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Kirigami is the art of cutting paper to create three-dimensional figures for primarily aesthetic purposes. However, it can also modify the mechanical behavior of the resulting structure. In the literature, kirigami has been applied to modify the material's structural behavior, such as by changing its elasticity, rigidity, volume, or any other characteristic. This article examines the behavior of a pattern of rectangular kirigami cuts on a thermoplastic polyurethane soft material structure and its influence on the mechanical parameters of the macrostructure. The results demonstrate that rectangular kirigami patterns significantly affect the stiffness of the test specimens, changing from 1635 N/m to 4020 N/m. In elongation, there is a variation from 176.6% to 218% by simply altering the height of the rectangular cut. This enables the adjustment of the soft material structure's stiffness based on the geometry of the propagating kirigami cuts. [ABSTRACT FROM AUTHOR]

In recent years, demographers have parsed variation in survivorship into two distinct components: the shape and the pace of ageing. The pace of ageing is defined by measures of longevity such as mean life expectancy or maximum longevity, whereas measures of the shape of ageing attempt to classify different shapes of the survivorship curve. We recently published a paper pointing out that a commonly used discretization of a shape measure, Keyfitz' entropy, does not correctly classify survivorship curves into negatively and positively senescing curves (de Vries et al., 2023). In that paper, we also suggested an alternative, accurate discrete‐time version of Keyfitz' entropy. de Vries et al. (2023) ended with two open questions, both of which have been answered by Giaimo (2024) now: (1) Can a discrete‐time entropy measure of survivorship be generalized beyond age‐based population models? Giaimo (2024) introduce a new formula that achieves this. (2) Will a discretization of Keyfitz' derivation of his measure as the elasticity of lifespan to a uniform change in mortality lead to the same formula as a discretization of Keyfitz' result? Giaimo (2024) answers: no.Here, we briefly discuss the implications of the results obtained by Giaimo (2024), and the implementation of his new formula into the Rpackage Rage, which is widely used for comparative demographic studies.We showcase the strength of the new method by reanalysing a comparison of Keyfitz' entropy to another shape measure. We find that the comparison is significantly altered by using Giaimo's new Keyfitz' formula.This example strengthens Giaimo's (2004) words of warning in approaching discretizations with attentiveness. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present two Anand's model parameter sets for the multilayer silver–tin (AgSn) transient liquid phase (TLP) foils. Design/methodology/approach: The AgSn TLP test samples are manufactured using pre-defined optimized TLP bonding process parameters. Consequently, tensile and creep tests are conducted at various loading temperatures to generate stress–strain and creep data to accurately determine the elastic properties and two sets of Anand model creep coefficients. The resultant tensile- and creep-based constitutive models are subsequently used in extensive finite element simulations to precisely survey the mechanical response of the AgSn TLP bonds in power electronics due to different thermal loads. Findings: The response of both models is thoroughly addressed in terms of stress–strain relationships, inelastic strain energy densities and equivalent plastic strains. The simulation results revealed that the testing conditions and parameters can significantly influence the values of the fitted Anand coefficients and consequently affect the resultant FEA-computed mechanical response of the TLP bonds. Therefore, this paper suggests that extreme care has to be taken when planning experiments for the estimation of creep parameters of the AgSn TLP joints. Originality/value: In literature, there is no constitutive modeling data on the AgSn TLP bonds. [ABSTRACT FROM AUTHOR]

This paper proposes, for particle-based materials, a higher-order nonlocal elasticity continuum model that includes the Piola peridynamics and the Eringen nonlocal elasticity. When referring to particle-based materials, we denote systems that can be modeled as assemblies of material points (or particles). Note that this paper is not devoted to granular materials, then factors such as the topology of contacts, granulometry, grain sizes, shapes, and geometric structure are not considered. Additionally, when referring to Piola peridynamics, we specifically denote the particular peridynamic model developed by Piola, which differs from the commonly adopted approach to peridynamics. The proposed higher-order nonlocal elasticity continuum model offers several advantages. First, it can describe interactions between material points over longer ranges than those considered by Eringen nonlocal elasticity. Second, it exhibits similar characteristics to gradient-type theories and Piola peridynamics, enabling the consideration of more complex external and contact actions, including Nth order forces and stresses. Furthermore, the proposed deterministic model is developed to lay the foundation for a stochastic formulation applicable to uncertain particle-based materials. We want to emphasize that the aim of this paper is not to unify Eringen nonlocal elasticity with the various existing peridynamic models. [ABSTRACT FROM AUTHOR]

The paper presents an identification process of model parameters of a thin nickel-titanium alloy wire based on experimental research. The wire made of NiTi alloy was subjected to a tensile test to obtain the stress-strain characteristic. Parameters of the non-linear material model were identified based on the obtained experimental results. The material model used in the conducted research may be used for simulation of the shape memory effect and pseudoelasticity of the shape memory alloy. The generated results of numerical simulations have a good approximation with the conducted experimental tests. [ABSTRACT FROM AUTHOR]

