Equivalent Material Properties Research Articles

Symmetric/Asymmetric Vibrational Characteristics of Bi-Directional Functionally Graded Annular Microplates

In this study, a free vibration model of bi-directional functionally graded (BD-FG) annular microplates is established based on the modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT), and the corresponding governing equations are derived from Hamilton’s principle. The annular microplates are assumed to be composed of metal and ceramic materials, and the equivalent material properties are a combination of power-law function and exponential ones. The generalized differential quadrature method (GDQM) is used to obtain the vibration frequencies and mode displacements for the C–C, S–C, C–S, and S–S (S: simply supported; C: clamped) annular microplates. The convergence and validity of the proposed model are verified through selective numerical examples. Further, the effects of gradient index, material length scale parameter, boundary conditions, and geometrical dimensions on the symmetric/asymmetric vibration frequencies of the annular microplate are explored. The modal assurance criterion is applied to estimate the influence of the radial gradient index and material length scale parameter on different-order mode displacements of the annular microplate. The results show that: (1) the vibration frequencies of the annular microplate are sensitive to changes in the geometry and boundary conditions; (2) compared with the axial gradient index, the radial gradient index not only affects the vibration frequencies of the annular microplate, but also impacts the distribution of the highest and lowest points of the vibration mode displacements as well as the vibration mode nodal lines; (3) as the material length scale parameter increases, the vibration frequencies are significantly increased, and the higher-order vibration modes of the annular microplate also change.

On the free vibration characteristics of multiscale hybrid conical panels utilizing Chebyshev–Ritz route

This study investigates the vibrational behavior of three-phase polymer-glass fiber (FG)-carbon nanotubes (CNT) nanocomposites conical panels. Effects of the wavy shape of CNTs and the viscoelastic nature of the polymer matrix are considered. First and foremost, the equivalent material properties are estimated in the context of a three-step hierarchical approach. Then, the governing equations are attained by combining the first-order shear deformation theory (FSDT) and Hamilton’s principle. Furthermore, the Ritz method is employed to extract the frequency responses with the help of Chebyshev polynomials for both simply supported and clamped ends panels. For the parametrical studies, the effect of different geometrical constraints, for instance, the effects of relaxation time and the effect of considering different waviness coefficients for the CNT, are reported. The findings of this paper reveal the significant effect of the viscoelastic properties of the polymer matrix on the estimation of the dimensionless frequency. For instance, under simply supported boundary conditions and a relaxation parameter of 60 s, the frequency of the structure reduces by approximately 23% after 100 s.

Multiscale analysis of shrinkage-induced performance degradation of shear wall and application to structural analysis

Shrinkage-induced cracks reduce the stiffness of concrete structures. Shear walls are more sensitive to drying shrinkage than other members because of their fully restricted condition and large surface areas exposed to air. This study examines how concrete structural performance is affected by shrinkage due to moisture loss via hydration or dissipation by applying multiscale integrated finite element analysis. First, a cyclic shear loading test on shear wall specimens subjected to drying in a previous study was reproduced. Based on the reproduction analysis model, parametric analysis was conducted, focusing on the member scale, mix proportion, and surface treatment of concrete. Shrinkage-induced cracks reduced member stiffness, and the effects of the member scale on drying speed were shown. The dominance of autogenous shrinkage in the case of high-strength concrete was also observed. The sealing of the concrete surface effectively prevented moisture dissipation, but moisture supply from ambient air was also blocked when the humidity inside the concrete was low. Thus, a proper surface protection method should be selected considering water consumption via hydration. Finally, the use of equivalent material properties for considering initial damage due to shrinkage was proposed as a simple way to account for drying effects in structural analyses.

Subwavelength negative refraction and flexural wave lens design via resonant double-negative piezoelectric metamaterial

We report the concept and demonstration of a double-negative, resonant metamaterial characterized by both dynamic negative mass and stiffness for negative refraction of flexural wave modes by means of a lens designed using this concept. The negative equivalent material properties are obtained in the subwavelength regime by concurrently exploiting both the effect of mechanical resonators (negative mass) and of piezoelectric patches with inductive resonant shunts (negative stiffness), leading to double-negative behavior. Following the theoretical foundations based on a modal framework, we analytically derive the frequency-dependent mass and stiffness properties as a function of the electromechanical parameters. The findings are corroborated by numerical computation of dispersion properties and simulations showing the focusing of a point source. As a case study, energy harvesting performance enhancement by exploiting the piezoelectric effect at the focal spot is also discussed.

