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Magneto-electro-elastic (MEE) materials usually consist of piezoelectric (PE) and piezomagnetic (PM) phases. Between different constituent phases, there exist lots of interfaces with discontinuous MEE properties. Complex interface distribution brings a great difficulty to the fracture analysis of MEE materials since the present fracture mechanics methods can hardly solve the fracture parameters efficiently of a crack surrounded by complex interfaces. This paper develops a new domain formulation of the interaction integral for the computation of the fracture parameters including stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF) for linear MEE materials. The formulation derived here does not involve any derivatives of material properties and moreover, it can be proved that an arbitrary interface in the integral domain does not affect the validity and the value of the interaction integral. Namely, the interaction integral is domain-independent for material interfaces and thus, its application does not require material parameters to be continuous. Due to this advantage, the interaction integral becomes an effective approach for extracting the fracture parameters of MEE materials with complex interfaces. Combined with the extended finite element method (XFEM), the interaction integral is employed to solve several representative problems to verify its accuracy and domain-independence. Good results show the effectiveness of the present method in the fracture analysis of MEE materials with continuous and discontinuous properties. Finally, the particulate MEE composites composed of PE and PM phases are considered and four schemes of different property-homogenization level are proposed for comparing their effectiveness.

Multistable mechanical metamaterials are known for their unique mechanical characteristics, such as snap-through behaviors, negative stiffness effects, and reusability, thus they exhibit unique advantages in some applications. However, traditional multistable materials exhibit fairly low strength and stiffness. Herein, inspired by some activities and mechanisms in the biological organs, a new type of multistable metamaterial comprising a periodic arrangement of sleeves is designed and investigated. The compression experiments show that the material is characterized by typical multistable behaviors and exhibits other advantages such as lightweight, ultra-high stiffness and strength. Moreover, the cycle experiment shows that the material is reusable even though very large deformation occurs. The mechanism of those behaviors is analyzed, and a theory is established for the design of such materials. Based on this outcome, the effects of the important parameters that can control the materials to exhibit snap-through behavior or friction-dominated behavior are discussed.

Since the concept of invisible cloak was proposed by Pendry and Leonhardt in 2006, many researchers have applied the theory of coordinate transformation to thermodynamics and overcome the complexity of inhomogeneous and anisotropic of material parameters. However, only two-dimensional (2D) thermal illusion devices are researched recently. According to this situation, our study focuses on three-dimensional (3D) thermal illusion devices including shrinker (or invisible cloak), concentrator, amplifier, reshaper, and rotator with arbitrary shape in a general way. In this paper, the corresponding material parameters of thermal illusion devices mentioned above are derived based on the theory of transformation thermodynamics and the simulated results agree well with the theoretical derivations. In addition, the conventional invisible cloak just controls the temperature gradient rather than the temperature value which is more concerned in physical applications. Here, we find that the temperature value of the cloaked object can be controlled by adjusting the location of the original point of the coordinate system.

The vibration and damping performances of hybrid carbon fiber composite pyramidal truss sandwich panels with viscoelastic layers embedded in the face sheets were investigated in this paper. Hybrid carbon fiber composite pyramidal truss sandwich panels containing different thickness of viscoelastic layers were manufactured using a hot press molding method. Analytical models based on modal strain energy approach were developed using ABAQUS software to estimate the damping property of the hybrid sandwich structures. A set of modal tests were carried out to investigate the vibration and damping characteristics of such hybrid sandwich panels with or without viscoelastic layers. The damping loss factors of composite slender beams with different fiber orientations were tested to determine the constitutive damping properties of parent materials for such hybrid sandwich panels. The numerical simulation results showed good agreement with the experimental tests. The damping loss factors of hybrid sandwich panels increased distinctly compared with previous sandwich panels due to the viscoelastic layer embedded in the face sheets.