The paper investigates a problem concerning the equilibrium of a solid body containing a thin rigid inclusion and a crack. It is assumed that the body is hyperelastic, therefore, it is described within the framework of finite strain theory. One of the peculiarities of this problem is a global injectivity constraint, which prevents the body, the crack faces and the inclusion from both mutual and self penetration. First, the paper deals with the differential formulation of the problem. Next, we consider energy minimization, showing that the latter provides the weak formulation of the former. Finally, the existence of the weak solution is demonstrated through the use of the variational technique. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping (- Δ) 2 θ v t with θ ∈ [ 1 2 , 1 ] . By using the semigroup method and the multiplier technique, we obtain the exact polynomial decay rates, and find that the polynomial decay rate of the system is determined by the inertia/elasticity ratios and the fractional damping order. Specifically, when the inertia/elasticity ratios are not equal and θ ∈ [ 1 2 , 3 4 ] , the polynomial decay rate of the system is t - 1 / (10 - 4 θ) . When the inertia/elasticity ratios are not equal and θ ∈ [ 3 4 , 1 ] , the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . When the inertia/elasticity ratios are equal, the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . Furthermore it has been proven that the obtained decay rates are all optimal. The obtained results extend the results of Oquendo and Suárez (Z Angew Math Phys 70(3):88, 2019) for the case of fractional damping exponent 2 θ from [0, 1] to [1, 2]. [ABSTRACT FROM AUTHOR]

Purpose: The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil. Design/methodology/approach: First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs. Findings: Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown. Originality/value: This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper. [ABSTRACT FROM AUTHOR]

Novel engine fan blades are made of 3D woven composite materials and incorporate a protective metallic layer at the leading edge. The end-of-life of such structures involves complicated disassembly and recycling processes. In this paper, laser-shock is being investigated as an environmentally friendly disassembly method. In this context, symmetric laser-shock experiments that have been conducted in a previous work using a time delay between the shots have been proven successful for debonding initiation and propagation as they manage to effectively focus the tensile stress field developed by the shock waves at the bondline. In this paper, a numerical model simulating the symmetric laser-shock disassembly of titanium/CFRP specimens has been developed using the LS-Dyna explicit FE code. The aim is to give a deeper insight into the physical mechanisms and to optimize the experimental process. To simulate the behavior of the titanium part, the Johnson-Cook material model in combination with Grüneisen equation of state has been employed, while for the composite part a progressive damage material model incorporating high-strain rate effects has been used. The bondline between the two parts has been modeled using cohesive zone elements. To obtain tensile and shear elastic and strength properties at high strain rates for the composite damage model, tension and punch shear Split-Hopkinson Bar tests have been conducted. The numerical results correlate well with back-face velocity profiles obtained from single sided laser shock experiments and with debonding patterns in the adhesive, observed in electron microscopy images, induced by symmetrical laser shock experiments. After the validation, the numerical model has been used successfully to simulate a larger disassembly process composed of 16 consecutive shots. [ABSTRACT FROM AUTHOR]

The term "viscoelastic pipe" refers to high polymer pipes that exhibit both elastic and viscoelastic properties. Owing to their widespread use in water transport systems, it is important to understand the transient flow characteristics of these materials for pipeline safety. Despite extensive research, these characteristics have not been sufficiently explored. This study evaluates the impact of friction models on the transient flow of viscoelastic pipes across various Reynolds numbers by employing an energy analysis approach. Given the complexity and computational demands of two-dimensional models, this paper compares the accuracy of one-dimensional and quasi-two-dimensional models. Notably, the superiority of the quasi-two-dimensional model in simulating viscoelastic pipelines is demonstrated. Owing to the interaction between pressure waves and fluid within viscoelastic pipes, fluid–structure coupling significantly attenuates pressure waves during transmission. These findings shed light on the constitutive properties of viscoelastic pipes and the influence of pipe wall friction models on transient hydraulic characteristics, building upon prior studies focused on elastic pipes. Nevertheless, numerous factors affecting transient flow in viscoelastic pipes remain unexplored. This paper suggests further analysis of strain effects, starting with temperature and pipe dynamics, to enhance the understanding of the coupling laws and flow mechanisms in viscoelastic pipelines. [ABSTRACT FROM AUTHOR]

Recently, composite PVDF membranes with good performance have triggered enormous interest because of their great potential application. However, the uncertainty of mechanical properties limits their application. Herein, this paper reveals the elastic modulus properties of the loading angle between warp and tensile direction using the uni-axial tensile test of SH-1050P membrane textile. In addition, the bi-axial tensile test with different loading ratios was implemented. Both uni-axial and bi-axial ductile load-displacement/stress-strain curves are featured. It is the first to establish a relationship between the elastic modulus and the loading angle using a theoretical method based on the assumption that there is no slippage and crease between yarns and matric. Furthermore, simulations with different textile parameters were carried out to verify the theoretical results. The key finding is that the elastic modulus under uni-axial load can be divided into two stages, which are elasticity and plasticity. Both of which are proportional to the sine function applied to two times the loading angle. The Poisson's ratio of SH-1050P textile can be considered as a fixed value of 0.11. This conclusion can be extended to similar textiles. The outcome of this paper contributes to a deeper understanding of the PVDF memrane's mechanical behavior and presents a novel insight into its response to different loading conditions. [ABSTRACT FROM AUTHOR]

