the macroscale is the (local) displacement field. The rotation of a material element is not independent but is determined by the antisymmetric part of the displacement gradient. The objective of this study is to investigate, mainly by means of discrete-element method simulations, whether the average particle rotation is equal to the continuum rotation determined from the average displacement gradient. In the three-dimensional discrete-element method simulations of shear tests (with nonzero average continuum rotation), simulations with and without contact couples have been analyzed. The simulation results show that the average particle rotation is effectively equal to the continuum rotation, over the whole range of strains. Additionally, the results of an X-ray tomography test of a rounded granular soil under triaxial compression are analyzed. The average rotation of soil particles inside shear bands agrees well with the average continuum rotation determined from the particle displacements. Comparison of simulation results with contact couples to those where contact couples were not considered reveals that the presence of contact couples has a significant effect on the stress ratio and on the volumetric strain. The stress tensor is symmetric, even when contact couples are included.

Vibration-based damage detection techniques usually focus on the changes in the modal properties as a result of any structural damage. For the last three decades, varying levels of success have been achieved in identifying damage using modal frequencies as well as mode shapes. The present study aims at using the damage-induced changes in the fundamental mode shape for evaluating the severity of damage in structures. For this purpose, the concept of the spectral element method was applied to derive the expression for mode shapes in the frequency domain. The difference between the fundamental mode shape of the damaged and undamaged structures was formulated and mathematical correlation established to derive the measure of damage quantity. A numerical analysis involving a 14-story shear building was performed to show the effectiveness of the proposed approach in damage quantification. In order to check the efficiency under real measurement conditions, the approach was also verified experimentally on a three-dimensional miniature model of a 6-story shear building in the laboratory environment. Both simulation and experimental investigations show the competency of the fundamental mode shape in structural damage quantification. Also, the use of fundamental mode shape makes the proposed methodology easy to implement on real structures.

During the last years, several mechanics-based macromodels have been proposed to assess the cyclic response of infilled RC frames. However, the uncertainties behind the assumptions on damage and failure mechanisms compromise the reliability of such approaches. For this reason, this paper proposes a new data-driven hysteresis model for the cyclic response of infilled RC frames. The infill panel is schematized as a single-degree-of-freedom element, whose constitutive law is given by the proposed hysteresis model. The model combines a degrading Bouc–Wen element with a slip-lock element, which is introduced specifically to reproduce the pinching effect due to crack openings in the masonry panel. The parameters governing the model have clear physical meanings and are calibrated on the basis of an experimental data set of cyclic responses of single-story single-bay RC infilled frames. The calibrations are carried out by means of a genetic algorithm–based optimization. Analytical correlation laws linking the model parameters with geometric and mechanical properties of the RC infilled frame are proposed and validated by blind validation tests. Results show adequate accuracy of the model in reproducing the cyclic response of infilled frames characterized by significantly different geometrical and mechanical features. The model is defined by a smooth analytical hysteresis law, with great advantages regarding numerical stability and computational effort. This makes it suitable for dynamic and stochastic simulations.

Origami-based structures have gained interest in recent years due to their potential to develop lattice materials, called metamaterials, the mechanics of which are primarily driven by the unit cell geometry. The folding deformations of typical origami metamaterials result in stretch-dependent Poisson’s ratios, and therefore in Poisson functions with significant variability across finite deformation. This limits their applicability, because the desired response is retained only for a narrow strain range. To overcome this limitation, a class of composite origami metamaterials with a nearly a constant Poisson function, specifically in the range $-0.5$ to 1.2 over a finite stretch of up to 3.0 with a minimum of 1.1, is presented. Drawing from the recently proposed Morph pattern, the composite system is built as a compatible combination of two sets of cells with contrasting Poisson effects. The number and dimensions of the cells were optimized for a stretch-independent Poisson function. The effects of various strain measures in defining the Poisson function were discussed. The results of the study were validated using a bar-and-hinge-based numerical framework capable of simulating the finite deformation behavior of the proposed designs.

Line contact usually causes stress concentration, resulting in the wear and failure of materials and structures. The characterization of the contact phenomenon thus plays an important role in the safety evaluation of materials and structures. In this paper, an inverse method is developed that can identify the principal parameters in contact by employing the experimentally measured displacements and mathematical optimization. Basing on the contact theory, the relationship between the contact parameters and displacements on the interface is modeled. The parameters are then inversed by matching the modeled displacements to the experimentally measured data through optimization. Only the displacements on the surface of the contact member are required in this method, which can be easily measured by a segmentation-aided digital image correlation approach. By utilizing the proposed method, the contact between a cylinder and a plate is characterized and the variations of the contact parameters associated with the applied loads and cylinder’s radius are discussed. Error estimation is carried out by implementing the proposed method with the finite element simulated data. Results show that the proposed method can provide reliable identification results under the influence of different kinds of disturbances.

