Effective Mechanical Properties Research Articles

GEOMETRICLY NONLINEAR BENDING OF FUNCTIONAL-GRADIENT SHALLOW SHELLS ON AN ELASTIC FOUNDASHION

The paper considers the problem of geometrically nonlinear bending of shallow elements of structures made of functional gradient materials (FGM) under the influence of various transverse loads. The shallow shells under consideration can have arbitrary plan shapes and be in contact with an elastic base of the Winkler-Pasternak type. The mathematical formulation is made within the framework of classical geometric-nonlinear theory. To linearize the nonlinear system of differential equations of equilibrium, the sequential load method in combination with Newton's method is used. The effective mechanical properties of FGM vary along the thickness and are calculated according to the power law. The use of the theory of R-functions made it possible to build the necessary systems of coordinate functions for shells with arbitrary geometry and support conditions. The proposed approach is implemented in software, tested, and applied to solve the problems of bending shallow shells of complex plan shapes with holes. The influence of the elasticity coefficients of the base, the gradient index in the distribution of metal and ceramic particles, as well as other parameters on the deflections of structural elements, was studied.

Effective elastic properties of 3D lattice materials with intrinsic stresses: Bottom-up spectral characterization and constitutive programming

Analytical investigations to characterize the effective mechanical properties of lattice materials allow an in-depth exploration of the parameter space efficiently following an insightful, yet elegant framework. 2D lattice materials, which have been extensively dealt with in the literature following analytical as well as numerical and experimental approaches, have limitations concerning multi-directional stiffness and Poisson's ratio tunability. The primary objective of this paper is to develop mechanics-based formulations for a more complex analysis of 3D lattices, leading to a physically insightful analytical approach capable of accounting the beam-level mechanics of pre-existing intrinsic stresses along with their interaction with 3D unit cell architecture. We have investigated the in-plane and out-of-plane effective elastic properties to portray the physics behind the deformation of 3D lattices under externally applied far-field normal and shear stresses. The considered effect of beam-level intrinsic stresses therein can be regarded as a consequence of inevitable temperature variation, pre-stress during fabrication, inelastic and non-uniform deformation, manufacturing irregularities etc. Such effects can notably impact the effective elastic properties of lattice materials, quantifying which for 3D honeycombs is the central focus of this work. Further, from the material innovation viewpoint, the intrinsic stresses can be deliberately introduced to expand the microstructural design space for effective elastic property modulation of 3D lattices. This will lead to programming of effective properties as a function of intrinsic stresses without altering the microstructural geometry and lattice density. We have proposed a generic spectral framework of analyzing 3D lattices analytically, wherein the beam-level stiffness matrix including the effect of bending, axial, shear and twisting deformations along with intrinsic stresses can be coupled with the unit cell mechanics for obtaining the effective elastic properties.

Numerical investigation of the effective mechanical properties of architected structures: a comparative study of flexural stiffness, homogenization, and elastic anisotropy

Abstract The mechanical behavior of architected structures is influenced by various parameters, including the topology of their unit cells. This anisotropic nature requires the determination of the mechanical properties under different loading scenarios. This study employs numerical investigation to characterize the influence of topology on the mechanical properties of eight architected structures, focusing on effective elastic properties and anisotropic elastic behavior. The analyzed topologies encompass four based on struts (lattices) and four based on triply periodic minimal surfaces (TPMS), comprising Sheet and Network phases. Initially, beams composed of architected structures are subjected to flexure, with Euler–Bernoulli and Tymoshenko’s theories utilized in a first numerical approach to determine their effective properties. Subsequently, a numerical homogenization method along with the Voigt-Reuss-Hill scheme is employed in a second approach. A more substantial influence of topology on the effective properties is observed in low relative densities. The study revealed that for a relative density of 10%, the appropriate selection of the topology increases the stiffness of a structure by up to ∼126%. The EBT approach underestimated the stiffness by up to ∼26% due to neglecting the impact of shear on beam deflection. The tensorial anisotropy index revealed up to ∼27% higher anisotropy compared to the Zener index. These findings provide a valuable numerical tool for the comparison and selection of architected structures suitable for diverse applications.

