Journal of Engineering Mechanics

In this paper, a modified/extended rotational hardening (RH) rule is applied to the nonassociated simple anisotropic constitutive model, SANICLAY-D, for clayey soils. In the proposed model, the destructuration mechanism, as well as zero and nonzero fabric anisotropy at critical state (CS), are considered. A detailed model formulation with the RH rule that yields a unique CS in the $e\text{-}\ln (p^{\prime })$ space is presented including an appropriate form of the relatively simple substepping integration algorithm. In addition, the model is implemented into ABAQUS finite-element software using a User-defined Material (UMAT) subroutine and used in the simulation of various experimental tests. The modified SANICLAY-D model (SANICLAY-MD) is meticulously calibrated step by step for Saint-Alban sensitive soft clay. Drained and undrained triaxial tests after various consolidation paths as well as the direct simple shear (DSS) test are simulated for Saint-Alban and Bothkennar clays as a boundary value problem. Simulation results approve the SANICLAY-MD model’s performance in the prediction of the natural soil behavior. Results show that neglecting the effect of fabric anisotropy at CS and destructuration of natural clays can lead to inaccurate prediction in the constitutive modeling of intact soft soils.

Story isolation systems (SIS) have great application potential in the seismic design of some special structures. This paper studied the seismic control performance of SIS using a tuned mass damper inerter (TMDI) considering two installation modes, namely TMDI-A and TMDI-B. First, a four-degree-of-freedom (4DOF) simplified model including the masses of the substructure, superstructure, isolation layer, and TMDI is proposed, and three cases with different isolation layer locations were designed. Second, numerical optimization based on the $H_2$ norm was used to obtain the optimal parameters of the TMDI considering the influence of the tuned mass ratio and the design period and damping of the isolation layer. Third, a comparative study was conducted on the optimal performance of the TMDI-A and TMDI-B schemes compared with their corresponding tuned mass damper (TMD) schemes (i.e., TMD-A and TMD-B) by time-history analysis. Finally, an 11-story SIS was designed as an example to investigate the effectiveness of the TMDI in a multistory structure. Results showed that the optimal performance of the two TMDI schemes can be significantly enhanced with the increase of the inertance–mass ratio, and also will be improved with the rise of the isolation layer location, whereas the increase of the tuned mass ratio had a converse effect on the performance of TMDI-A and TMDI-B. In addition, both TMDI schemes had better performance when the isolation layer was in a low-damping state, and the isolated period of the superstructure only affected the control performance of the TMDI-B scheme. In summary, the TMDI schemes had remarkable superiority over the TMD schemes, and TMDI-B had better performance than the TMDI-A scheme, which was verified by the analysis of the simplified model and the multistory structure.

Highly flexible plate structures are subjected to various loading and edge conditions in many engineering applications, such as in the aerospace and civil industries. In this paper, the post-buckling response of rectangular plates subjected to axial and shear loadings is investigated by employing the Carrera Unified Formulation (CUF). As in previous works, only isolated plates have been considered, regardless of the effects of the stiffeners and boundary conditions imposed by the surroundings. However, in this research, different plate models are implemented, and the effects of boundary conditions imposed by the stiffeners are evaluated precisely. Comprehensive assessments are provided for the geometrically nonlinear equilibrium curves of the plate structures using the Newton–Raphson linearization method with the path-following constraint. Furthermore, the comparisons of different geometrically nonlinear assumptions according to the full Green–Lagrange nonlinear model and von Kármán nonlinear plate theory are presented. The importance of strain–displacement relationships and stiffeners’ effects in the nonlinear response of plate structures is highlighted. As a result, the accuracy and effectiveness of the presented CUF-2D model are demonstrated.

This paper presents the results of a series of laboratory experiments, by placing a turbulent wall jet in the upstream and downstream of a 90° channel bend, to investigate the effects of secondary flow on formation of local sediment erosion and deposition. The effects of jet and current flow intensities on the erosion pattern were characterized by the jet’s Reynolds number, $Re$, channel Froude number, $Fr$, and the ratio of water depth to nozzle diameter, $h/d_{\mathrm{o}}$. The geometrical characteristics of local erosion such as jet trajectory, maximum scour depth, $d_s$, and maximum mound height, $h_m$, were measured. The area and volume of scours and mounds were calculated from measurements, and the results were correlated with the controlling parameters. Experimental observations indicated the existence of distinct scour patterns due to variations of channel Froude number. Two additional scour holes were identified due to the effect of stream interactions and formation of vortex regions immediately downstream of sediment mound. It was found that both channel and jet flows contributed to trajectory of the jet and the footprint of erosion. A threshold Froude number of $Fr=0.091$ was identified at which the current and jet flow were in equilibrium. The results showed that for a constant value of $Fr$, all scour parameters increased with increasing Reynolds number. However, $Re$ did not have any effects on the jet’s deflection. Comparing the erosion profiles in the upstream and downstream bend indicated that the secondary current and turbulent redistribution altered the erosion and mound formation in the downstream of the bend in relatively high Reynolds (i.e., $Re\ge \mathrm{23,000}$), high channel Froude numbers (i.e., $Fr>0.091$) and high jet submergence (i.e., $h/d_o>10.53$).