A combined experimental and numerical study is conducted to assess the effects of impact energy, impact site and core density on the compression-after-impact (CAI) strength of pyramidal truss core sandwich structures. It is found that the severity of impact damage highly depends on the impact site. The CAI tests show that the local buckling occurs for both the un-impact specimens and the specimens impacted under lower energy, while debonding is observed for the specimens impacted under higher energy. In case of the specimens impacted on the middle point of the four adjacent nodes, only a crack appears in the impact-damaged facesheet, which propagates transversely across the facesheet. It is observed that the CAI strength of specimens impacted on the middle point of four adjacent nodes drop much more than that of specimens impacted on the node, and that the specimens with higher density cores have slightly lower normalized CAI strength reduction. Moreover, it is found that the CAI strength of specimens impacted on the node decreases with the impact energy increasing. In addition to experimental tests, the numerical simulation performs well in capturing the failure modes for impact-damaged specimens under compressive load.

We present a novel method for fabricating carbon fiber composite sandwich panels with lattice core construction by means of electrical discharge machining (EDM). First, flat-top corrugated carbon fiber composite cores were fabricated by a hot press molding method. Then, two composite face sheets were bonded to each corrugated core to create precursor sandwich panels. These panels were transformed into sandwich panels with near-pyramidal truss cores by EDM plunge-cutting the corrugated core between the face sheets with a shaped cuprite electrode. The flat top corrugation permits adhesive to be applied consistently, and the selected dimensions leave a substantial bond area after cutting, resulting in a strong core-to-sheet bond. The crushing behavior of this novel construction was investigated in flatwise compression, and the results were compared to analytical expressions for strength and stiffness.

In this research, carbon fiber reinforced polymer (CFRP) composite sandwich structures with pyramidal lattice core subjected to high velocity impact ranging from 180 to 2,000 m/s have been investigated by experimental and numerical methods. Experiments using a two-stage light gas gun are conducted to investigate the impact process and to validate the finite element (FE) model. The energy absorption efficiency (EAE) in carbon fiber composite sandwich panels is compared with that of 304 stainless-steel and aluminum alloy lattice core sandwich structures. In a specific impact energy range, energy absorption efficiency in carbon fiber composite sandwich panels is higher than that of 304 stainless-steel sandwich panels and aluminum alloy sandwich panels owing to the big density of metal materials. Therefore, in addition to the multi-functional applications, carbon fiber composite sandwich panels have a potential advantage to substitute the metal sandwich panels as high velocity impact resistance structures under a specific impact energy range.

Free vibration problems of lattice sandwich beams under several typical boundary conditions are investigated in the present paper. The lattice sandwich beam is transformed to an equivalent homogeneous three-layered sandwich beam. Unlike the traditional analytical model in which the rotation angles of the face sheets and the core are assumed the same, different rotation angles are considered in this paper to characterize the real response of sandwich beams. The analytical solutions of the natural frequencies for several typical boundary conditions are obtained. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with multiple parallel symmetric mode-III cracks.

In this paper, response of carbon fiber reinforced polymer (CFRP) laminates subjected to high velocity impact has been investigated by experimental and numerical methods. Experiments using a two-stage light gas gun were conducted to investigate the impact process and to validate the finite element model. The energy absorption efficiency (EAE) of CFRP laminates with different thickness was investigated. According to the results of experiments and numerical calculations, thin CFRP laminates have a good EAE under relative higher velocity impact; by contraries, a superior EAE is displayed in thick laminates under relative lower velocity impact. Subsequently, EAE of CFRP laminates was compared with that of 304 stainless-steel plates. In a specific impact velocity range, EAE of CFRP laminates is higher than that of 304 stainless-steel. Thus, CFRP laminates have a potential advantage to substitute the metal plates to be used in high velocity impact resistance structures under a specific impact velocity range.

An attempt has been made here to evaluate the effect of thermal exposure on the mechanical behavior and failure mechanisms of carbon fiber composite sandwich panel with pyramidal truss core under axial compression. Analytical formulae for the collapse strength of composite sandwich panel after thermal exposure were derived. Axial compression tests of composite laminates and sandwich panels after thermal exposure were conducted at room temperature to assess the degradation caused by the thermal exposure. Experimental results showed that the failure of sandwich panel are not only temperature dependent, but are time dependent as well. The decrease in residual compressive strength is mainly attributed to the degradation of the matrix and the degradation of fiber–matrix interface, as well as the formation of cracks and pores when specimens are exposed to high temperature. The measured failure loads obtained in the experiments showed reasonable agreement with the analytical predictions.

The solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material was investigated by using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relations between the electric filed, the magnetic flux field and the stress field near the crack edges were obtained and the effects of the shape of the rectangular crack on the stress, the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed.

In this paper, the pyramidal truss core sandwich structures consisting of carbon fiber reinforced polymer (CFRP) facesheets and aluminum alloy cores were manufactured based on the slot-fitting method. This hybrid concept is to maximize the specific bending stiffness/strength as well as obtain excellent energy absorption ability. Quasi-static compression tests were conducted to get the stress–strain curves and to evaluate the energy absorption mechanism. Low velocity impact tests were carried out to investigate the damage resistance of such structures. The compressive measurements show that the low density aluminum alloy pyramidal truss cores have superior energy absorption ability compared with other lightweight lattice cores. In the impact tests, the failure of matrix cracking, fiber breakage, delamination of CFRP facesheets and buckling of truss members occurred and the extent of damage was significantly affected by the impact site. In addition to experimental testing, finite element models for compression and impact simulations have been developed using ABAQUS software. The numerical results were validated compared with the experimental tests.

Soft micro-lattice materials with different lattice geometries were fabricated using a self-propagating photopolymer waveguide process. The parent polymer was characterized by dynamic mechanical analysis and the glass transition temperature shifted with equivalent strain rate. Quasi-static and dynamic compression tests were subsequently carried out to investigate the inertial stabilization of lattice member buckling as a function of strain rate and structural geometry (e.g. relative density and lattice aspect ratio). A high-speed digital camera was used to record the progression of deformation and failure events during compression. The micro-lattice structures exhibited super compressibility and increased strength. The observed strength increase, particularly for high aspect ratio and high strain rate, was attributed to inertial stabilization.

According to the combination of the complementary medium and transformation optics, the shape of two-dimensional (2D) internal-external cloaks has been generalized into any geometry to adapt to the variety of object shapes. In order to adapt to the practical application, some approximations have been introduced to eliminate the infinite singularity of the parameters in the compressed region by adjusting the principle sketch out of the plane. Firstly, the general parameter equations of the nonsingular cloak with arbitrary cross-section are deduced strictly by the mathematical method based on coordinate transformations in the cylindrical coordinate system. Secondly, taking into account the discontinuous property of the curve functions of arbitrary polygons, a supplementary investigation is given for the nonsingular cloak with arbitrary polygonal cross-section. The transformations in the supplementary study are carried out in the Cartesian coordinate system directly and referred to the coordinates of the polygon’s vertices rather than the curve function of the polygon. Last, the invisibility effect of the corresponding cloak is studied by full-wave simulations based on the finite element method. The applicable scope of the 2D internal-external cloak is expanded greatly by the methods and results given in this paper.

Composite lattice structures can be regarded as hierarchical when trusses have their own structure (e.g. different stacking sequences are incorporated). In this study, hollow composite pyramidal lattice sandwich structures in end compression were analyzed, measured and evaluated with respect to the designable properties of sandwich cores, such as relative density and truss stacking sequence. Collapse mechanism charts were constructed for both component elements and sandwich columns to illustrate the influence of structural geometries and properties of composite pyramidal lattice cores on failure modes. Operative failure modes were identified and the analytical models were shown to be accurate when compared to the measured response. The minimum weight design for the hollow composite pyramidal lattice sandwich column in end compression was carried out and the structural efficiency was also discussed.

Hierarchical composite pyramidal lattice (CPL) cores with foam-core sandwich struts were designed, and two stacking patterns were fabricated and tested in out-of-plane compression. Analytical expressions for five possible failure modes were derived considering not only stretching and bending deformation but also shear deformation of struts. Core shear failure was absent from collapse mechanism maps for both Patterns-I and II CPL cores. Optimized Pattern-I hierarchical CPL cores were more efficient than Pattern-II cores. The following comparison with almost all competing composite sandwich cores revealed that the hierarchical CPL structures here, the assembly of both stretch- and bend-dominated constructions, could perform among the most efficient sandwich cores. Meanwhile, the construction concept can also enable multifunctionality by judicious selection of strut core materials without compromising structural efficiency.