Driving response analysis of twisted and coiled polymer actuators by considering the viscoelastic behavior of their precursor fibers

Twisted and coiled polymer actuators (TCPA) represent a type of artificial muscle predominantly composed of viscoelastic polymers in their precursor fibers. An integral form of the viscoelastic constitutive model has been developed to predict the mechanical deformation of the precursor fibers. The model successfully accounts for the first-cycle effect and the creep deformation near the glass transition temperature of the precursor fibers. Combined with the multilayer model by Gao and Wang (2024 Smart Mater. Struct. 33 045031), which predicts the effective mechanical and thermal properties of TCPA, the proposed viscoelastic constitutive model accurately predicts the thermo-mechanical response of TCPA under the heating and cooling cycle and applied loads. It is noted that the driving strain of TCPA is sensitive to the heating and cooling cycles. When the cycle duration is short, the proposed viscoelastic model can be simplified to a linear elastic model. The numerical implementation of the viscoelastic constitutive model is detailed, with validation conducted on two polymer materials, polypropylene, and polyamide 66. The proposed constitutive model can effectively predict the driving response of TCPA under complex loading conditions.

Zinc and copper effect mechanical cell adhesion properties of the amyloid precursor protein.

The amyloid precursor protein (APP) can be modulated by the binding of copper and zinc ions. Both ions bind with low nanomolar affinities to both subdomains (E1and E2) in the extracellular domain of APP. However, the impact of ion binding on structural and mechanical trans-dimerization properties is yet unclear. Using a bead aggregation assay (BAA), we found that zinc ions increase the dimerization of both subdomains, while copper promotes only dimerization of the E1 domain. In line with this, scanning force spectroscopy (SFS) analysis revealed an increase in APP adhesion force up to three-fold for copper and zinc. Interestingly, however, copper did not alter the separation length of APP dimers, whereas high zinc concentrations caused alterations in the structural features and a decrease of separation length. Together, our data provide clear differences in copper and zinc mediated APP trans-dimerization and indicate that zinc binding might favor a less flexible APP structure. This fact is of significant interest since changes in zinc and copper ion homeostasis are observed in Alzheimer's disease (AD) and were reported to affect synaptic plasticity. Thus, modulation of APP trans-dimerization by copper and zinc could contribute to early synaptic instability in AD.

Investigations of three-dimensional fiber orientation on mechanical impact behavior of short glass-fiber-reinforced PEEK composites

This work presents experimental and numerical investigations of three-dimensional (3D) fiber orientation on mechanical impact behavior of short glass-fiber-reinforced polyether ether ketone (SGFR PEEK) composites. The incorporation of short fibers significantly enhances the stiffness and strength of the composites while reducing the ductility, thereby, making the study of their impact response essential. To this end, we firstly manufactured the composite components using injection molding, and used the micro-computed tomography (µCT) to measure the fiber orientation distribution in 3D space for mechanical behavior prediction. Then, by studying the molded components across the thickness based on the actual observation, a distinct laminate structure with seven layers was quantitatively evaluated. A representative volume element (RVE) micromechanical computational method was developed and compared with the experimental results. Furthermore, homogenization method with the periodic boundary condition was implemented to evaluate the effective mechanical properties of the molded components. Finally, the phenomenological Johnson Cook (JC) model with fracture behavior was conducted to analyze the impact response of the injected components with different fiber orientation distributions. The new framework is demonstrated by acceptable energy absorption capability prediction of the SGFR PEEK composites.

3D bi-directional auxetic square metastructure with programmable thermal expansion and Poisson's ratio

Multifunctional integration research on metastructures has become the current development trend and hotspot, especially satellite platforms and hypersonic aircraft in the aerospace field. A 3D bi-directional auxetic square metastructure (BASM) with the programmable coefficient of thermal expansion (CTE) and Poisson's ratio (PR) is designed through the combination of re-entrant hexagonal structures and bi-material triangles. Specimens in the form of the 1*2 array are designed and fabricated through 3D printing. The correctness of the results of finite element analysis (FEA) of the BASM is verified by uniaxial compression experiments. Additionally, FEA is adopted to investigate the effective mechanical properties of the BASM with the form of the 2*3 array, and deformation mechanisms are further explored. Results indicate that the CTE, PR, and stiffness of the BASM depend on material combinations and geometric parameters. Under thermal and mechanical loads, the BASM achieves bi-directional regulation of the CTE and PR, encompassing both axial and circumferential deformations. Notably, the deformation mechanisms and critical conditions of the BASM are explored under the thermo-mechanical load. A novel strategy for programming the PR of the BASM is proposed in addition to changing the geometric parameters and the material combinations.

