Journal of Engineering Mechanics

This paper applies the smoothed particle Galerkin (SPG) method to the analysis of penetration and perforation of metal targets. The SPG weak form is integrated using the direct nodal integration (DNI) technique with a nonresidual penalty–type stabilization term derived from strain smoothing. An adaptive anisotropic Lagrangian kernel is used to model the large deformation in the penetration and perforation processes. To model material breakup and fragmentation while avoiding potential spurious self-healing of meshfree approximations used in the failure analysis, a strain-based bond failure mechanism is implemented and the sensitivity to the failure criterion is numerically investigated. Two experiments are analyzed using the SPG formulation. The numerical results are compared with the experimental data to evaluate the effectiveness of the present method. The convergence behavior of the SPG formulation is also studied.

Lattice discrete particle models (LDPM) effectively relate concrete heterogeneity in terms of coarse aggregate–paste structure to damage patterns and load-displacement response. Interest in this type of model is enhanced by its ability to overcome issues that plague traditional methods, such as mesh dependence and need for energy regularization. Herein, an experimental procedure is developed to identify the mechanical parameters defined at the concrete mesoscale. The bounding surface of the LDPM is modified to accept the mesoscale parameters as inputs. Based on the parameter values identified through the multiscale experimental campaign, the macroscopic response to compressive load is simulated. Accuracy of the approach is demonstrated through comparisons with experimental results.

The traditional extended finite-element method (XFEM) encounters some challenges in the problems of frictional contact because the contact forces acting on the interface of cracks are difficult to determine. In this paper, a new method for the simulation for frictional contact on crack slip in the framework of the XFEM is proposed. Coulomb’s frictional model is introduced as the frictional constitutive model. The detection points are sowed on the interface to detect the contact states of the cracks and to interpolate the displacement of the grid node. The formulations of the contact forces and the penalty terms are established in the framework of the XFEM. Moreover, testing of a specimen containing two pre-existing flaws under uniaxial compression was conducted. In this experiment, an image processing technique is introduced to deal with the pictures of the real-time process of the specimen, which are captured by a high-speed dynamic recording system. The results from the proposed numerical method are in good agreement with the experimental data.

Common practice overlooks the highly heterogeneous nature of asphalt concrete (AC). Doing so equates to disregarding the effect of material properties’ spatial variability on the field behavior of AC mixtures. This paper presents an alternative computational approach to assess the effect of AC heterogeneity on the performance of a pavement structure. Using finite elements, a three-dimensional, flexible pavement structure is subjected to a moving load. Each time the structure is modeled, a unique internal distribution of mechanical properties is assigned to the AC layer. Thus, several simulations of the pavement structure are prepared, modeling a different AC layer each time. Two sets of pavement structures were simulated, considering mechanical properties of the AC layer as having two levels of variability (intermediate and high). The results present qualitative and quantitative estimates of the actual effect of material spatial variability (i.e., the heterogeneity of material properties) on the performance of a flexible pavement structure via strain analyses. The results also highlight the importance of consistency and quality in AC compaction.

The aim of this work is to explore the potential of two hierarchic sets, one polynomial and the other trigonometric, in the construction of versatile Ritz bases to accurately solve the linear buckling of anisotropic Kirchhoff plates. Focus is placed on reporting the basis ability to surmount numerical degrading effects associated with anisotropy. Several examples are presented to illustrate the merits and demerits of each set in terms of accuracy and rate of convergence, mainly by comparing their results with those obtained from traditional Ritz bases and finite-element models.

Three models—the viscous damping model, the new hysteretic damping model, and the Coulomb damping model—are studied in this paper. For the viscous damping and the Coulomb damping models, the free vibration problem is reviewed and demonstrated by animations. Regarding the new hysteretic damping model, the free vibration problem for the different range of parameters, namely $0<\eta <1$, $\eta =1$, and $\eta >1$ are analytically derived and are also demonstrated by animations. In particular, the exact solutions of the latter two cases are derived for the first time. In animations, the trajectories for three damping models in the phase plane consist of straight lines, quarter ellipses, and hyperbolic curves. For the case of $\eta \ge 1$, it is interesting that permanent deformation may occur. In addition, the dead zone for the Coulomb damping model in the phase plane is also addressed. The envelope for the amplitude decay yields exponential, geometric, and linear curves for the viscous damping model, the new hysteretic damping model and the Coulomb damping model, respectively. It is also the primary focus that the same period and the same ratio of amplitude decay for the relation between the viscous coefficient and the hysteretic parameter are constructed. All animations are produced using the symbolic software Mathematica because it is easy for readers to understand the physical behavior of three damping models.