Multilayer films composed of azide-functional polymer and polyphenylene dendrimer-stabilized gold nanoparticles with alkynes in their peripheries have been fabricated using a layer-by-layer (LBL) approach via "click" chemistry. This method permits facile covalent linking of the polymer/nanoparticle interlayers in the mixture of DMF and water, which provides a general and powerful technique for preparing uniform nanoparticle (NP) thin films. The deposition process is linearly related to the number of bilayers as monitored by UV-vis spectroscopy. The multilayer structure and morphology have been characterized by X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), and contact angle.

Free vibration of AISI 304 stainless steel sandwich beams with pyramidal truss core is investigated in the present paper. The lattice truss core is transformed to a continuous homogeneous material. Considering the deformation characteristics of the sandwich beam, the following assumptions are made: (1) the thickness of the sandwich beam remains constant during deformation; (2) for the thin face sheets, only bending deformation is considered, neglecting the effect of transverse shear deformation; (3) for the core, only shear deformation is considered as the core is too weak to provide a significant contribution to the bending stiffness of the sandwich beam. The shear stress is assumed to be constant along the thickness of the core. The governing equation of free vibration is derived from Hamilton's principle, and the natural frequencies are calculated under simply supported boundary conditions. Finally, numerical simulation is carried out to get the mode shapes and natural frequencies. Our results show that the theoretical solutions agree well with the numerical results. It indicates the present method would be useful for free vibration analysis of sandwich beams with lattice truss core.

A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal inclusions on the bounds of the effective elastic moduli are analyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.

A series of compression tests were conducted to investigate the mechanical properties and failure mechanisms of carbon fiber composite sandwich panels using pyramidal truss cores subjected to temperatures ranging from −100°C to 350°C. The compressive strength and stiffness of sandwich panels decreased as temperature increased. Cryogenic temperatures caused an increase in strength and stiffness, while elevated temperatures resulted in a reduction of strength and stiffness. The effect of temperature on the failure mode of the sandwich panel was revealed as well. The interface between the fiber and matrix was examined by a scanning electron microscope (SEM) in order to study the effect of temperature on strengthening the mechanism and good bonding conditions within the fiber-matrix interface was observed at cryogenic temperatures. The comparison of the predicted and experimental data indicated that the stiffness and strength of the composite sandwich panels for temperature variation was consistent.

A study on the mechanical property degradation of carbon fiber composite sandwich panel with pyramidal truss cores by high temperature exposure is performed. Analytical formulae for the residual bending strength of composite sandwich panel after thermal exposure are presented for possible competing failure modes. The composite sandwich panels were fabricated from unidirectional carbon/epoxy prepreg, and were exposed to different temperatures for different time. The bending properties of the exposed specimens were measured by three-point bending tests. Then the effect of high temperature exposure on the bending properties and damage mechanism were analyzed. The results have shown that the residual bending strength of composite sandwich panels decreased with increasing exposure temperature and time, which was caused by the degradation of the matrix property and fiber-matrix interface property at high temperature. The effect of thermal exposure on failure mode of composite sandwich panel was observed as well. The measured failure loads showed good agreement with the analytical predictions. It is expected that this study can provide useful information on the design and application of carbon fiber composite sandwich panel at high temperature.

This paper presents a novel method for rapid fabrication and prototyping of low-density carbon fiber sandwich panel cores based on laser beam cutting (LBC). Using LCB, sandwich panels with lattice core constructions with oblique and vertical strut morphologies were fabricated from two fiber-orientation architectures. Scanning electron microscopy images illustrate the relatively small extent of damage from laser cutting. The shear strength of the lattice cores was improved by eliminating core-to-face sheet bond failures. Crushing and shear responses of fabricated truss cores were measured, and analytical models are presented to predict the stiffness, strength and dominant failure modes under each loading condition. The sandwich-panel cores investigated appear to be promising candidates for lightweight systems and multifunctional applications.