In this work, the study of a complex masonry umbrella vault located within Masegra Castle (Museum of Sondrio territory, Northern Italy) is presented. Built during the renewal of the castle in the 16th century, the umbrella vault of Masegra Castle is characterized by a total of eight sails, with four half-cross vaults added at the corners, supported by four walls, and resulting in a quadrangular horizontal plan. The observed crack pattern seems to derive from vertical settlement phenomena involving at least one of the supporting walls. A multidisciplinary approach based on innovative technologies for the geometric reconstruction, detailed analysis of the construction, the historical evolution, and its state of conservation, has been followed. Starting from dense laser scanner point clouds and photogrammetric surveys, historical building information modeling (HBIM) models have been created and allowed the generation of an accurate geometrical representation of the umbrella vault through nonuniform rational basis-splines (NURBS) surfaces. Starting from the NURBS-based model, an adaptive kinematic procedure is used to determine the failure behavior under settlements. A discretization through triangular NURBS elements, in which the real geometry remains unvaried, is adopted. Each element is idealized as a rigid block and jumps of displacement are allowed at the boundaries only. By applying the principle of virtual works, a discontinuous displacement field deriving from an imposed settlement is obtained. As a consequence of the reduced number of elements adopted, a metaheuristic mesh adaptation procedure is finally applied to find the correct disposition of fracture lines. Different settlement typologies are adopted in the analyses to reproduce the crack pattern observed on the umbrella vault. Finally, an inverse analysis is conducted to estimate the shape of the occurred settlements starting from the observed crack pattern.

In the seismic performance assessment of reinforced concrete (RC) frames, a reliable estimation of the capacity of unreinforced masonry (URM) infill walls is of utmost importance to ensure structural safety conditions. With particular attention to the out-of-plane (OoP) capacity of URM infill walls after in-plane (IP) damage, the issue of defining reliable analytical prediction models for the assessment of the capacity is an ongoing study. In this paper, empirical equations are proposed for the evaluation of the infilled frame’s OoP capacity, with or without IP damage, based on an extensive numerical parametric analysis, focusing on the influence of the key parameters that govern the mechanical model. The OoP capacity of URM infill walls, considering the variation in their geometrical and mechanical properties, was evaluated by using a macroelement model. The OoP strength was found to be largely influenced by the compressive strength, slenderness ratio, aspect ratio, and, additionally, level of IP damage. The reduction of OoP strength and stiffness due to IP damage was largely governed by the strength and the slenderness ratio of the URM infill wall. The reliability of the proposed model was also proved by comparisons with experimental results and some of the analytical models already available in the literature. The proposed equations provide reliable estimates of the OoP capacity by strongly indicating the suitability of the adopted macroelement model in capturing the OoP response of URM infills.

The Föppl-von Karman equations describe the highly nonlinear postbuckling behavior of elastic plates but are notorious for their unwieldiness. Owing to the lack of a sufficiently general solution, the practical design of plates against local buckling is instead based on the empirical Winter equation. This paper aims to connect both concepts by analytically deriving a Winter-type equation, taking the Föppl-von Karman equations as a starting point. The latter equations are first simplified in a way that preserves the main mechanics of the postbuckling behavior of plates and are combined with a failure criterion based on von Karman’s effective width concept. The resulting equation is solved by means of a truncated Fourier series. This yields excellent predictions of the plate behavior over an ever more extended range of postbuckling behavior as the number of Fourier terms increases, both for geometrically perfect and imperfect plates. As a crowning result, a closed-form expression is presented as an equivalent to the empirical Winter equation. This new expression agrees closely with the Winter curve and allows an analysis of the various factors affecting the local buckling capacity of plates.

We analyze in two dimensions the mechanical behavior of materials with granular microstructures modeled by means of a variationally formulated strain-gradient continuum approach based on micromechanics and show that it can capture microstructural-size-dependent effects. Tension-compression asymmetry of grain-assembly interactions, as well as microscale damage, is taken into account and the continuum scale is linked to the grain-scale mechanisms. Numerical results are provided for finite deformations and substantiate previous research. As expected, results show interesting size-dependent effects that are typical of strain-gradient modeling.