Observations in extreme wind events, such as hurricanes/typhoons and downbursts, present strong nonstationarities. While nonstationary features of incident winds are typically ignored in the conventional analysis framework of wind-induced effects on structures, advances made in the interpretation of aerodynamic characteristics of the wind–structure interaction system over the last several decades have spurred demand for more accurate simulations of wind-velocity inputs. In this study, a Hilbert transform using the wavelet packet decomposition technique (Hilbert-wavelet-based scheme) is utilized to simulate the nonstationary wind process. The original broadband wind process is first decomposed into a series of monocomponent signals using the wavelet projection. The equivalent relation between the correlation and coherence functions is demonstrated to be applicable to the locally stationary process of each decomposition scale. This facilitates the use of available frequency-domain coherence relations in the time-domain simulation of multivariate nonstationary processes based on a multiscale spatial correlation approach. The prescribed spatial correlation of wind processes at multiple locations could be simultaneously achieved by generating appropriate instantaneous phase difference distributions, which are solutions of the equation set representing the relation between the instantaneous phase differences and correlation coefficients. The results of the numerical example indicate a remarkable potential of the proposed multiscale spatial correlation nested Hilbert-wavelet scheme in the simulation of nonstationary wind fields.

This paper presents an analytical method to determine the effective thermal conductivity of asphalt mixture, considering morphological characteristics and thermal properties of each component. The heat transfer process in asphalt mixture was modeled through reasonable simplifications. A multiscale model was developed to calculate the effective thermal conductivity of asphalt mixture based on the principle of minimum thermal resistance. The thermal prediction results were validated with experimental data reported in the literature. A new parameter, regarded as the morphological factor, was deduced to quantify the contribution of dispersed phase morphology to thermal conductivity of asphalt mixtures. The results show that the morphological factor of coarse aggregate, generally ranging from 0.2 to 0.7, can be represented by normal distribution. The sphericity and orientation angle of coarse aggregate have combined effects on the effective thermal conductivity of asphalt mixture, which can be characterized by the proposed morphological factor. Moreover, the effective thermal conductivity is positively related to aggregate content, thermal conductivity of aggregate, and fine aggregate matrix, but negatively correlated with morphological factor and porosity.

Two-level consistent secant operators are proposed for the nonlinear simulation of structures especially under cyclic loading. At the structural level, the quasi-Newton (Q-N) update of stiffness matrix is used to search the equilibrium of the overall system. At the material level, the general formulas of secant operators are proposed for the nonlinear material model. The consistency between the Q-N stiffness matrix at the structural level and the secant operator at the material level is proposed and considered as a good trade-off between efficiency and robustness. Applications are made to numerical examples that include strain-softening and cyclic loading. Significant improvements are demonstrated in relation to the full Newton methods and the inconsistent secant methods.

A molecular dynamics (MD)–based structural mechanics approach is proposed for the assessment of resilience of buildings. At the core of the approach, potentials of mean force (PMFs) suitable for structural members for both two-body (stretch) and three-body (bending) interactions are derived to define the energy states between mass points discretizing structural members. An original potential parameter calibration procedure is proposed: for close-to-equilibrium potential parameters, the procedure is based on matching measured frequency of a structure with the frequency of the molecular model. In turn, for bond-rupture parameters, it is shown that classical interatomic potential expressions, such as Morse potential, can be used to calibrate the energy content of many structural members and connections. By way of example, the MD-based structural mechanics approach is applied to a large-scale structure. Compared with classical continuum-based approaches, the added value of the method thus proposed is a rational means of determining the progressive structural collapse load of structures based on thermodynamic integration. By redefining structural mechanics within the context of statistical physics, molecular simulations, and potentials of mean force, the approach provides a powerful means of determining fragility curves required for the assessment of resilience of buildings.

Micromechanical modeling provides significant insight into the fundamental mechanism of soil liquefaction. In this study, a series of undrained cyclic simple shear simulations were conducted by using discrete element method (DEM). The particle-scale information provided by DEM was used to quantify the local void distribution around particles. Two microscale descriptors, named as the shape-elongation descriptor ($E_d$) and the orientation-anisotropy descriptor ($A_d$), were proposed to quantify the overall anisotropy of local void distribution in the granular packing. Before initial liquefaction, the particle-void distribution remains to be globally isotropic for isotropically consolidated samples. An irreversible development of anisotropy in terms of $E_d$ and $A_d$ mainly occurs in the post-liquefaction stage. In addition, jamming transition of the liquefied soil is determined by using these descriptors because a unique hardening state line (HSL) is found in the $E_d-A_d$ space that can differentiate a post-liquefaction flow state from a hardening or jamming state. Furthermore, large post-liquefaction flow strains are found to be closely correlated to the descriptors.

The peristaltic transport of an electromagnetic nanofluid (copper and water) in a wall-compliance channel is presented. The influence of the induced electric and magnetic fields on the conducting fluid is taken into consideration. The effects of the Brownian motion and thermophoretic diffusion of nanoparticles are also presented. The analytical solution has been derived for the stream function, electric field, magnetic field, temperature, and nanoparticles concentration by using a perturbation method. The homotopy perturbation method is also taken into account to complete the solution for both the temperature and nanoparticles concentration. Some special cases are reported on appropriate data choices. In addition, effects of the various physical parameters on the different distributions are discussed graphically.