This paper develops an interaction integral method for extracting the T-stress of an interface crack in the materials with complex interfaces. In numerical computations, the interaction integral should be converted into an equivalent domain formulation to ensure numerical precision. It can be found that the present domain formulation does not contain any terms related to material interfaces, namely, the interaction integral is domain-independent for material interfaces. As a deduction, the present interaction integral can be used to solve the T-stress for a crack located on a curved interface effectively. Combined with the extended finite element method, the interaction integral method is employed to solve several interface crack problems. Good accuracy can be obtained for the interface fracture of a typical bimaterial strip. Meanwhile, it can be noted that the T-stress converges to a stable value only when the integral domain reaches up to an enough size. Since it is extremely difficult to select a large enough integral domain without any interfaces for the materials with complex interfaces, the domain-independence of the present interaction integral for interfaces is practical significant. Due to this point, the interaction integral method will become a quite reliable and convenient technique to solve the T-stress of an interface crack in the materials with complex interfaces. Finally, the interfacial fracture problem is investigated for several representative centrosymmetric structures formed by two constituent materials.

An effective model is developed to bound the effective magnetic permeability of three-phase composites with coated spherical inclusions. In the present model, the trial magnetic potential for the upper bound and the trial magnetic induction field for the lower bound are constructed to satisfy continuity interface conditions. According to the variational principle, the upper and lower bounds on the effective magnetic permeability of three-phase composites with coated spherical inclusions are derived. In this paper, trial magnetic potentials with different function forms are taken and the optimal upper bound is obtained for the trail magnetic potential corresponding to the third-order function. When the three-phase model degenerates into the composite spheres assemblage model [1] , it is interesting that the optimal upper and lower bounds are the same. The effects of the volume fraction of coated spherical inclusions and the thickness and magnetic permeability of coated layers between the matrix and spherical inclusions on the effective magnetic permeability of composites are analyzed. The upper and lower bounds are finite non-zero values when the magnetic permeability of spherical inclusions tends to ∞ and 0, respectively.

A novel hybrid truss construction concept is presented that incorporates a second-phase core material into trusses of carbon fiber (CF) composite pyramidal lattice (CPL) structures. Embedded core materials of wood and silicone rubber are selected for trial structures. Hybrid CPL structures were fabricated using a hot press molding approach and out-of-plane compression tests were performed to investigate properties. For prototype wood–core truss CPL, structural efficiencies increased comparing with solid truss CPL, while energy absorption capability was enhanced for rubber–core truss CPL. Employing the hybrid truss construction, the density-specific performance space of CF composite lattice structures can be expanded, and desired functional potential can be realized by judicious selection of core materials while simultaneously retaining structural properties.

The solutions of a three-dimensional rectangular limited-permeable crack or two three-dimensional rectangular limited-permeable cracks in the piezoelectric/piezomagnetic composite materials were investigated by using the generalized Almansi’s theorem and the Schmidt method. Finally, the relations among the electric field, the magnetic flux field and the stress field near the crack tips were obtained and the effects of the electric permittivity, the magnetic permeability of the air inside the crack, the shape of the rectangular crack on the stress, the electric displacement and magnetic flux intensity factors in the piezoelectric/piezomagnetic composite materials were analyzed.

The non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi’s theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoelectric/piezomagnetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.

SUMMARY A new equivalent domain integral of the interaction integral is derived for the computation of the T-stress in nonhomogeneous materials with continuous or discontinuous properties. It can be found that the derived expression does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the integral domain contains material interfaces. Therefore, the present method can be used to extract the T-stress of nonhomogeneous materials with complex interfaces effectively. The interaction integral method in conjunction with the extended FEM is used to solve several representative examples to show its validity. Finally, using this method, the influences of material properties on the T-stress are investigated. Numerical results show that the mechanical properties and their first-order derivatives affect the T-stress greatly, while the higher-order derivatives affect the T-stress slightly. Copyright © 2012 John Wiley & Sons, Ltd.