Shape sensing is an emerging technique for the reconstruction of deformed shapes using data from a discrete network of strain sensors. The prominence is due to its suitability in promising applications such as structural health monitoring in multiple engineering fields and shape capturing in the medical field. In this work, a physics-informed deep learning model, named SenseNet, was developed for shape sensing applications. Unlike existing neural network approaches for shape sensing, SenseNet incorporates the knowledge of the physics of the problem, so its performance does not rely on the choices of the training data. Compared with numerical physics-based approaches, SenseNet is a mesh-free method, and therefore it offers convenience to problems with complex geometries. SenseNet is composed of two parts: a neural network to predict displacements at the given input coordinates, and a physics part to compute the loss using a function incorporated with physics information. The prior knowledge considered in the loss function includes the boundary conditions and physics relations such as the strain–displacement relation, material constitutive equation, and the governing equation obtained from the law of balance of linear momentum. SenseNet was validated with finite-element solutions for cases with nonlinear displacement fields and stress fields using bending and fixed tension tests, respectively, in both two and three dimensions. A study of the sensor density effects illustrated the fact that the accuracy of the model can be improved using a larger amount of strain data. Because general three dimensional governing equations are incorporated in the model, it was found that SenseNet is capable of reconstructing deformations in volumes with reasonable accuracy using just the surface strain data. Hence, unlike most existing models, SenseNet is not specialized for certain types of elements, and can be extended universally for even thick-body applications.

Short fiber–reinforced composites (SFRCs) are high-performance engineering materials for lightweight structural applications in the automotive and electronics industries. Typically, SFRC structures are manufactured by injection molding, which induces heterogeneous microstructures, and the resulting nonlinear anisotropic behaviors are challenging to predict by conventional micromechanical analyses. In this work, we present a machine learning–based multiscale method by integrating injection molding–induced microstructures, material homogenization, and deep material network (DMN) in the finite-element simulation software LS-DYNA for structural analysis of SFRC. DMN is a physics-embedded machine learning model that learns the microscale material morphologies hidden in representative volume elements of composites through offline training. By coupling DMN with finite elements, we have developed a highly accurate and efficient data-driven approach that predicts nonlinear behaviors of composite materials and structures at a computational speed orders of magnitude faster than the high-fidelity direct numerical simulation. To model industrial-scale SFRC products, transfer learning is utilized to generate a unified DMN database, which effectively captures the effects of injection molding–induced fiber orientations and volume fractions on the overall composite properties. Numerical examples are presented to demonstrate the promising performance of this LS-DYNA machine learning–based multiscale method for SFRC modeling.

The present study developed a three-dimensional (3D) multiscale modeling approach to investigate the mesoscale damage behavior of curved ramp bridge deck pavement subjected to tire loading. First, a full-scale tire–bridge interaction finite element (FE) model was established to solve the macroscopic response of deck pavement during vehicle turning. Subsequently, the 3D mesostructure of the asphalt concrete layer was reconstructed from X-ray computer tomography (CT) images through a digital image processing (DIP) technology. Finally, a homogenization method was adopted to link the mechanical properties of deck pavement at two different scales, and a mapping procedure was employed to transfer the boundary displacements from macroscale pavement target element to the mesoscale representative volume element (RVE) model. Also, the bilinear cohesive elements were applied to simulate damage initiation in the RVEs. The results showed that smaller curvature radius and higher travel speed can promote unbalanced stress and local damage of the outer loading zone. From the mesoscale viewpoint, reducing curvature radius or increasing travel speed could result in crack direction shifts and increase the irregularity of microcrack distribution. In addition, transverse microcracks are commonly found in the center of the tire load, while longitudinal microcracks are distributed on the deck pavement surface around the tire edges and the dual-tire clearance center.

Efficiently computing the transient response of a linear hysteretic damping (LHD) system that is noncausal to deterministic loading that is regular or irregular is challenging. In this study, we developed a time-shifting causalization procedure and efficient solution methods to compute the transient response, conducted in the frequency or Laplace domain based on pole-residue operations. Because these operations require the causalized system’s transfer function to be in its pole-residue form, true poles were extracted by the Prony-SS method for the Laplace-domain method. In contrast, the frequency-domain method designates imaginary poles directly from the system’s frequency response function. Overall, the latter method was easier to implement and more computationally efficient but less capable of computing longer responses due to the imposition of the periodic oscillator. The proposed methods were used in numerical studies for oscillators with hysteretic damping and mixed viscous-hysteretic damping to earthquake-induced loading; correctness was verified by a time-domain method.