The nitrogen sorption isotherm is conventionally used to deduce the specific surface area of porous materials. However, it often exhibits a sharp drop around 0.5 relative pressure. A theory explicitly accounting for intermolecular-scale pressure, instead of classical theories of constant disjoining pressure in condensed liquid, is constructed and used to determine cavitation during desorption. Intermolecular-scale liquid pressure distribution is quantified using a recently developed soil sorptive potential framework, showing compressive liquid nitrogen pressure decaying nonlinearly with increasing distance to the particle surface. A range of cavitation pressure is predicted by classical nucleation theory and the van der Waals equation of state. Cavitation is shown to be triggered when nitrogen’s global minimum liquid pressure falls within the cavitation threshold. It is shown that this criterion is valid for all tested soils. Computed minimum liquid pressure always occurs at 0.5 relative pressure, which is in accordance with experimental isotherm data and further indicates the validity of the cavitation onset criterion.

The interactions between particles in dense particulate systems are organized in force networks, mesoscale features that influence the macroscopic response to applied stresses. The detailed structure of these networks is, however, difficult to extract from experiments that cannot resolve individual contact forces. In this study, we showed that certain persistent homology (PH) measures extracted from data accessible to experiment are strongly correlated with the same features extracted from the full contact force network. We performed simulations known to accurately model experiments on an intruder being pushed through a two-dimensional (2D) granular layer and compared PH properties of full contact force networks and networks constructed using only the sum of the normal forces on each grain. We found that the main features were highly correlated, suggesting that data commonly available in experiments are sufficient for quantifying the structure of force networks in evolving granular systems.

The construction and long-term use of underwater tunnels suffer from hazards associated with the pore pressure and water inflow. Analytical approaches quickly can predict the seepage field, through which the water inflow into tunnels can be estimated. In this study, the exact analytical solution of seepage field for underwater multiple tunnel problems was addressed successfully for the first time using the Schwartz alternating method combined with conformal mapping, taking into account the arbitrary tunnel arrangement and tunnel interaction. It was validated that high-accuracy results can be obtained after only two to three iterations. Comparing the analytical results with those from numerical simulations and the mirror image superposition method, the results in this study were in good agreement with the numerical results throughout the entirety of the ground, whereas the superposition results had a large deviation from the exact values in the region close to the tunnel boundary. Through a case study, the applicability of the analytical model was verified. Finally, based on the obtained analytical solution, a parametric study was conducted to investigate the influence of the key parameters on the hydraulic head distribution and the water inflow into the tunnels. Several dimensionless charts for ease of use of practitioners are provided.

The paper presents a study of particle shape effect on microstructure within granular materials in gravitational environments using samples acquired from three-dimensional (3D) discrete element method (DEM) modeling and simulation (M&S) of gravitational pluviations. Three-axis ellipsoidal particles with various aspect ratios are examined for their spatial orientations, and the three-axis probability density functions (PDF) are analyzed before and after pluviation. A complicated data structure, convex hull, is employed to construct tetrahedra that connect particle centroids and investigate the internal topology and fabric of particle assemblies composed of various particle shapes. The Qhull-constructed connected tetrahedra within granular materials may serve as a useful tool to study the geometrical fabric (such as tetrahedron shape, solid angles, and void ratio), investigate particle collision requirements in sample preparation, describe strain/deformation/failure mechanisms, and explore stress distribution over granular materials.

This work evaluated the remarkable influence of stereotomy on discrete methods adopted for the dynamic response of an ancient masonry structure. The historic building used as a case study is the Church of Santa Maria of Varano in Muccia, in the province of Macerata, Italy, which was exposed to the severe seismic sequence that hit Central Italy in 2016, namely the major events of Accumoli, Visso, and Norcia. The structure was modeled using the actual stereotomy of blocks and three hypothetical arrangements of blocks of the masonry walls to investigate the existing crack pattern and vulnerabilities of the church. Sensitivity analyses were performed using the nonsmooth contact dynamics and discrete-element methods. These novel approaches suitably reproduced complex behaviors, considering large displacements and complete block separations, which is useful for upcoming retrofitting works.

Complicated interactions among embankment soil, geo-reinforcement, vertical piles, and surrounding soils make it difficult to model the behavior of geosynthetic-reinforced and pile-supported embankments (GRPSE). In particular, soil arching within embankment soil plays an important role in the behavior of GRPSEs and evolves with the pile-soil differential settlement. An improved estimation of pile-soil differential settlement by including the pile top settlement can enhance the assessment of the arching effect, compared with existing methods. In this study, a simplified model with evolved arching was developed based on the unit cell, to tightly integrate all possible load transfer mechanisms of GRPSE and derive a pile-soil differential settlement dependent theoretical solution of the critical arch height. Relevant solutions were proposed and validated by comparing experimental results and other existing methods. In particular, it was found that the predicted critical height is not constant but can evolve with the pile-soil differential settlement, indicating that the evolution of the soil arching can be, in theory, monitored step-by-step.