A method of manufacturing carbon fibre reinforced polymer (CFRP) tetrahedral lattice truss core sandwich structure by thermal expansion silicon rubber mould was developed. The sandwich structure was manufactured integrally without secondary bonding and the silicon rubber mould can be made mass-production with low cost in this approach. The intrinsic property of the CFRP was fully exploited because of carbon fibres aligned in the axial orientation of the truss member. The mechanical properties of CFRP tetrahedral lattice truss core sandwich structures were investigated by flatwise compression and shear test. The experimental results indicate that CFRP tetrahedral lattice truss core sandwich structures have higher weight-specific compressive strength than some metal truss cores, and are competitive with conventional honeycombs.

Crack growth in particle reinforced composites is significantly influenced by the character of the reinforcement particles. To accurately deal with such problems, the extended finite element method (XFEM) was employed and improved. The simulations are accomplished by using a new domain expression of an interaction integral for evaluating stress intensity factors (SIFs), and by adopting the maximum hoop stress criterion for crack-growth direction prediction. Crack deflection/attraction mechanisms and their associated energy release rate variations are investigated. It is shown that the applied numerical method allows a considerable flexibility and can be used in more general situations. The crack-tip shielding and amplifying behaviors are clearly observed.

Structural performance in direct (pure) shear and three-point bending was investigated for sandwich panels with a carbon fiber pyramidal truss core. Analytical estimates for sandwich panel strength for each loading condition were presented for possible competing failure modes. In the experimental part of the study, pyramidal truss cores were made using the hot press molding technique and then attached to flat carbon fiber composite face sheets to build all-composite sandwich panels. Panels with different configurations (e.g., core relative density and face sheet thickness) were tested to probe different failure modes and investigate the mechanical properties. In general, measured failure loads showed good agreement with the analytical predictions. Failure mechanism maps illustrate the controlling failure mechanisms in various regions of parameter space.

Quasi-static uniform compression tests and low-velocity concentrated impact tests were conducted to reveal the failure mechanisms and energy absorption capacity of two-layer carbon fiber composite sandwich panels with pyramidal truss cores. Three different volume-fraction cores (i.e., with different relative densities) were fabricated: 1.25%, 1.81%, and 2.27%. Two-layer sandwich panels with identical volume-fraction cores (either 1.25% or 2.27%), and also stepwise graded panels consisting of one light and one heavy core, were investigated under uniform quasi-static compression. Under quasi-static compression, load peaks were identified with complete failure of individual truss layers due to strut buckling or strut crushing, and specific energy absorption was estimated for different core configurations. In the impact test, the damage resulting from low-velocity concentrated impact was investigated. Our results show that compared with glass fiber woven textile truss cores, two-layer carbon fiber composite pyramidal truss cores have comparable specific energy absorptions, and thus could be used in the development of novel light-weight multifunctional structures.

Water-soluble starlike polymers containing concentrated carboxyl groups were conveniently synthesized via the combination of “click” chemistry and atom transfer radical polymerization. The starlike polymer was composed of a shorter polyacrylate main chain and longer poly(acrylic acid) side chains. Alkyne and azide groups were introduced to the structure units of the main chain by esterification and the chain end of the side chain by substitution reaction of NaN3 to bromine, respectively. By click chemistry between alkyne and azide group, well-defined starlike polymers were obtained. FT-IR, gel permeation chromatography, and 1H NMR were used to characterize the resulting polymers. Aggregation behavior demonstrated by transmission electron microscopy was observed when the starlike polymers were dispersed in water at pH 7.0–7.5. Using the starlike polymers as templates, water-soluble silver nanoclusters mainly consisting of Ag2 supported by the generated nanoparticles and carboxyl groups were successfully synthesized. Also, their optical properties and morphology were characterized by UV–vis absorption spectra and TEM.