The determination of the long-term extreme distribution for a wave-loaded structure requires computing the second-order statistics of the responses and their time derivatives under various short-term sea states. In a spectral context, these statistics are typically obtained on a modal basis by integrating the power spectral densities of the corresponding responses over frequency. In this paper, a semianalytical approximation is developed for computing these integrals with the aim to reduce the computational cost of each short-term analysis. To do so, a state-space formulation is considered for the equations of motion, and the general framework provided by the multiple timescale spectral analysis is implemented. It hinges on the existence of distinct peaks in the integrands to express the variances and the covariances of the modal state responses as the sum of two components with simple expressions: the resonant and the loading component. New techniques are investigated to formulate them. For the former, the structural kernel is expanded in partial fractions while it is fitted by a monomial of a given degree for the latter. The resulting decomposition is validated on a minimalistic example first and is then verified on a simplified model inspired by the Bergsøysund Bridge, which is an actual floating pontoon bridge located in Norway.

A Bayesian formulation for inference of material properties from experimental signals is proposed with a normal likelihood quantifying noise and an inverse gamma prior expressing uncertainty about noise variance. Asymptotic analysis shows that, for large samples, the posterior distribution is maximized at the database signal that minimizes an $L_2$ norm between the experimental data and database entries. The largest posterior probability tends to 1 as the number of data points on the signals tends to $\infty$. There exists a critical ratio between the mode of the inverse gamma prior and the true variance of the normally distributed noise. This ratio determines how the posterior probability varies with the shape parameter of the inverse gamma prior. Numerical results based on an analytical expression and simulations confirm the conclusions from the asymptotic analysis. These results show that posterior probabilities are insensitive to the choice of prior mode when the prior’s shape parameter is taken to be small. In spite of the use of interpolation in database construction, the approach is limited to cases where a small number of parameters is to be identified. When multiple signal types are analyzed simultaneously, a method using a weighted average of posterior distributions from the different signal types is proposed. This method is compared with a classical Bayesian approach that uses a joint likelihood. Effective choices of prior parameters are recommended.

Data-driven modeling of nonlinear dynamical systems is essential because of the need for a trade-off among complexity, efficiency, and reliability in analytical or numerical studies as well as the difficulty of deriving fully physics-based models. An important limitation is commonly seen in existing works: modeling of a new dynamical system typically starts from scratch, requiring a large amount of data and intensive computation, though some prior experience or knowledge is available from a previously collected database of similar but different systems. However, on the one hand, the data amount for the new dynamical system is often limited, especially for real-world dynamical systems. On the other hand, the computational resource is also limited and a data-driven modeling task is usually computationally expensive, especially for large-scale systems. To improve data efficiency and computational efficiency in data-driven modeling of nonlinear systems, we present an enhanced data-driven modeling approach by incorporating metalearning into a physics-integrated deep learning framework. The core idea is to learn the metaknowledge about how to model a new system from a previously collected database of similar but different systems. Then this metaknowledge is leveraged to enable efficient modeling of a new system with limited data. For validations we conducted numerical experiments on three sets of fundamental nonlinear systems, including Duffing oscillators, nonlinear pendulums, and van der Pol oscillators. We performed both interpolation and extrapolation modelings to investigate the generalization ability of the presented approach. Furthermore, we conducted a quantitative analysis on data efficiency, addressing two critical issues: how few data are sufficient for the new system modeling and how much prior experience (previously collected database of similar but different systems) is needed for the metalearning. The results show that the presented approach improves both data efficiency and computational efficiency, compared with the conventional data-driven modeling approach (without leverage of the prior database) and the pretraining-based approach (simply using the prior database but without metalearning idea). We also discuss the limitations of this work and potential future study.

This paper considers the global configuration space of postbuckled structures. Initially, a slender buckled beam is considered. The boundary conditions are pinned at one end and fully fixed at the other. The pin-end of the initially flat beam is moved toward the other end by a small amount. This causes the beam to buckle laterally (the beam is axially inextensional) with a characteristic shape. Since this is the outcome of a stable-symmetric pitchfork bifurcation, the buckled shape possesses a near mirror-image shape on the other side. Which of the two available equilibrium configurations is taken up depends on the usual, often small, symmetry-breaking effects commonly encountered in axially loaded systems. Given fixed conditions to maintain this initial buckled shape we then apply a moment at the pinned end. The relation between the applied moment and the change in shape is the primary focus of this study. The extent of the buckling (end shortening) is varied, with the magnitude of the moment, as a function of the angle, providing considerable information about the potential energy landscape in which the axially loaded system operates. The applied moment can be thought of as a probing mechanism whereby various equilibrium configurations are revealed, together with information regarding their stability and robustness. A similar approach is then used where the structure consists of two nominally identical beams attached at a right angle. In both cases, the opposite end from the actuation is clamped. An experimental study is conducted on 3D-printed specimens, and this is compared with a finite element analysis using ANSYS, and a large-deflection elastica analysis.