A method to calculate seismic behavior of a corroded beam-to-column joint considering distribution randomness of corrosion depth

When conventional uniform corrosion method and equivalent material property method are applied to predict the seismic performance of corroded steel beam-to-column joints, distribution randomness of corrosion depth can't be considered, once damage occurs at a position where there is a large corrosion pit, there will be a great error between the actual damage and the damage predicted by the two methods. The current work aims to overcome this problem. Firstly, accelerated corrosion test was conducted on mild steel coupons. Secondly, topography of the corrosion pits was scanned, and distribution characteristic of the corrosion depth was obtained. According to the distribution characteristic, a FE modeling method (namely, stochastic corrosion method) that considers distribution randomness of the corrosion depth was proposed. The proposed method, together with uniform corrosion method and equivalent material property method were then applied on the seismic performance prediction of a corroded steel beam-to-column joint. The results show that 1) The depth of the corrosion pits on the specimens subjected to accelerated corrosion approximately obeys lognormal distribution. 2) The corroded steel beam-to-column joints' hysteretic behavior predicted by stochastic corrosion method is more accurate than those predicted by the other two methods. Compared with uniform corrosion method, the maximum calculation accuracy improvement of stochastic corrosion method can reach 90%. 3) The reason which leads to prediction error of uniform corrosion method is that localized buckling of some positions on the structural member is overlooked, while the reason leads to prediction error of equivalent material property method is that the kinematic hardening parameter C is assumed to increase with the increase of corrosion time period. Both the prediction errors of the two methods increase with the increase of corrosion time.

Low-velocity impact resistance of all composite cylindrical shell panels with a foam filled honeycomb core: Theoretical and experimental investigation

The low-velocity impact resistance of all composite cylindrical shell panels (CCSPs) with a foam filled honeycomb core (FFCHC) is studied experimentally and theoretically. Initially, a dynamical model of the FFCHC-CCSPs is proposed, with the equivalent material properties of the core being determined by combining the Hamilton equivalence theory and the Gibson theory. By using the virtual work principle and quasi-static method, together with the von Karman's theory and the high order shear deformation shell theory, the constitutive relationship related to each damage case is derived. Also, by considering the influence of collapse of the FFCHC, the failure criteria and damage modes are modified. The impact displacement, load and impact energy absorption are solved by using the elastoplastic contact principle and energy principle. Several numerical results from the literature are employed for preliminary validation of the model. Furthermore, the FFCHC-CCSP specimens with and without polyurethane foam are fabricated and the detailed measurements associated with different impact energies are performed to provide a solid validation of the present model as well as to evaluate the structural impact resistance. Finally, the influences of the thickness of FFCHC, wall thickness and side length of honeycomb cell and density of foam on the impact resistance of the FFCHC-CCSP structures are discussed, with some useful conclusions being refined for better impact suppression design and manufacture of such advanced shells.

An experimental study of the effects of degrees of confinement on the response of thermoplastic fibre–metal laminates subjected to blast loading

A series of tests on the dynamic response of thermoplastic fibre–metal laminates (TFMLs) subjected to blast loading with three different degrees of confinement (unconfined, vented and fully confined) were performed. The deflection time histories, the residual deformation, the internal delamination and damage mode of the TFMLs were recorded or observed by employing the digital image correlation, the 3D scanning and X-ray computed tomography techniques. Based on equivalent material properties combined with dimensionless damage numbers φq, the deformation of fibre–metal hybrid structures of different configurations can be effectively predicted and verified by experimental data. In addition, the effective load applied to the hybrid structure within the saturation response time is a key factor in determining the blast performance at different degrees of confinement. Vented explosions can result in the same dynamic response as fully confined explosions with even more severe internal delamination. The presence of quasi-static pressure in fully confined explosions can contribute more than 20% to the final deformation. The results can provide a basis for further understanding of the dynamic response and failure behaviour of fibre–metal hybrid structures subjected to blast loading with different degrees of confinement.

Impact Response Analysis on Orthogrid Stiffened Composite Sandwich Plates Embedded with Viscoelastic Material Considering Temperature and Moisture Effects

In this work, a new composite sandwich plate including a viscoelastic material (VEM) filling orthogrid core is proposed. Taking temperature and moisture effects into consideration, the dynamic ‘analysis for impact responses of this structure is presented. The equivalent material properties of the composite core layer are calculated using the Halpin–Tsai model. In order to model the impact force between the impactor and the structure, the modified Hertz contact law is utilized. The governing equations of the structure are derived by employing the Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle. Then the governing equations are solved through the Galerkin method with the aid of the Newmark direct integration scheme. After verifying the reliability and accuracy of this model, the effects of temperature, moisture, initial velocity of the impactor and boundary condition on the contact force and central deflection of the structure are discussed in detail. It has been demonstrated that changes of environmental temperature and moisture play a significant effect on the damping characteristics and impact responses of the composite sandwich plates.

Determination of Equivalent Material Properties of Microsystem Structure for Structural Simulation Analysis

Determination of Equivalent Material Properties of Microsystem Structure for Structural Simulation Analysis

An RDL Modeling and Thermo-Mechanical Simulation Method of 2.5D/3D Advanced Package Considering the Layout Impact Based on Machine Learning.

The decreasing-width, increasing-aspect-ratio RDL presents significant challenges to the design for reliability (DFR) of an advanced package. Therefore, this paper proposes an ML-based RDL modeling and simulation method. In the method, RDL was divided into blocks and subdivided into pixels of metal percentage, and the RDL was digitalized as tensors. Then, an ANN-based surrogate model was built and trained using a subset of tensors to predict the equivalent material properties of each block. Lastly, all blocks were transformed into elements for simulations. For validation, line bending simulations were conducted on an RDL, with the reaction force as an accuracy indicator. The results show that neglecting layout impact caused critical errors as the substrate thinned. According to the method, the reaction force error was 2.81% and the layout impact could be accurately considered with 200 × 200 elements. For application, the TCT maximum temperature state simulation was conducted on a CPU chip. The simulation indicated that for an advanced package, the maximum stress was more likely to occur in RDL rather than in bumps; both RDL and bumps were critically impacted by layouts, and RDL stress was also impacted by vias/bumps. The proposed method precisely concerned layout impacts with few resources, presenting an opportunity for efficient improvement.

Vibration-based numerical identification of effective orthotropic elastic properties for finite element model of cross-laminated timber panel

The influence of non-gluing of narrow surfaces of boards on all effective orthotropic elastic moduli for shell or solid finite element models of cross-laminated timber (CLT) panels is investigated. This lack of gluing leads to discontinuous layers and severe meshing difficulties. The objective of this study is to create an equivalent homogeneous layer and equivalent material properties in this case. Two finite element (FE) models were built for comparison. The first model, using solid elements, is the reference without gluing the narrow surfaces. The second considers homogeneous layers and equivalent material properties. Thanks to an identification process, all the elastic moduli of the model with homogeneous layers are adjusted to minimize the difference in vibration frequencies between the two models. A method is proposed to significantly speed-up the calculation of first derivatives, which are necessary for the identification process. The process was applied for 36 configurations of CLT panels with different geometrical properties (number of layers, width and thickness of boards) within the practical range. Metamodels are proposed to quickly calculate the effective moduli based on the vibration properties of CLT panels. The Verification and Validation methodology was applied to evaluate the performance of the two simplified FE models using the effective moduli.

Additive manufacturing of a high-performance aluminum alloy from cold mechanically derived non-spherical powder

Metal additive manufacturing provides a path to optimized component design with significant realized advantages in the medical and aerospace industries. Limitations to expansion to other industries, e.g. automotive, and to enabling supply chain relief is the limited number of materials available and the ability to produce material on demand. Current additive manufacturing powder feedstock is produced at large, remote atomization facilities with long lead times. Here we identify a new “on-demand” powder production technology, cold mechanically derived, able to produce non-spherical powder for additive manufacturing, with high efficiency, and wrought equivalent material properties. We analyze the powder flow characteristics and mechanical properties comparing typical gas atomized with the new process demonstrating wrought property equivalence despite power sourcing. This research will enable expansion of additional alloy systems as well as encourage the processing of non-spherical powders to expand the available supply base of new alloys for additive manufacturing.

Topology optimized design and validation of sandwich structures with pure-lattice/solid-lattice infill by additive manufacturing

Compared to standard structures with pure solid members, sandwich structures behave mechanical advantages in terms of strength-to-weight, stiffness-to-weight, energy absorption capabilities, yet lightweight potentials. Sandwich structures can be driven by both exterior layout and infill configuration design to improve structural performance while reduce the weight. In this paper, sandwich structures with pure-lattice / solid-lattice infill by additive manufacturing is systematically investigated in combination with topology optimized design and validation. The equivalent material properties of infill BCC and F2BCC lattices are determined though finite element simulation. The newly developed sandwich structural topology optimization algorithm based on two-step density filtering is employed to obtain the conceptual designs with pure or hybrid infill. The topology optimized structures are fabricated by additive manufacturing, which are validated through three-point bending experiments and numerical simulations.

Two-Scale analysis of fretting fatigue crack initiation in heterogeneous materials using Continuum Damage Mechanics

The phenomenon of fretting fatigue damage is related to tribological behaviour and commonly occurs at the contact interface between two bodies that sustain oscillation loads. Based on the complicated mechanical situation, several methods have been developed to predict the crack initiation location and life. The Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Method (FEM) is used in this paper. The fretting fatigue lifetime includes two parts, crack initiation lifetime and crack propagation lifetime, and this paper focuses on the crack initiation phase. Homogeneous materials are usually studied in fretting fatigue problems, and the influence of defects is necessary to be considered. In this study, the authors proposed several models to consider the effect of heterogeneity on crack initiation location and lifetime. The numerical model is a 2D one with plane strain assumption. To get more accurate numerical results with low computational cost, a Two-Scale Analysis approach is developed in this paper. Two macroscopic models and three microscopic models are proposed, including a Macroscopic homogeneous model (Macro-HOMO), a Multiscale Homogenization model with Direct Numerical Simulation (MH-DNS), a Microscopic homogeneous model (Micro-HOMO), a Microscopic Model with equivalent material properties by using Mean Field Homogenization method (Micro-MFH), and a microscopic model with Direct Numerical Simulation (Micro-DNS). The results obtained by using the CDM approach with different microscopic models are compared, and show that the prediction accuracy of the Micro-DNS is the best. In addition, in terms of computational cost, the Micro-DNS model shows great advantages as well comparing to the Macro-DNS model.

Adaptive control on flexural waves by a piezoelectric-based elastic metasurface with hybrid shunting circuits

In aspects of its simple configuration and tunability, piezoelectric-based metasurface has benefited over its mechanical counterpart in adaptive wavefront manipulation. By tuning the circuitry elements in the shunting circuits properly, the equivalent material properties of the metasurface can be modified to attain a complete phase shift and to maintain high transmission at desired working frequencies. In this paper, a piezoelectric-based elastic metasurface with hybrid shunting circuits (–– shunts) are proposed to adaptively control the propagation of flexural waves. Through tuning of negative capacitance and inductance simultaneously, the proposed elastic metasurface can cover a phase shift ranging from while having a high transmission (0.7). It is discovered that any similar metasurface structural design with solely single shunting circuit presently available could not achieve the same results as the proposed elastic metasurface. In addition, analytical modeling based on equivalent Young’s modulus is developed and a finite element model is built to study the transmission and phase shift of the proposed metasurface. It is demonstrated numerically that the proposed piezoelectric-based elastic metasurface is capable of performing switchable functionalities, such as wave refraction and focusing, at different working frequencies (3500 Hz, 5000 Hz, etc.).

Uniaxial compressive performance of an aramid and aluminum honeycomb sandwich structure

In recent years, explosion and impact resistance capacity of composite sandwich structures has been widely studied. However, the study of their basic mechanical properties is still lacking, which severely hinders the application of composite sandwich structures. This paper focuses on uniaxial compressive performance of a sandwich structure, so as to provide design guidance and promote application of such structures. Firstly, a novel aramid and aluminum honeycomb sandwich structure is proposed for explosion and impact resistance. Secondly, experimental and numerical studies on uniaxial compressive performance of the structure were conducted. Seven indices including yield compressive load were introduced to assess compressive behavior of the structure. A simulation framework to predict load-carrying capacity of the structure is proposed, in which the complex aluminum honeycomb was modeled as a cube with equivalent material properties. The mechanism of how the structure collapses under uniaxial compressive load was revealed. Thirdly, parametric sensitivity analysis was conducted. According to experimental and calculated results, the structure approximately undergoes five stages under progressive compression: uniform shrinkage in vertical direction, yielding at local regions of the weaker panel (rear panel), plastic deformation development on the rear panel, overall bending of the whole specimen, and fracture of localized welds. Front panel thickness and initial imperfection have little influence on compressive behavior of the structure, while thickness of the weaker panel (rear panel) is the decisive factor of compressive load-carrying capacity. Yield load, yield displacement, ultimate load, and elastic stiffness increase linearly with the increase of rear panel (316L) thickness, while ductility coefficient decreases linearly with the increase of rear panel (316L) thickness.

Multi-Scale Analysis for Assessing the Impact of Material Composition and Weave on the Ultimate Strength of GFRP Stiffened Panels

A micro-meso-macro analysis framework based on the multi-scale method was employed to analyse the mechanical behaviour of marine GFRP stiffened panels. The study aims to establish a procedure for assessing the impact of material composition and weave on the ultimate strength of GFRP stiffened panels. The ultimate strength assessment was an essential step in the design process, and the investigation of construction materials has a great benefit to the lightweight design of marine composite structures. The micro- and meso-scale RVE models of components used in GFRP materials are established, and their failure criteria and stiffness degradation models are created using the user-defined material subroutine VUMAT in ABAQUS. The equivalent material properties at the micro-scale (meso-scale) obtained by a homogenisation method are used to define the meso-scale (macro-scale) mechanical properties in the finite element analyses. The multi-scale method assesses the macro-mechanics of composites, and it is shown that the ultimate strength of GFRP stiffened panels is mainly determined by the failure of CSM fibre bundles and WR yarns. Parametric study of the meso-mechanics of composite materials can provide an analysis tool to obtain the optimal macro ultimate strength of the composite stiffened panel.

Equivalent material properties of the heat-affected zone in welded cold-formed rectangular hollow section connections

A welded connection consists of three main material zones, the base material (BM), the heat-affect zone (HAZ), and the weld metal (WM). The strength of HAZ depends on the BM grade and manufacturing process, electrode grade, and welding parameters. Under certain conditions, HAZ has the lowest material strength, especially for high-strength steel. Therefore, a semi-empirical methodology is proposed to establish a constitutive model of HAZ necessary for predicting the fracture position of welded connections. This methodology is based on an engineering approach to consider HAZ as an isotropic and homogeneous material, with no consideration of different volumetric fractions of microstructures within a HAZ. The equivalent material properties of HAZ in butt-welded hollow section connections were investigated experimentally and numerically. Hardness tests and microstructure investigations were conducted to determine the boundaries of material variations and the width of HAZ. The stress–strain relationship of HAZ was established and calibrated based on tensile coupon tests and finite element analyses. Using the calibrated HAZ stress–strain relationship, the effect of transverse constraint imposed by the adjacent and stronger material (BM and WM) on HAZ was evaluated in the welded connections. Finally, the new methodology of a semi-empirical constitutive model based on the Swift model was used to propose equivalent characteristics of HAZ as a function of the mechanical properties of BM for a specific welding procedure considered in the project.

Damage Detection of FRP Composite Plates from Dynamical Responses using Finite Element Model Updating: Equivalent Material Properties as Parameters

Fibre reinforced plastic (FRP) composite structures are extensively used in weight sensitive applications, such as in aircrafts, ships, etc. Such structures are susceptible to damages during their usual operation or during extreme loading from environment. Due to the anisotropic nature of FRP composite plates, damage detection is difficult for such layered materials particularly when the damage site is inaccessible. The localised loss of stiffness resulting from damage is reflected into the global dynamic responses of such structures. Finite element model updating is a convenient inverse approach in which these changes in stiffness due to damages are estimated from measured dynamical responses using optimization. The equivalent stiffness changes can be expressed in terms of either geometric or material property or both. In most of the cases, changes in geometric parameters physically represent the actual damage scenario with larger sensitivity. On the other hand, material property changes in the damaged area are a very convenient parameter to deal with. In the present work, updating parameters in the finite element model updating procedure are chosen in terms of material property. Detection of local stiffness changes from experimentally measured natural frequencies, mode shapes and/or frequency response functions are investigated. Experimental modal testing is performed on a rectangular FRP composite plate both in its undamaged and damaged state. Baseline finite element model of the composite plate is correlated with experimental model, followed by a sensitivity based finite element model updating algorithm. The results show the rapid convergence and accurate determination of local stiffness change in terms of elastic material parameters alone in all three orthogonal directions. This indicates that material properties like the in-plane Young’s moduli and in-plane Shear modulus within the localised region of damage, can well be used as convenient means for detecting equivalent stiffness loss in damaged structures.

Thermomechanical buckling of tubularly chiral thermo-metamaterials

This study aims to investigate the buckling response under thermal and mechanical excitations for the tubularly chiral thermo-metamaterials (TCTM). The proposed TCTM are designed using the material of thermoplastic polymers into the structure of chiral tubes. To characterize the temperature-responsive of the material, a general theoretical model that can predict the temperature-dependent Young’s modulus and yield strength is utilized. The Young’s modulus and Poisson’s ratio of the chiral tubes are theoretically derived to indicate the structural properties. The superposition method is applied to integrate the material and structural properties to model the equivalent material properties of the TCTM. The thermomechanical buckling response of the TCTM is theoretically analyzed using the equivalent material properties. The presented theoretical models are validated by comparing with the numerical simulations and existed researches, and the satisfactory consistencies are observed. Parametric studies are conducted to investigate the controllability of the Young’s modulus, Poisson’s ratio and buckling performance of the TCTM. The reported TCTM provide an effective approach to obtain highly maneuverable, thermomechanical response, which can be used to design advanced thermomechanical devices such as temperature warning devices.