Pyramidal lattice sandwich structures with hollow composite trusses were fabricated using a thermal expansion molding approach. Composite lattice structures with three relative densities were fabricated with two fiber architectures and the out-of-plane compression properties were measured and compared. Lattice cores with a fraction of carbon fibers circumferentially wound around the hollow trusses (Variant 2) exhibited superior mechanical properties compared with similar structures comprised of unidirectional fibers (Variant 1). The out-of-plane compressive properties of composite pyramidal lattice structures in Variant 2 were well-matched by analytical predictions. Unusual strain hardening behavior was observed in the plateau region for Variant 2, and the energy absorption capabilities were measured and compared with the similarly constructed silicone rubber–core truss pyramidal lattice structures (Variant 3). The energy absorption per unit mass of selected hollow truss composite lattice structures reported here surpassed that of both hybrid truss counterparts (Variant 3) and hollow truss metallic lattice structures.

The effects of temperature on the mechanical behaviors of composite rods and carbon fiber composite truss sandwich cores were investigated in this paper. Strength and stiffness of composite rods in fiber-aligned direction were measured in the range of −60 °C to 260 °C and characterized as functions of temperature. The research on out-of-plane compressive properties of sandwich panels with truss cores for temperature variation indicated that strength and failure modes of sandwich panels were significantly dependent on temperature. The stiffness and strength of composite rods and sandwich panels decreased progressively as temperature increased. The decreasing of stiffness and strength at high temperature was mainly attributed to softening of the polymer matrix. The increasing of stiffness and strength at cryogenic temperature was due to reduced mobility of the polymer chains within the resin matrix and the more closely compacted molecules of resin matrix. In order to provide insight into the effect of temperature on failure mechanism, the interface between fiber and matrix was examined using scanning electron microscope, and good interfacial bonding condition was observed at cryogenic temperature. The stiffness and strength of sandwich panels at different temperatures were predicted with proposed method and compared with measured results. Good agreement was observed between the measured values and predictions.

A combined theoretical, experimental and numerical investigation of carbon fiber composite pyramidal core sandwich plates subjected to torsion loading is conducted. Pyramidal core sandwich plates are made from carbon fiber composite material by a hot compression molding method. Based on the Classical Laminate Plate Theory and Shear Deformation Theory, the equivalent mechanical properties of laminated face-sheet are obtained; based on a homogenization concept combined with a mechanical of materials approach, the equivalent in-plane and out-of-plane shear moduli of pyramidal core are obtained. A torsion solution is derived with Prandtl stress function and can be used in the sandwich plate with orthotropic face-sheets and orthotropic core. The influences of material properties and geometrical parameters on the equivalent torsional stiffness are explored. In order to verify the accuracy of the analytical torsion solution, experimental tests of sandwich plate samples with different face-sheet thicknesses are conducted and two types of finite element models are developed. Good agreements among analytical predictions, finite element simulations and experimental evaluations are achieved, which prove the validity of the present derivation and simulation. The proposed method could also be applied in design applications and optimization of the pyramidal core sandwich structures.

With the equivalent mechanical properties of composite materials, analytical formulae of critical load for an all-composite sandwich column with pyramidal truss core are derived. Four failure modes are considered: macro Euler buckling, macro shear buckling, face-sheet wrinkling and face-sheet crushing. Failure mechanism maps are constructed with the four competing failure modes, and the relationship between the failure mechanism maps and material mechanical properties is discussed. Selected experiments validate the analytical predictions, and reasonable agreement is obtained. Macro shear buckling is the main failure mode for the sandwich column specimens, which is attributed to the low stiffness of core. The final failure loads is related to the strength of the nodes between face-sheets and truss core, so the node strength is the key of improving the failure load. Given by numerical simulations, the failure loads and failure modes agree well with analytical predictions.

In this paper, low-velocity impact characteristics and residual tensile strength of carbon fiber composite lattice core sandwich structures are investigated by experimentally and numerically. Low-velocity impact tests and residual tensile strength tests are performed using an instrumented drop-weight machine (Instron 9250HV) and static test machine (Instron 5569), respectively. The FE (finite element) software, ABAQUS/Explicit is employed to simulate low-velocity impact characteristics and predict residual tensile strength of carbon fiber composite lattice core sandwich structures. These numerical investigations create a user-defined material subroutine (VUMAT) to enhance the damage simulation which includes Hashin and Yeh failure criteria. The impact contact force and the tensile strength are accurately estimated using the present method. From results of this paper, the degradation of residual tensile strength can be divided to three stages for different impact energies, and amplitudes of degradation are affected by stacking sequences.