Nanofibers are known to have incredible properties and applications in diverse field such as defense, energy, aerospace, filtration, and biotechnology, to name a few. Forcespinning (FS) is a new experimental process that can produce nanoscale fibers under the action of rotating forces. In the usual FS process, a mesoscale fluid jet is forced through an orifice of a rotating spinneret, where the ambient fluid is air. This leads to the formation of a jet with a curved centerline. In this study we apply multiscale and perturbation techniques to investigate rotating fiber jets and their stabilities in the presence of aerodynamic drag force due to the ambient air that is known to exist experimentally in the FS process. First, we calculate numerically the expressions for the leading-order steady solutions for jet quantities such as radius, speed, and trajectory versus arc length, and we determine, in particular, the results for such quantities and their variations in the presence of aerodynamic effect. Next, we calculate the stability of the fiber jet versus temporally growing, spatially growing, or spatiotemporally growing perturbations and determine the results for the growth rates of the effective perturbations versus jet flow parameters.

This paper presents a new time domain method for reconstructing unknown incident seismic input waves entering into a truncated heterogeneous soil domain from a soil surface response. The problem is cast into a partial differential equation (PDE)–constrained optimization problem where a misfit between a measured response at a sensor on the ground surface induced by a target signal and a computed wave solution induced by an estimate signal is minimized. Using this method allows for fast and accurate evaluation of the sensitivity of a misfit functional (i.e., gradient or Fréchet derivative) with respect to control parameters. Both forward and adjoint problems are solved by using the finite-element method (FEM). The numerical results prove that the presented method can identify a targeted incident seismic input signal into a truncated soil domain without providing the numerical optimizer with any hint about the target. In presence of noise in measurement, this inversion process recovers a target signal more accurately than the deconvolution does.

This paper examines the size-dependent fracture of a piezoelectric double cantilever beam (DCB) specimen based on large deformation–strain gradient theory. The governing equations with relevant boundary conditions for a piezoelectric cantilever beam with simultaneous consideration of surface piezoelectricity, surface elasticity, surface residual stress, and large deformation are obtained and solved numerically. These results are further utilized to investigate the fracture behavior of a DCB. Results show that the strain gradient effect is more pronounced when the beam height is less than the material length scale parameter. The strain gradient model anticipates significant stiffening behavior at micro/nanoscales. The effect of the surface residual stress is more substantial than that of surface elasticity and surface piezoelectricity. The study further established that the strain energy release rate of the short-circuit boundary condition is larger than that of open-circuit boundary condition. Using strain gradient model, the effect of the uncracked part of DCB is more noticeable on a smaller scale and should not be ignored even for slender beams.

In this article a numerical approach is proposed for the investigation of composite materials, like masonry. A number of simulations of a nonlinear, heterogeneous microstructure with gradually increasing loading, are considered. Average stress and stiffness are also derived. Then, this information is incorporated in databases, and a metamodel is created based on the data and used in an overall macroscopic analysis. On the micro scale, a classical plasticity model for masonry or a unilateral contact law representing a potential crack are considered. A satisfactory comparison between the proposed models and direct macroscopic models arises, indicating that the method can be used for an initial, quick assessment of the failure of heterogeneous materials on the structural scale. Due to its simplicity, it can be applied even by using commercial software for the creation of the databases. Thus, the creation of complex, sophisticated, nonlinear finite element codes may be avoided within the framework of this approach.

This paper proposes an anisotropic plasticity model to address the effect of consolidation conditions on the responses of soils within the framework of the anisotropic critical state theory (ACST). Double-yield surfaces are employed to describe the plastic deformation caused by both deviatoric shear and compression. A fabric tensor is defined to quantify the internal structure of soils and its evolution during the plastic deformation under both loading mechanisms is explicitly proposed. The novel expression of the fabric evolution rules allows for both “hardening” and “softening” types of variation in the fabric norm that are manifested by discrete element method simulations. A modified anisotropic variable is proposed, engaging with the effect of the anisotropic consolidation and the subsequent loading path and rendering the combined dilation–contraction deformation patterns being simulated, which are exclusively pertinent to the anisotropic consolidation conditions. The complex sand and clay responses caused by the varying consolidation conditions in terms of the anisotropic consolidation ratio and the over-consolidation ratio (OCR) can be simulated in a unified manner. The predictive capacity of the model is demonstrated by triaxial tests on both sand and clay. A satisfactory comparison is found between the model response and test results.

In the present study, an attempt has been made to establish and analyze a model of a composite working system combining an upper pavement structure and a geocell-reinforced embankment. In the model, the geocell-reinforced layer, carrying the self-weight of embankment fill and the distributed loads caused by vehicle loads, has been assumed to have finite bending stiffness and substantial interface resistance on both its top and bottom sides. In addition, the pavement structure and the geocell-reinforced layer have been respectively idealized as the upper and the lower Euler–Bernoulli beams supported by a series of discrete linear springs with different stiffness in both vertical and horizontal directions. Governing differential equations for the flexural response of the system have been derived and solved by a decoupled iteration method. Analytical solutions for each iteration step, in closed form, have been obtained with appropriate boundary conditions. A parametric study has been undertaken to investigate the factors that influence the behavior of the upper pavement structure and the geocell-reinforced layer using the proposed solutions.