Unrestricted micromorphic continuum: Curvature constraints effects

AbstractThe properties of two‐phase materials, with the special case of foams, strongly depend on their microstructure. These structures are generally modeled with Hill homogenization methods to reduce the computational effort compared to full‐resolution simulations. For applications where the macroscopic dimensions of the structure under consideration are only a few multiples of its internal length, size effects occur, that is, the effective mechanical properties depend on the structure size. To achieve adequate homogenization, higher‐order continuum theories must then be used to account for strong gradients in mechanical quantities. The present contribution extends the classical approach with the corresponding micromorphic degrees of freedom. In contrast to previous studies in the literature, all components of the micromorphic curvature tensor are incorporated. It has shown how the individual components of the third‐order curvature tensor have to be implemented. Their effects on the structural behavior are investigated in depth.

Evaluation of the Effective Mechanical Properties of a Particle-Reinforced Polymer Composite with Low-Modulus Inclusions

Evaluation of the Effective Mechanical Properties of a Particle-Reinforced Polymer Composite with Low-Modulus Inclusions

On the nonlinear mechanics of hybrid skew aerospace structures

This study proposes a functionally graded (FG) nanocomposite hybrid skew plate element which is fabricated from a polymeric matrix and is reinforced with two well-known nanoscale reinforcements, namely, carbon nanotubes (CNTs) and graphene platelets (GPLs). The Mori–Tanaka approach, the Halpin-Tsai scheme and standard rule of mixtures are employed to estimate the effective mechanical properties of the hybrid plates. To model this structural element, Reddy's third-order shear deformation theory (TSDT) is used. By considering the von-Kármán assumptions and using the Hamilton's principle, the nonlinear static bending and free vibration governing equations are determined. Then the isogeometric analysis (IGA) is employed to establish the structural stiffness and mass matrices of the skew hybrid plates. After validating the correctness of the presented solution procedure with the previously published results, the effects of various variables such as number of layers, distribution pattern of reinforcements (CNTs and GPLs) and their volume fractions, skew angle and width-to-thickness ratio are investigated. It is found that with considering nonlinear von-Kármán relationship in the strain field, the distributions of σxx and σyy about the mid-plane are no longer symmetric.

Reversible photochromic effect and excellent mechanical properties of Nd3+-doped Zr6Nb2O17 purple ceramics

The development of colored ceramics is limited because it can only display a single color. Therefore, colored ceramics that can achieve reversible switching between two different colors can make up for this deficiency. In this study, we report a novel rare-earth doped colored ceramic, Zr6Nb2O17: xNd3+ (abbreviated as ZNO: xNd), which has been successfully obtained with good mechanical and photochromic properties of purple ceramics by component adjustment. The doping of rare earth Nd3+ ions changed the color of the ceramic matrix from light curry to light purple, and more importantly, enhanced its mechanical properties, with optimal Vickers hardness and fracture toughness values of 16.53 GPa and 5.2 MPa·m1/2, respectively. Alternating 365 nm irradiation and 350°C thermal stimulation, the ceramic samples exhibited good photochromic properties, with the highest photochromic contrast of 21.1 %, and good reversibility and cyclic stability. Finally, it is important to clarify that the photochromic mechanism is mainly caused by the formation of color centers resulting from electrons or holes being trapped by intrinsic or extrinsic defects. These results indicate that ZNO: xNd purple ceramics can be applied in the field of colored ceramics and provide a new path for the development of rare earth-colored ceramics.

Design and Development of Film Forming Gel of Tavaborole by using Factorial Design

Film forming gel (FFG) could be a novel approach in film forming drug delivery system which has pulled in the intrigued of pharmaceutical researcher in improvement and characterization of skin drug delivery system. FFG were developed by varying concentration of the polymers and plasticizer. The formulations were prepared using 32 full factorial design. FFG were evaluated for important parameters like drying time, drug release, antifungal activity, skin irritation and stability studies. The FFG was characterized for pH, viscosity, drug content, effective dosage volume and mechanical properties of the film formed after application; bioadhesion and water vapour permeability were also tested. All the formulations showed results within acceptable range for various tests. The optimized formulation showed drug release of 98.76% and antifungal activity in terms of efficacy as 95.83%. It is stated that the created formulation will shorten therapy duration, increase patient acceptance, and represent a breakthrough in the treatment of skin infections.

Novel additively manufactured dihedral tiling architected metamaterial conformed with pentagon and rhombus: design and mechanical properties

The design of novel mechanical metamaterials has drawn inspiration from several sources to develop new structures. Additionally, additive manufacturing has widened the possibilities for producing intricate geometries. With this in mind, a novel architected metamaterial based on dihedral tiling is presented here, and its mechanical response is characterized experimentally. The architecture comprises two shapes: a pentagon and rhombuses, arranged in a manner dependent on each other. Three parameters were defined as variables to generate several design variations and analyze the impact of geometry on their effective mechanical properties: pentagon edge length (l), pattern rotation angle (θ), and strut thickness (t). For this purpose, the selected designs were additively manufactured using Thermoplastic Polyurethane (TPU) and tested under compression. It was found that t is directly proportional to relative density, and consequently, to apparent stiffness, while l is inversely proportional to both properties. On the other hand, θ has a minor influence on apparent stiffness and is more related to the deformed shape obtained. Overall, it was observed that the response depends on the combination of all geometrical parameters, meaning the apparent properties cannot be related to the response of only one of the shapes. This behavior differs from lattices based on a singular shape, in which the properties of the whole metamaterial are usually related to those of the unit cell.

Determining the characteristics of representative volume elements in severely deformed aluminum-matrix composite

The accurate evaluation of the effective mechanical properties of composites mainly depends on the characteristics of representative volume elements (RVEs). This paper mainly investigates the RVE size. Additionally, the effect of volume fraction of reinforcement, the edge effect, and RVE types on the critical size are discussed. First, the Al/Ni multilayered composites were processed by nine cycles of the cross-accumulative roll bonding (CARB) method. Then, one type of RVEs was created based on cross-sectional micrographs of composites to consider their inhomogeneities. Another type was generated by using the random sequential adsorption (RSA) procedure. Thereafter, the homogenized effective elastic properties of both types of microstructure-based RVEs and RSA-based RVEs were computed and compared as a function of the volume fraction of Ni and RVE size. The results showed that by increasing the Ni fragments, the RVEs indicated stiffer elastic behavior. By increasing the volume fraction of Ni from 0.2 Vf to 0.8 Vf, the Poisson ratio decreased by 7 % and the elastic modulus increased by 83 % for RSA-based RVE. Regarding the size of microstructure-based RVE of Al/Ni (0.8 Vf), from the largest size (size 1) with a length of 575 μm and a width of 575 μm to the smallest size (size 5) with a length of 287.5 μm and a width of 287.5 μm, the elastic modulus and the Poisson ratio showed 16 % and 0.8 % decrease, respectively.

Predicting the modulus of elasticity of clayey soil composites reinforced with scrap tire rubber fibers using a composite material model

In this study, composite material models are used to predict the modulus of elasticity of a composite consisting of scrap tire rubber fibers and clayey soils. The calculated modulus of elasticity is compared with the reference modulus obtained from experimental testing. Predicting the effective mechanical properties of composites is crucial in situations where testing is impractical, challenging, or costly. The analysis involves various approaches within the elasticity framework, utilizing rheological models such as Voigt, Reuss, Hirsch-Dougill, Popovics, Halpin-Tsai, Hashin, and the Bache & Napper–Christensen estimation. These models aim to predict the effective Young's modulus of the composite system comprising soil and rubber fibers. The maximum discrepancies observed are 10.66%, 12.71%, and 12.98% for both soils. Voigt, Hashin, and Bache estimations provide highly accurate predictions of the effective Young's modulus, showing excellent agreement with experimental results across different fiber volume fractions ranging from 10% to 50%.

Analytical and numerical evaluation of the effective properties of macro fiber composite (MFC)

The piezoelectric fibers of Macro Fiber Composite (MFC) have a rectangular cross-section with an aspect ratio of 2. This heterogeneity poses challenges for micromechanical modeling to predict the effective mechanical properties. The High-Fidelity Generalized Method of Cells (HFGMCs) is commonly used to calculate the properties of composite materials. In this paper, a Modified High-Fidelity Generalized Method of Cells (MHFGMC) is proposed to analyze MFC properties, in which the interaction between subcells is considered by defining the quadratic directional coupling term and the shear connection matrix. The accuracy of the proposed MHFGMC model is verified by using the finite element method and experimental tests. The results show that the MHFGMC can accurately predict the effective mechanical properties of MFC, and the relative error of tensile properties compared to experimental results is within 2.29%. The MHFGMC significantly improve the accuracy of the HFGMC, the relative error of its shear modulus is decreased from 105.13% to 0.71%.

Nonlocal strain gradient-based nonlinear vibration analysis of nonlinear FG three-phase HJCNT/MWCNT/epoxy composite microbeam resonators using a modified micromechanical model

This paper aims to study nonlinear dynamic behavior of functionally graded (FG) three-phase composite microbeam resonators made of an epoxy matrix and two reinforcements namely multi-walled carbon nanotubes (MWCNTs) and hetero-junction carbon nanotubes (HJCNTs). The effective mechanical properties of the composite microbeam are obtained using the modified Halpin-Tsai micromechanical model. The microbeam surrounding medium is simulated using a two-parameter elastic foundation. The von-Karman’s geometric nonlinearity relations are incorporated and the equations of motion are derived based on the nonlocal strain gradient Euler–Bernoulli beam model. A new closed-form analytical solution is obtained using the homotopy perturbation method. The effects of vibration amplitude, nanofiber volume fraction, nanofiber distribution pattern, small-scale parameters and the foundation parameters on the nonlinear frequency and deflection of the FG three-phase composite microbeams are studied in detail. The findings of the paper are valuable for researchers in the field of microbeam resonators.

Multi deep learning-based stochastic microstructure reconstruction and high-fidelity micromechanics simulation of time-dependent ceramic matrix composite response

A multi deep learning-based framework is developed for efficient, automated microstructure reconstruction and generation of stochastic representative volume elements (SRVEs) with periodic boundary conditions (PBCs) for accurate modeling of ceramic matrix composite (CMC) response. The methodology comprises a convolutional neural network coupled with regression layers to act as a vanilla regression network for semantic segmentation of the microstructure, allowing accurate characterization of the phases and their distributions at the microscale. Scanning electron microscope and confocal microscope are used to obtain C/SiNC and SiC/SiNC CMCs micrographs for vanilla regression testing. Microstructure variability in terms of fiber volume fraction and porosity are quantified through the output regression layer, ensuring accurate representation of material variability in SRVE construction. Generative adversarial network (GAN) and its variants are designed to produce high-fidelity SRVE, spanning CMCs microstructure variability space. A circular padding algorithm is developed to generate SRVEs with PBCs during training of GANs. The accuracy of the generated SRVEs is established through micromechanics simulations, where an efficient formulation of the high-fidelity generalized methods of cells (HFGMC) approach is used to compute the effective mechanical properties. An iterative algorithm is implemented in the HFGMC solver to simulate time-dependent deformation of SiC/SiNC subjected to creep loading conditions.

Mechanical response of 3D printed irregular sutural tessellations with Voronoi tile patterns under tension

The mechanical response of bio-inspired irregular sutural tessellations with Voronoi tile patterns are designed and fabricated via multi-material 3D printing. The effective mechanical properties of the designs were characterized via uni-axial tension mechanical experiments on the 3D printed specimens. Systematic nonlinear finite element simulations are conducted to explore the damage initiation and evolution of the designs. The influences of important design parameters, including tile length aspect ratio R, tile size irregularity Cstd, suture amplitude irregularity Astd, and stiffness ratio between the soft and hard phases, were evaluated. The effective stiffness, Poisson’s ratio, strength, toughness, and failure mechanisms are systematically quantified. The results demonstrate that an optimized level of suture irregularity exists for maximizing the modulus of toughness. The results provide a general design guideline for designing functionally graded two-phase tessellations with high mechanical performance.

Designing three-dimensional lattice structures with anticipated properties through a deep learning method

Lattice structures have been a hot topic recently owing to their superior mechanical properties, which are significantly influenced by the unit cell structure. By leveraging the power of deep learning, inverse design can be conducted on the unit cell structure based on the mechanical properties of its lattice structure. Assisted by deep learning, this study introduces a novel data-driven approach to design three-dimensional (3D) unit cells for lattice structures with anticipated properties. The approach can be efficiently and accurately applied to various unit cell structures. An auto-encoder is trained to extract the geometric features from unit cell point clouds. The effective mechanical properties of the lattice structures are calculated by combining the homogenization method and the finite element method. Subsequently, a mapping relationship between mechanical properties and geometric features is established through the multi-layer perceptron neural network. The models are ultimately employed to design 3D unit cells given anticipated properties of lattice structures. The results show that the mechanical properties of the generated unit cells satisfy the anticipated values. The applications of proposed method are demonstrated in orthopedic implants, new hybrid unit cells, and functionally gradient structures. Furthermore, the method can be extended to unit cell design across diverse domains.