A series of analytical and experimental investigations is presented to study the response and failure of pyramidal truss core sandwich panels made of carbon fiber composite under axial compression. In the analytical part of the study, three failure modes: (i) Euler or core shear macro-buckling, (ii) face wrinkling, and (iii) face sheet crushing, were considered and theoretical relationships for predicting the failure load associated with each mode were presented. In the experimental part of the study, three different sets of specimens were manufactured to probe the three failure modes mentioned above. Pyramidal truss cores were fabricated using a hot-press molding technique and were bonded to composite face sheets made of fiber reinforced composite. The response of the sandwich panels under axial compression was measured up to failure. The measured peak loads obtained in the experiments showed good agreement with the analytical predictions. The experiments also provide insight into the post-failure response of the sandwich panels.

J ep-integral is derived for characterizing the fracture behavior of elastic-plastic materials. The J ep-integral differs from Rice’s J-integral in that the free energy density rather than the stress working density is employed to define energy-momentum tensor. The J ep-integral is proved to be path-dependent regardless of incremental plasticity and deformation plasticity. The J ep-integral possesses clearly clear physical meaning: (1) the value J tip ep evaluated on the infinitely small contour surrounding the crack tip represents the crack tip energy dissipation; (2) when the global steadystate crack growth condition is approached, the value of J far-ss ep calculated along the boundary contour equals to the sum of crack tip dissipation and bulk dissipation of plastic zone. The theoretical results are verified by simulating mode I crack problems.

The mechanical performance of an all-composite pyramidal lattice truss core sandwich structure was investigated both theoretically and experimentally. Sandwich structures were fabricated with a hot compression molding method using carbon fiber reinforced composite T700/3234. The out-of-plane compression and shear tests were conducted. Experimental results showed that the all-composite pyramidal lattice truss core sandwich structures were more weight efficient than other metallic lattice truss core sandwich structures. Failure modes revealed that node rupture dominated the mechanical behavior of sandwich structures.

The non-local theory solution of a limited-permeable mode-I crack in a piezoelectric/piezomagnetic media was given by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the lattice parameter, the crack length, the electric permittivity, and the magnetic permeability of the air inside the crack on the stress field, the electric displacement field, and the magnetic field near the crack tip. Different from the classical solution that the present solution exhibits no stress, electric displacement, and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic media.

A new method for fabricating carbon fiber composite pyramidal truss cores was developed based on the molding hot-press technique. In this method, all the continuous fibers of composite are aligned in the direction of struts and thus, the truss structure can fully exploit the intrinsic strength of the fiber reinforced composite. The microstructure and organizations of fibers of fabricated composite structures were examined using scanning electron microscope. The crushing response of the truss cores was also investigated and the corresponding failure modes were studied and complemented with an analytic model of the core crushing response. Our results show that the fabricated low-density truss cores have superior compressive strength and thus, could be used in development of novel lightweight multifunctional structures.

A new model is developed to bound the effective thermal conductivity of composites with thermal contact resistance between spherical inclusions and matrix. To construct the trial temperature and heat flux fields which satisfy the necessary interface conditions, the transition layer for each spherical inclusion is introduced. For the upper bound, the trial temperature field needs to satisfy the thermal contact resistance conditions between spherical inclusions and transition layers and the continuous interface conditions between transition layers and remnant matrix. For the lower bound, the trial heat flux field needs to satisfy the continuous interface conditions between different regions. It should be pointed out that the continuous interface conditions mentioned above are absolutely necessary for the application of variational principles, and the thermal contact resistance conditions between spherical inclusions and transition layers are suggested by the author. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with imperfect interfaces are rigorously derived. The effects of the size and distribution of spherical inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and does not need to calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides an entirely different way to bound the effective thermal conductivity of composites with imperfect interface, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds are finite when the thermal conductivity of spherical inclusions tends to ∞ and 0, respectively.

In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method. The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials.