Motion and deposition of solid particles in fibrous filter with circular, diamond, and square fibers are numerically investigated. A coupled Lattice Boltzmann (LB) and discrete element (DE) method is presented and applied to simulate the filtration process in particulate flow, taking into account the mutual interaction between fluid and particle. The influence of pertinent parameters such as the Reynolds number, the particle-to-fiber diameter ratio, and the particle-to-fluid density ratio on filtration performance (pressure drop and capture efficiency) is analyzed for fibrous filter with different fiber cross-sectional shapes. The simulation results indicate that both the pressure drop and the capture efficiency of filter are considerably affected by the fiber’s shape. Dimensionless drag force increases with the Reynolds number when Re > 1. The filter with diamond fiber has a lower pressure drop than that of the circular and square cases. Meanwhile, the deposition of particles on the surface of square fiber is more favorable. From the filter quality factor standpoint, filter with diamond fiber exhibits a better filtration performance.

Negative Poisson’s ratio materials, or auxetics, have drawn attention for the past 30 years. The auxetic effect could lead to improved mechanical properties such as acoustic damping, indentation resistance, or crashworthiness. In this work, two 3D auxetic lattices are introduced. Auxeticity is achieved by design through pre-buckling of the lattice struts. The influence of geometrical parameters on the effective elastic properties is investigated using computational homogenization method with periodic boundary conditions. Effective Young’s modulus is 3D mapped to reveal anisotropy and identify spatial orientations of interest. The effective Poisson ratio is computed for various geometric configurations to characterize auxeticity. Finally, the influence of effective elastic properties on energy dissipation under compression is explored for elastoplastic lattices with different loading directions, using finite element simulations. Results suggest that loading 3D auxetic lattices along their stiffest direction maximizes their crashworthiness.

Two-dimensional hexachiral lattices belong to the family of honeycomb-like mechanical metamaterials such as triangular, hexagonal, and kagome lattices. The common feature of this family of beam-based metamaterials is their six-fold rotational symmetry which guarantees their (transversely-) isotropic elastic response. In the case of hexachiral lattices, a single geometric parameter may be introduced to control the degree of chirality such that the elastic Poisson's ratio can be adjusted between 0.33 and −0.8. Detailed finite element simulations are performed to establish the structure–property relationships for hexachiral lattices for relative densities ranging from 1% to 45%. It is shown that both the Young's and shear moduli are always lower for hexachiral structures than for optimal lattices (triangular and kagome). This result is in line with the general understanding that stretching-dominated architectures outperform bending-dominated architectures. The same conclusions may be drawn from the comparison of the tensile yield strength. However, hexachiral structures provide a lower degree of plastic anisotropy than stretching-dominated lattices. Furthermore, special hexachiral configurations have been identified that exhibit a slightly higher shear yield strength than triangular and kagome lattices, thereby presenting an example of bending-dominated architectures outperforming stretching-dominated architectures of equal mass. Tensile specimens have been additively manufactured from a tough PLA polymer and tested to partially validate the simulation results.

In this work, we study the effect of network architecture on the nonlinear elastic behavior and strength of athermal random fiber networks of cellular type. We introduce a topology modification of Poisson–Voronoi (PV) networks with convex cells, leading to networks with stochastic nonconvex cells. Geometric measures are developed to characterize this new class of nonconvex Voronoi (NCV) networks. These are softer than the reference PV networks at the same nominal network parameters such as density, cross-link density, fiber diameter, and connectivity number. Their response is linear elastic over a broad range of strains, unlike PV networks that exhibit a gradual increase of the tangent stiffness starting from small strains. NCV networks exhibit much smaller Poisson contraction than any network of same nominal parameters. Interestingly, the strength of NCV networks increases continuously with an increasing degree of nonconvexity of the cells. These exceptional properties render this class of networks of interest in a variety of applications, such as tissue scaffolds, nonwovens, and protective clothing.

We propose a modeling strategy to predict the mechanical response of porous solids to imposed multiaxial strain histories. A coarse representation of the microstructure of a porous material is obtained by subdividing a volume element into cubic cells by a regular tessellation; some of these cells are modeled as a plastically incompressible elastic-plastic solid, representing the parent material, while the remaining cells, representing the pores, are treated as a weak and soft compressible solid displaying densification behavior at large compressive strains. The evolution of homogenized deviatoric and hydrostatic stress is explored for different porosities by finite element simulations. The predictions are found in good agreement with previously published numerical studies in which the microstructural geometry was explicitly modeled.

Inorganic stretchable electronics based on the island-bridge layout have attracted great attention in recent years due to their excellent electrical performance under the extreme condition of large deformations. During the mechanics design of interconnects in such devices, the major task is not only to maximize the elastic stretchability of device but also to smoothen the whole deformation process of interconnects. In this work, a novel design strategy is proposed for free-standing fractal serpentine interconnects to improve their elastic performance comprehensively without reducing the areal coverage of functional/active components of device. By modifying the classical design slightly, the new strategy can achieve a larger elastic stretchability, a smaller maximum out-of-plane displacement, and most strikingly, a smoother post-buckling deformation. This study will provide helpful guidance to the mechanics design of stretchable electronics with free-standing interconnects.

A new type of all-solid metamaterial model with anisotropic density and fluid-like elasticity is proposed for controlling acoustic propagation in an underwater environment. The model consists of a regular hexagonal lattice as the host that defines the overall isotropic stiffness, in which all lattice beams have been sharpened at both ends to significantly diminish the shear resistance. The inclusion structure, which involves epoxy, rubber, and lead material constituents, is designed to attain a large density–anisotropy ratio in the broad frequency range. The wave-control capability of metamaterials is evaluated in terms of underwater acoustic stretching, shifting, and ground cloaking, which are generated by the transformation acoustic method. The decoupling design method was developed for the metamaterial microstructure using band-structure, effective-medium, and modal-field analyses. The acoustic performance of these metamaterial devices was finally verified with full-wave numerical simulations. Our study provides new insight into broadband underwater acoustic manipulation by all-solid anisotropic-density metamaterials.

It is crucial to investigate the dynamic mechanical behavior of materials at the nanoscale to create nanostructured protective systems that have superior ballistic impact resistance. Inspired from recent experimental advances that enable ballistic materials testing at small scales, here we report a comparative analysis of the dynamic behavior of nanoscale thin films made from multilayer graphene (MLG), polymer, gold, and aluminum under high-speed projectile impact. We employ atomistic and coarse-grained (CG) molecular dynamics (MD) simulations to measure the ballistic limit velocity (V 50 ) and penetration energy (E p ) of these nanoscale films and investigate their distinctive failure mechanisms over a wide range of impact velocities (V i ). For the local penetration failure mechanism observed in polymer and metal films, we find that the intrinsic mechanical properties influence E p at low V i , while material density tends to govern E p at high V i . MLG films uniquely show a large impact propagation zone (IPZ), which transfers the highly localized impact energy into elastic deformation energy in a much larger area through cone wave propagation. We present theoretical analyses that corroborate that the size of IPZ should depend not only on material properties but also on a geometrical factor, specifically, the ratio between the projectile radius and film thickness. This study clearly illustrates how material properties and geometrical factors relate to the ballistic penetration energy, thereby allowing a quantitative comparison of the nanoscale ballistic response of different materials.

In this paper, we present an experimental study on strain hardening of amorphous thermosets. A series of amorphous polymers is synthesized with similar glass transition regions and different network densities. Uniaxial compression tests are then performed at two different strain rates spanning the glass transition region. The results show that a more pronounced hardening response can be observed as decreasing temperature and increasing strain rate and network density. We also use the Neo-Hookean model and Arruda–Boyce model to fit strain hardening responses. The Neo-Hookean model can only describe strain hardening of the lightly cross-linked polymers, while the Arruda–Boyce model can well describe hardening behaviors of all amorphous networks. The locking stretch of the Arruda–Boyce model decreases significantly with increasing network density. However, for each amorphous network, the locking stretch is the same regardless of the deformation temperature and rate. The hardening modulus exhibits a sharp transition with temperature. The transition behaviors of hardening modulus also vary with the network density. For lightly crosslinked networks, the hardening modulus changes 60 times with temperature. In contrast, for heavily crosslinked polymers, the hardening modulus in the glassy state is only 2 times of that in the rubbery state. Different from the results from molecular dynamic simulation in literatures, the hardening modulus of polymers in the glassy state does not necessarily increase with network density. Rather, the more significant hardening behaviors in more heavily crosslinked polymers are attributed to a lower value of the stretch limit.

This paper presents B-splines and nonuniform rational B-splines (NURBS)-based finite element method for self-consistent solution of the Schrödinger wave equation (SWE). The new equilibrium position of the atoms is determined as a function of evolving stretching of the underlying primitive lattice vectors and it gets reflected via the evolving effective potential that is employed in the SWE. The nonlinear SWE is solved in a self-consistent fashion (SCF) wherein a Poisson problem that models the Hartree and local potentials is solved as a function of the electron charge density. The complex-valued generalized eigenvalue problem arising from SWE yields evolving band gaps that result in changing electronic properties of the semiconductor materials. The method is applied to indium, silicon, and germanium that are commonly used semiconductor materials. It is then applied to the material system comprised of silicon layer on silicon–germanium buffer to show the range of application of the method.

Fiber-based materials are prevalent around us. While microscopically these systems resemble a discrete assembly of randomly interconnected fibers, the network architecture varies from one system to another. To identify the role of the network architecture, we study here cellular and fibrous random networks in tension and compression, and in the context of large strain elasticity. We observe that, compared to cellular networks of same global parameter set, fibrous networks exhibit in tension reduced strain stiffening, reduced fiber alignment, and reduced Poisson's contraction in uniaxial tension. These effects are due to the larger number of kinematic constraints in the form of cross-links per fiber in the fibrous case. The dependence of the small strain modulus on network density is cubic in the fibrous case and quadratic in the cellular case. This difference persists when the number of cross-links per fiber in the fibrous case is rendered equal to that of the cellular case, which indicates that the different scaling is due to the higher structural disorder of the fibrous networks. The behavior of the two network types in compression is similar, although softening induced by fiber buckling and strain localization is less pronounced in the fibrous case. The contribution of transient interfiber contacts is weak in tension and important in compression.

A major challenge in designing a perfect invisibility cloak for elastic waves is that the mass density and elasticity tensor need to be independent functions of its radius with a linear transformation medium. The traditional cloak for out-of-plane shear waves in elastic membranes exhibits material properties with inhomogeneous and anisotropic shear moduli and densities, which yields a poor or even negative cloaking efficiency. This paper presents the design of a cylindrical cloak for elastic shear waves based on a nonlinear transformation. This excellent broadband nonlinear cloak only requires variation of its shear modulus, while the density in the cloak region remains unchanged. A nonlinear ray trajectory equation for out-of-plane shear waves is derived and a parameter to adjust the efficiency of the cylindrical cloak is introduced. Qualities of the nonlinear invisibility cloak are discussed by comparison with those of a cloak with the linear transformation. Numerical examples show that the nonlinear cloak is more effective for shielding out-of-plane elastic shear waves from outside the cloak than the linear cloak and illustrate that the nonlinear cloak for shear waves remains highly efficient in a broad frequency range. The proposed nonlinear transformation in conjunction with the ray trajectory equation can also be used to design nonlinear cloaks for other elastic waves.

In this paper, a new strategy based on generalized cell mapping (GCM) method will be introduced to investigate the stochastic response of a class of impact systems. Significant difference of the proposed procedure lies in the choice of a novel impact-to-impact mapping, which is built to calculate the one-step transition probability matrix, and then, the probability density functions (PDFs) of the stochastic response can be obtained. The present strategy retains the characteristics of the impact systems, and is applicable to almost all types of impact systems indiscriminately. Further discussion proves that our strategy is reliable for different white noise excitations. Numerical simulations verify the efficiency and accuracy of the suggested strategy.

The idealized inverse-opal lattice is a network of slender struts that has cubic symmetry. We analytically investigate the elastoplastic properties of the idealized inverse-opal lattice. The analysis reveals that the inverse-opal lattice is bending-dominated under all loadings, except under pure hydrostatic compression or tension. Under hydrostatic loading, the lattice exhibits a stretching dominated behavior. Interestingly, for this lattice, Young's modulus and shear modulus are equal in magnitude. The analytical estimates for the elastic constants and yield behavior are validated by performing unit-cell finite element (FE) simulations. The hydrostatic buckling response of the idealized inverse-opal lattice is also investigated using the Floquet–Bloch wave method.

This work focuses on elastic wave propagation in three-dimensional (3D) low-density lattices and explores their wave directionality and energy flow characteristics. In particular, we examine the dynamic response of Kelvin foam, a simple-and framed-cubic lattice, as well as the octet lattice, spanning this way a range of average nodal connectivities and both stretching-and bending-dominated behavior. Bloch wave analysis on unit periodic cells is employed and frequency diagrams are constructed. Our results show that in the low relative-density regime analyzed here, only the framed-cubic lattice displays a complete bandgap in its frequency diagram. New representations of iso-frequency contours and group-velocity plots are introduced to further analyze dispersive behavior, wave directionality, and the presence of partial bandgaps in each lattice. Significant wave beaming is observed for the simple-cubic and octet lattices in the low frequency regime, while Kelvin foam exhibits a nearly isotropic behavior in low frequencies for the first propagating mode. Results of Bloch wave analysis are verified by explicit numerical simulations on finite size domains under a harmonic perturbation.

Flexural propagation behavior of a metamaterial beam with circular membrane-mass structures is presented. Each cell is comprised of a base structure containing circular cavities filled by an elastic membrane with a centrally loaded mass. Numerical results show that there exist two kinds of bandgaps in such a system. One is called Bragg bandgap caused by structural periodicity; the other is called locally resonant (LR) bandgap caused by the resonant behavior of substructures. By altering the properties of the membrane-mass structure, the location of the resonant-type bandgap can be easily tuned. An analytical model is proposed to predict the lowest bandgap location. A good agreement is seen between the theoretical results and finite element (FE) results. Frequencies with negative mass density lie in the resonant-type bandgap.

Benefits of a functionally graded core increasing wrinkling stability of sandwich panels have been demonstrated in a recent paper (Birman, V., and Vo, N., 2017, “Wrinkling in Sandwich Structures With a Functionally Graded Core,” ASME J. Appl. Mech., 84 (2) , p. 021002), where a several-fold increase in the wrinkling stress was achieved, without a significant weight penalty, using a stiffer core adjacent to the facings. In this paper, wrinkling is analyzed in case where the facings are subject to biaxial compression and/or in-plane shear loading, and the core is arbitrary graded through the thickness. Two issues addressed are the effect of biaxial or in-plane shear loads on wrinkling stability of panels with both graded and ungraded core, and the verification that functional grading of the core remains an effective tool increasing wrinkling stability under such two-dimensional (2D) loads. As follows from the study, biaxial compression and in-plane shear cause a reduction in the wrinkling stress compared to the case of a uniaxial compression in all grading scenarios. Accordingly, even sandwich panels whose mode of failure under uniaxial compression was global buckling, the loss of strength in the facings or core crimpling may become vulnerable to wrinkling under 2D in-plane loading. It is demonstrated that a functionally graded core with the material distributed to increase the local stiffness in the interface region with the facings is effective in preventing wrinkling under arbitrary in-plane loads compared to the equal weight homogeneous core.

The stationary response of multidegree-of-freedom (MDOF) strongly nonlinear system to fractional Gaussian noise (FGN) with Hurst index 1/2 < H < 1 is studied. First, the system is modeled as FGN-excited and -dissipated Hamiltonian system. Based on the integrability and resonance of the associated Hamiltonian system, the system is divided into five classes: partially integrable and resonant, partially integrable and nonresonant, completely integrable and resonant, completely integrable and nonresonant, and nonintegrable. Then, the averaged fractional stochastic differential equations (SDEs) for five classes of quasi-Hamiltonian systems with lower dimension and involving only slowly varying processes are derived. Finally, the approximate stationary probability densities and other statistics of two example systems are obtained by numerical simulation of the averaged fractional SDEs to illustrate the application and compared with those from original systems to show the advantages of the proposed procedure.

The size effect of nanoporous materials is generally believed to be caused by the large ratio of surface area to volume, so that it is also called surface effect. Based on a recently developed elastic theory, in which the surface effect of nanomaterials is characterized by the surface energy density, combined with two micromechanical models of composite materials, the surface effect of nanoporous materials is investigated. Closed-form solutions of both the effective bulk modulus and the effective shear one of nanoporous materials are achieved, which are related to the surface energy density of corresponding bulk materials and the surface relaxation parameter of nanomaterials, rather than the surface elastic constants in previous theories. An important finding is that the enhancement of mechanical properties of nanoporous materials mainly results from the compressive strain induced by nanovoid's surface relaxation. With a fixed volume fraction of nanovoids, the smaller the void size, the harder the nanoporous material will be. The results in this paper should give some insights for the design of nanodevices with advanced porous materials or structures.

A theoretical model of polyelectrolyte gels is presented to study continuous and discontinuous volume phase transitions induced by changing salt concentration in the external solution. Phase diagrams are constructed in terms of the polymer–solvent interaction parameters, external salt concentration, and concentration of fixed charges. Comparisons with previous experiments for an ionized acrylamide gel in mixed water–acetone solvents are made with good quantitative agreement for a monovalent salt (NaCl) but fair qualitative agreement for a divalent salt (MgCl 2 ), using a simple set of parameters for both cases. The effective polymer–solvent interactions vary with the volume fraction of acetone in the mixed solvent, leading to either continuous or discontinuous volume transitions. The presence of divalent ions (Mg 2+ ) in addition to monovalent ions in the external solution reduces the critical salt concentration for the discontinuous transition by several orders of magnitude. Moreover, a secondary continuous transition is predicted between two highly swollen states for the case of a divalent salt. The present model may be further extended to study volume phase transitions of polyelectrolyte gels in response to other stimuli such as temperature, pH and electrical field.