This paper investigates ESG from the perspective of changes in input elasticities of substitution and complementarity. Rather than compute these elasticities from the cost function, we compute them from the Input Distance Function (IDF). Our data are from Refinitiv Eikon Datastream database. We focus on the US economy due to her global role in the world economy and hence spillover effects of uncertainties on the rest of the world. The data consist of 5,798 companies comprising 38 US industries that span for 12 years from 2009 to 2020 and include: (i) financial data on sales, capital and employees; (ii) two financial ratios and (iii) three main ESG indicators. We compute Antonelli Elasticity of Complementarity (AEC) and Allen-Uzawa Elasticity of Substitution (AES) from the translog of IDF function. We find that the standard inputs have positive AEC elasticities; however, ESG cross-elasticities exhibit negative signs, classifying them as q-substitutes. Therefore, an increase in one of the ESG values leads to a decrease in the marginal value of the other. On the other hand, AES elasticities have a negative sign only for the Governance-Environment "doublet'; the rest of the pairs are positive implying that they are p-complements. [ABSTRACT FROM AUTHOR]

In this paper, we investigate various stabilisation problems of a hybrid system of elasticity, consisting of a thin tape, which moves axially between two sets of rollers. We present a control solution, which works simultaneously, for three variants of the tape model. In particular, we design boundary feedback control laws via Lyapunov's second method. The resulting closed-loop system for the general case is then analysed, where we prove the existence and uniqueness of solution using the semigroup theory of linear operators; furthermore, we prove the exponential decay of the solution via a frequency domain theorem. The stabilisation of the two other special cases is derived implicitly from the general case proofs presented in the paper. Finally, the paper is concluded by presenting computer simulations to support the theoretical results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the boundary conditions of explicit gradient elasticity of Mindlin's type in dynamics. It has been argued in an earlier paper that acceleration terms should not be present in the boundary tractions because of objectivity arguments. This is discussed in the present paper in more detail, and it is supplemented by assuming the validity of the principle of material frame indifference. Furthermore, new examples are discussed in order to illustrate that significant differences exist in the responses predicted by boundary tractions with and without acceleration terms. [ABSTRACT FROM AUTHOR]

This paper deals with an innovative nondestructive technique for composites (local-IET), which is based on the Impulse Excitation Technique (IET) and, in the presence of damage, assesses the degradation of the elastic properties of a local region of the laminate by reversibly clamping its boundaries. In this paper, a numerical analysis of the sensitivity of the local-IET to the delamination damage mechanism is conducted. Firstly, a Finite Element (FE) model of the local-IET test is determined through experimental investigations on undamaged composite laminates, which cover a wide range and are made of glass or carbon fibers, through resin infusion or pre-preg consolidation and with unidirectional or fabric textures. The vibrational response of a glass fiber composite with local delamination is then assessed with the local-IET. By modeling the delamination in the simulation environment, the effectiveness of the FE model in replicating the vibrational response, even in the presence of delamination, is shown through a comparison with the experimental results. Finally, the FE model is exploited to perform a sensitivity analysis, showing that the technique is able to detect the presence of delamination. [ABSTRACT FROM AUTHOR]

The paper contains a parametric dynamic analysis of cable-strut domes. The special structures named tensegrity are considered. Two qualitative different tensegrity domes, i.e., the Geiger dome and the Levy dome are taken into account. The aim of the study is to compare the dynamic behaviour of such structures. The first stage of analysis involves the identification of initial prestress forces (system of internal forces, which holds structural components in stable equilibrium) and infinitesimal mechanisms. The second stage focuses on calculating natural frequencies, while in the last, the impact of time-independent external loads on vibrations is studied. The influence of initial prestress and external load on the dynamic response of the structures is considered. A geometrically non-linear model is used to analysis. Presented considerations are crucial for the next step in the analysis, i.e., dynamic stability analysis of the behaviour of tensegrity structures under periodic loads. [ABSTRACT FROM AUTHOR]

In this paper, we have synthesised cholesteryl 4-allyloxybenzoate (MB), crosslinking agent dodecane-1,12-diyl bis(undec-10-enoate) (MG), and A'BGF series liquid crystalline elastomer (LCE) films which take polymethylhydrosiloxane (A') as the backbone, MB as the cholesteric liquid crystal (LC) monomer, and MG and bis-vinyl silicone oil (MF) with different reactivities as cross-linking agent for exploring the effect of the change of MF content on the properties of the elastomeric films. The experimental results show that the synthesised MB, MG, and the LCE films are all consistent with the molecular design; MB is an enantiotropic cholesteric LC. The synthesised LCE films are cholesteric LCs, have certain selective reflection characteristic, higher thermal stability, and their Tg decreased down to 3.9°C as MF increasing. During the heating and cooling, the liquid crystalline properties of the LCE films have a good reversibility. Among the synthesised LCE films, A'BGF-2 has stretching radio of 264.8% at room temperature, with the best elastic properties. By adjusting the ratio of MF, the content of small-molecule MB remained in the films can be changed, which will affect the optical properties and elasticity of the LCE films. The experiments provide a method for the preparation of highly elastic side chain LCE film. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of minimizing functionals of the form E (u) = ∫ B f (x , ∇ u) d x in a suitably prepared class of incompressible, planar maps u : B → R 2 . Here, B is the unit disk and f (x , ξ) is quadratic and convex in ξ . It is shown that if u is a stationary point of E in a sense that is made clear in the paper, then u is a unique global minimizer of E(u) provided the gradient of the corresponding pressure satisfies a suitable smallness condition. We apply this result to construct a non-autonomous, uniformly convex functional f (x , ξ) , depending smoothly on ξ but discontinuously on x, whose unique global minimizer is the so-called N - covering map, which is Lipschitz but not C 1 . [ABSTRACT FROM AUTHOR]

The literature about the asymptotic numerical method (ANM) is reviewed in this paper as well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation method based on the computation of Taylor series for solving nonlinear partial differential equations. Modern techniques of high-order differentiation provide simple tools for computing these power series, the corresponding algorithms for finite strain elasticity and elastoplasticity being summarized here. Taylor series is not only a computation tool, but it contains also useful information about the structure of the considered solution curve. The paper ends with a short historical account about the development of this numerical method. [ABSTRACT FROM AUTHOR]

By considering the joint effects of the KelvineHelmholtz (KH) and RayleigheTaylor (RT) instabilities, this paper presents an interpretation of the wavy patterns that occur in explosive welding. It is assumed that the elasticity of the material at the interface effectively determines the wavelength, because explosive welding is basically a solid-state welding process. To this end, an analytical model of elastic hydrodynamic instabilities is proposed, and the most unstable mode is selected in the solid phase. Similar approaches have been widely used to study the interfacial behavior of solid metals in high-energy-density physics. By comparing the experimental and theoretical results, it is concluded that thermal softening, which significantly reduces the shear modulus, is necessary and sufficient for successful welding. The thermal softening is verified by theoretical analysis of the increase in temperature due to the impacting and sliding of the flyer and base plates, and some experimental observations are qualitatively validated. In summary, the combined effect of the KH and RT instabilities in solids determines the wavy morphology, and our theoretical results are in good qualitative agreement with experimental and numerical observations. [ABSTRACT FROM AUTHOR]

In this paper, we study the long-time behavior of a nonlinear porous elasticity system. The system is subject to a viscoporous damping and a nonlinear source term which is locally Lipschitz and depends only on the volume fraction. The dynamical system associated with the solutions of the model is gradient, and under the hypothesis of equal speeds of propagation for the waves, we prove that it is also quasi-stable, which allows us to show the existence of a global attractor for the system, which is the main result of the paper. [ABSTRACT FROM AUTHOR]

This paper reports the systematic study on the structure, magnetic properties and magnetoelastic properties for the Fe100− x Ga x (001) thin films epitaxially grown on the different substrates of GaAs(001) and MgO(001) using the sputtering technique. The alloy composition dependence of effective magnetoelastic coupling coefficient B eff along the FeGa [110] direction indicated that the largest magnetoelastic coupling was obtained for the Fe–Ga layer with x = 30 grown on the MgO substrate, which was evaluated to be B eff = − 9.4 × 107 erg cm−3. Considering the results of structural analysis and magnetization measurement, the different crystallite sizes depending on the kind of substrate may give rise to the different magnetoelastic coupling strengths between the Fe–Ga layers on the MgO and the GaAs. The magnetostriction along the Fe–Ga [111] direction λ 111 was also estimated with the assumption of plausible elastic property of Fe–Ga, and showed the values comparable to the reported value of bulk Fe–Ga. This means the large magnetostriction can be obtained even for the Fe–Ga thin films epitaxially grown not only on the GaAs(001) but also on the MgO(001). The findings in this work will give a guideline for designing spintronic applications with a Fe–Ga layer exhibiting a large magnetoelastic coupling. [ABSTRACT FROM AUTHOR]

The physically based deformable curve models are widely used to simulate thin one-dimensional objects in computer graphics, interactive simulation, and surgery simulation. These models consider objects to be rods described by an adapted frame curve that contains the rod's centerline as well as the orthonormal material frame of each point on the centerline. However, they pose challenges including fine discretization, redundancy in modeling slender rods, and maintaining accuracy and stability. In this paper, we propose a novel physically based deformable B-spline curve model that regards curves as rods consisting of parallel fibers and derive elastic potential energy only from curves' representations. Therefore, our model does not take rotation-based adapted frames into consideration and reduces degree of freedom. Our model divides the curves into infinitesimal elements in parameter space and derives the analytical relationship between elastic potential energy function and curves' representations through the change of total length of infinitesimal elements' fibers. Our model can support material attributes in the real world and maintain the reality and stability of the solution. We employ isogeometric analysis to solve the dynamic equations derived from our deformable model as isogeometric analysis is suitable to solve the dynamic equations of parametric models. We compare the scenarios in the real world, our model's simulation results, and other model's results to demonstrate the reality of our models. The results are in line with expectation. We design several examples to demonstrate our models' applications. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of finding the necessary and sufficient conditions to be satisfied by the engineering moduli of an anisotropic material for the elastic energy to be positive for each state of strain or stress. The problem is solved first in the most general case of a triclinic material and then each possible case of elastic syngony is treated as a special case. The method of analysis is based upon a rather forgotten theorem of linear algebra and, in the most general case, the calculations, too much involved, are carried out using a formal computation code. New, specific bounds, concerning some of the technical constants, are also found. [ABSTRACT FROM AUTHOR]

As the size of a layered structure scales down, the adhesive layer thickness correspondingly decreases from macro- to micro-scale. The influence of the material microstructure of the adhesive becomes more pronounced, and possible size effect phenomena can appear. This paper describes the mechanical behaviour of composites made of two solids, bonded together by a thin layer, in the framework of strain gradient and micropolar elasticity. The adhesive layer is assumed to have the same stiffness properties as the adherents. By means of the asymptotic methods, the contact laws are derived at order 0 and order 1. These conditions represent a formal generalization of the hard elastic interface conditions. A simple benchmark equilibrium problem (a three-layer composite micro-bar subjected to an axial load) is developed to numerically assess the asymptotic model. Size effects and non-local phenomena, owing to high strain concentrations at the edges, are highlighted. The example proves the efficiency of the proposed approach in designing micro-scale-layered devices. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

The dynamic modulus of asphalt mixture is an important factor in the design of asphalt pavement, and many scholars have proposed different models for estimating the dynamic modulus of asphalt mixture, but there are almost no studies on the prediction of the dynamic modulus of semi-flexible materials. In order to analyze and estimate the dynamic modulus of semi-flexible materials, we set up a high-performance cementitious paste (HPCP) semi-flexible material and a reference group Stone Mastic Asphalt (SMA-16) under multiple conditions, first measured its dynamic modulus in the laboratory, and analyzed the dynamic modulus characteristics of the material, and then used the equation the estimation equation proposed by Witczak et al. (Witczak1-37A) as a benchmark to introduce a new parameter, grouting mass ratio (Pb) to develop a Witczak- G prediction model to compare and validate the predicted dynamic modulus with the measured values. The results show that compared with SMA-16, HPCP semi-flexible material exhibits higher dynamic modulus and lower phase angle, and its temperature sensitivity and deformation resistance are significantly better than those of SMA-16. Under the influence of porosity and Pb factor, the dynamic modulus is positively correlated with both factors, and the phase angle increases first and then decreases, showing strong elastic properties. In this paper, we propose a dynamic modulus prediction model based on viscosity and Pb, Witczak-G, which predicts the highest coefficient of determination (R2) of the predicted dynamic modulus as high as 0.99 after initial fitting and validation, which indicates that the Witczak-G model is suitable for predicting the dynamic modulus of semi-flexible materials injected with HPCP. [ABSTRACT FROM AUTHOR]

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In this paper, we introduce a new vectorized MATLAB-based algorithm for efficient serial computation of global matrix/force arising from finite element method (FEM) for meshes of any type and approximation order in linear elasticity. Because for-loops in MATLAB are very slow, we propose a modified process that takes advantage of vectorization and sparse assembly to achieve good performance while using the same memory as the standard algorithm. For this purpose, by using good programming practices, the implementation of this scheme is succinctly described and can be integrated into any MATLAB package dealing with FEM. Specifically, attention is paid to the calculation of the triplet (row index, column index, matrix components) as well as the assembly of the global stiffness matrix, mass matrix and force vector. Additionally, an extension of the proposed approach for Mindlin plate theory and functionally graded materials is outlined. Finally, the accuracy of this strategy is verified on selected numerical tests after comparing the obtained results with those of ABAQUS. In terms of performance, the study conducted on a set of meshes considering the standard algorithm and two other well-known MATLAB vectorized algorithms revealed that: (i) for a 2D beam problem meshed with P 1 -triangle elements, a speedup of about 8 and 15 is achieved with sparse and fsparse, respectively. (ii) for a 3D plate problem meshed with P 1 -tetrahedral elements, a speedup of about 4 and 8 is achieved with sparse and fsparse, respectively. When compared to ABAQUS performance, the proposed scheme results in a computational time that is about five times smaller. [ABSTRACT FROM AUTHOR]

This paper assesses thermoelastic damping (TED) in circular nanoplates by incorporation of the small-scale effect into structural and thermal domains. The nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model are exploited for achieving the size-dependent coupled thermoelastic equations. By choosing time-harmonic and asymmetric form for deflection and temperature change, and solving the size-dependent thermoelastic eigenvalue problem, the damped natural frequency of circular nanoplate is extracted. On the basis of the complex frequency approach, an analytical relation, for the description of TED in circular nanoplates, is derived. For different boundary conditions and vibration modes, a comparison study is performed between the size-dependent results and those provided by classical continuum mechanics and heat conduction theories. Outcomes show a discrepancy between results acquired by the size effect on the structure and heat conduction. It is elucidated that how nonlocal and DPL characteristic parameters can represent the size-dependent phenomenon and can affect the magnitude of TED. A comprehensive parametric study is conducted to specify the influence of boundary constraints, vibration mode and the type of material on the amount of energy loss from TED. [ABSTRACT FROM AUTHOR]

The importance of propeller effects and power contribution to the aerodynamics of small aircraft and unmanned aerial vehicles (UAVs) is indispensable. The aerodynamic analysis of wings in flight varies from rigid wing analysis due to wing deflection caused by transferred aerodynamic loads. This paper investigates the intertwined influence of propeller effects and elasticity on the aerodynamics of small propeller-driven aircraft and UAVs. Through a detailed methodology, a twin-engine propeller-driven aircraft is analyzed as a case study, providing insights into the proposed approach. Two critical analyses are presented: an examination of propeller effects in rigid aircraft and the incorporation of elastic wing properties. The former establishes a foundational understanding of aerodynamic behavior, while the latter explores the impact of wing elasticity on performance. Validation is achieved through comparative analysis with wind tunnel test results from a similar rigid structure aircraft. Utilizing NASTRAN software V2010.1, aerodynamic analysis of the elastic aircraft is conducted, complemented by semi-empirical insights. The results highlight the importance of these factors across different angles of attack. Furthermore, deviations from the rigid aircraft configuration emphasize the considerable influence of static aeroelasticity analysis, notably increasing longitudinal characteristics by approximately 20%, while showing a lower impact of 5% in lateral-directional characteristics. This study contributes to enhanced design and operational considerations for small propeller-driven aircraft, with implications for future research and innovation, particularly for the purpose of efficient concepts in advanced air mobility. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential approach, representing them as sums of Bessel functions. The determination of the coefficients for these expansions is accomplished in the Laplace space, where we compare the boundary conditions. By converting the inverse Laplace transforms into complex integrals using residue calculus, we successfully derive explicit expressions for the displacements and stress fields. Notably, these expressions encompass primary, secondary, and surface waves, providing a thorough characterization of the stress propagation phenomena within the disk. Our findings contribute to the understanding of mechanical behavior in disk-shaped components and can be valuable in the design and optimization of such structures across various engineering disciplines. [ABSTRACT FROM AUTHOR]

In this paper, we consider isotropic Mindlin–Toupin strain gradient elasticity theory, in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory, we developed an extended form of Boussinesq–Galerkin (BG) and Papkovich–Neuber (PN) general solutions. The obtained form of BG solution allows to define the displacement field through a single vector function that obeys the eight-order bi-harmonic/bi-Helmholtz equation. The developed PN form of the solution provides an additive decomposition of the displacement field into the classical and gradient parts that are defined through the standard Papkovich stress functions and modified Helmholtz decomposition, respectively. Relations between different stress functions and the completeness theorem for the derived general solutions are established. As an example, it is shown that a previously known fundamental solution within the strain gradient elasticity can be derived by using the developed PN general solution. [ABSTRACT FROM AUTHOR]

The Cauchy relations distinguish between rari- and multi-constant linear elasticity theories. These relations are treated in this paper in a form that is invariant under two groups of transformations: indices permutation and general linear transformations of the basis. The irreducible decomposition induced by the permutation group is outlined. The Cauchy relations are then formulated as a requirement of nullification of an invariant subspace. A successive decomposition under rotation group allows to define the partial Cauchy relations and two types of elastic materials. We explore several applications of the full and partial Cauchy relations in physics of materials. The structure's deviation from the basic physical assumptions of Cauchy's model is defined in an invariant form. The Cauchy and non-Cauchy contributions to Hooke's law and elasticity energy are explained. We identify wave velocities and polarization vectors that are independent of the non-Cauchy part for acoustic wave propagation. Several bounds are derived for the elasticity invariant parameters. [ABSTRACT FROM AUTHOR]

This paper is devoted to a new gauge of small dynamic bending deformations of structures. Unlike previously existing strain gauges that measure elongation or compression at a certain point on the surface of a deformable body, the proposed gauge measures the change in curvature at a point on the surface of a deformable body and does not respond to elongation–compression strains. The gauge is a layered bar made of piezoelectric and elastic materials. It functions using the direct piezoelectric effect. In order to competently study the deformed state of a structure at points on a surface, it is necessary to determine all components of the strain tensor. The gauges currently used measure only elongational or compressive strains, which does not provide a complete picture of the strain state. It is very important to complement these deformations with bending strains measured by the new gauge. [ABSTRACT FROM AUTHOR]

On the human face, the lips are one of the most important anatomical elements, both morphologically and functionally. Morphologically, they have a significant impact on aesthetics, and abnormal lip morphology causes sociopsychological problems. Functionally, they play a crucial role in breathing, articulation, feeding, and swallowing. An apparatus that can accurately and easily measure the elastic modulus of perioral tissues in clinical tests was developed, and its measurement sensitivity was evaluated. The apparatus is basically a uniaxial compression apparatus consisting of a force sensor and a displacement sensor. The displacement sensor works by enhancing the restoring force due to the deformation of soft materials. Using the apparatus, the force and the displacement were measured for polyurethane elastomers with various levels of softness, which are a model material of human tissues. The stress measured by the developed apparatus increased in proportion to Young's modulus, and was measured by the compression apparatus at the whole region of Young's modulus, indicating that the relation can be used for calibration. Clinical tests using the developed apparatus revealed that Young's moduli for upper lip, left cheek, and right cheek were evaluated to be 45, 4.0, and 9.9 kPa, respectively. In this paper, the advantages of this apparatus and the interpretation of the data obtained are discussed from the perspective of orthodontics. [ABSTRACT FROM AUTHOR]

In this paper, we present certain complete solutions in the dilatation theory of elasticity. This model can be derived as a special case of Eringen's linear theory of microstretched elastic solids when microrotations are absent. It is also a version of the theory of materials with voids. The dilatation theory can be considered the simplest theoretical model of microstructured materials and is suitable for investigating various phenomena that occur in engineering, geomechanics, and biomechanics. We establish three complete solutions to the displacement equations of equilibrium that are the counterpart of the Green–Lamé (GL), Boussinesq–Papkovich–Neuber (BPN), and Cauchy–Kowalevski–Somigliana (CKS) solutions of classical elasticity. The links between these BPN and CKS solutions are established. Then, we present a representation of the BPN solution in the case of axisymmetry. The results presented here are useful for solving axisymmetric problems in semi-infinite and infinite domains. [ABSTRACT FROM AUTHOR]

In this paper, theoretical investigations of structural, elastic and thermal properties of Zn3P2 material were done using Quantum ESPRESSO code based on density functional theory. The generalized gradient approximation (GGA) exchange correlation-functional helped to model the atomic interaction. First, the structural optimization procedure was carried out, and hence, the optimized structural parameters were utilized to obtain six independent elastic constants C 1 1 , C 1 2 , C 1 3 , C 3 3 , C 4 4 , and C 6 6 for the Zn3P2 tetragonal structure. Accordingly, these elastic constants were used to determine the elastic moduli such as the Bulk modulus, Young's modulus, and shear modulus, as well as other mechanical parameters such as Pugh's ratio, Poisson's ratio, anisotropic ratio, sound velocities and Debye temperature. Calculations of thermodynamic properties such as vibrational energies, vibrational free energies, and fixed volume heat capacities, were performed within the implementation of the Thermo_pw code. Elastic calculations confirmed that this compound is characterized by mechanical stability at zero pressure and 0K temperature, ionic bonding, a high degree of anisotropy, and typical ductility. An observable increase in Debye vibrational energies, entropies and constant volume heat capacities of this compound with increasing temperature was detected throughout the thermodynamic calculations, unlike vibrational free energy which revealed a pronounced decrease as temperature increased. [ABSTRACT FROM AUTHOR]

This paper illustrates how particle size affects the initial yield stress of particle-reinforced composites. A formulation in a closed form is presented to demonstrate the size effect of yielding of the composites. This paper also demonstrates that there is an upper bound and a lower bound for the size-dependent yield stress with the change of particle size. This means that decreasing particle size increases its yield stress up to an upper bound. Similarly, increasing particle size decrease its yield stress up to a lower bound. In this paper the asymptotic homogenization method is used in framework of the Cosserat elasticity. A virtual "unreinforced matrix" is introduced as a reference configuration. As a numerical example, the size effect of yielding of Sicp/Al is predicted. [ABSTRACT FROM AUTHOR]

This paper addresses the longstanding challenge of soft body dynamics with frictional contact through a novel combination of Projective Dynamics for elasticity simulation and Alternating Direction Method of Multipliers for frictional contact handling. The approach utilizes parallel local strain projection for deformable bodies and nonlinear Projected Gauss-Seidel for contact with Coulomb friction, consolidated by a pre-factorized global strain propagation step. Integration of contact stabilization, Matchstick anisotropic friction, and Rayleigh damping enhances reliability and usability. Effectiveness, accuracy, and computational efficiency are demonstrated in challenging cases, including multi-layer and persistent contacts. With a CPU-based parallel implementation, our method achieves visually plausible and stable simulation results at an interactive framerate in moderate-scale scenes, showcasing its applicability across various graphics applications. [ABSTRACT FROM AUTHOR]

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic perforated plate made of stiff material with holes filled by a soft matrix material. The structure is clamped on a cylindrical part. Two cases of asymptotic analysis are considered: one without pre-strain and the other with matrix pre-strain. In both cases, the total elastic energy is in the von-Kármán (vK) regime ( ε 5 ). A new splitting of the displacements is introduced to analyze the asymptotic behavior. The displacements are decomposed using the Kirchhoff–Love (KL) plate displacement decomposition. The use of a re-scaling unfolding operator allows for deriving the asymptotic behavior of the Green St. Venant's strain tensor in terms of displacements. The limit homogenized energy is shown to be of vK type with linear elastic cell problems, established using the Γ-convergence. Additionally, it is shown that for isotropic homogenized material, our limit vK plate is orthotropic. The derived results have practical applications in the design and analysis of composite structures. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of the horizon size on failure due to strain and damage localization in the case where peridynamics is a nonlocal theory by its own, which corresponds to most bond-based peridynamics models. Two constitutive relationships are discussed: the microelastic brittle model and a progressive damage model. The usual practice with the microelastic brittle model is to fit the microelastic constant for a given horizon size so that elasticity is recovered. At the same time, the fracture energy provides the critical bond stretch. This methodology yields an indirect determination of the tensile strength of the material, that goes to infinity as the horizon size trends to zero. With the damage model, the stretch at the inception of damage can be obtained from the tensile strength. Then, a simple one-dimensional case of wave propagation and interactions in a bar is considered. For fixed values of the horizon, convergence with a refinement of the discretization is checked. The energy dissipated upon fracture is found to be a linear function of the horizon. It is also a function of the softening response. The horizon cannot be chosen arbitrarily, unless the softening parameter is adjusted to fit the fracture energy, like in the crack band model. Surprisingly, such a methodology is very seldom mentioned in the current literature dealing with fracture modeled by peridynamics. [ABSTRACT FROM AUTHOR]

Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual thermo-mechanical properties as a result of the coupling between the entropic elasticity of rubber and the orientational phase transitions of liquid crystals. One of these intriguing properties is the soft behavior, where it is able to undergo significant deformations with almost no stress. While the phenomenon is well-known, it has largely been examined in the context of homogenous deformations. This paper investigates soft behavior in complex inhomogeneous deformations. We model these materials as hyperelastic, isotropic, incompressible solids and exploit the seminal work of Ericksen, who established the existence of non-trivial universal deformations, those that satisfy the equations of equilibrium in every hyperelastic, isotropic, incompressible solid. We study the inflation of spherical and cylindrical balloons, cavitation and bending. [ABSTRACT FROM AUTHOR]

This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm. [ABSTRACT FROM AUTHOR]

Cloud federation has been proposed as a new model enabling Cloud providers to cooperate and exchange resources among multiple Clouds to provide uninterrupted services and fulfil the requirements of Cloud users. To sustain the many benefits offered by this environment, it is crucial to have an accurate performance evaluation model. However, evaluating the performance of the federated Clouds environment is challenging for several reasons: the dynamic nature of this environment, the exponential growth of users and the diversity of requests. Therefore, to better satisfy user requests in the federated Clouds environment, we propose in this paper a performance evaluation model using an open Jackson network. Our model considers the key characteristics of the Cloud, such as the diversity of Cloud services and their exponential growth (IaaS, PaaS, and SaaS), as well as the increasing number of user requests, to obtain essential performance metrics, including response time and utilization. These two parameters are obtained analytically and are used to quantify the elasticity of the federated Clouds environment. Several experiments were carried out to evaluate the proposed solution. The results showed that our model outperforms the state-of-the-art and it is usefulness for designing real cloud computing systems. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the behaviour of two symmetric mode-III collinear cracks in a functionally graded material (FGM). The fundamental goal of this paper is to provide insight on the interaction of two cracks in FGMs with the strain gradient effect. To assess the influence of gradient elasticity, we have considered two key parameters ℓ and ℓ ′ , which describe the size scale effect caused by the underlying microstructure and are related to volumetric and surface strain energy, respectively. The crack boundary value problem have been solved by the approach involving Fourier transforms and the innovative hyper-singular integro-differential equation method, where the integral equation contains the two terms in integrals for the both cracks. A system of equations has been constructed by employing the Chebyshev polynomial expansion and then by choosing the suitable collocation points the system of equation have been solved. Our investigation involves the determination of stress intensity factors at both crack tips. These factors are vital for understanding the material's fracture behavior and structural integrity. Furthermore, we explore the variations in the displacement profile when the distance between the cracks is reduced to close proximity. This particular scenario is of significant interest as it provides insights into how the interaction between the cracks impacts the overall structural response. [ABSTRACT FROM AUTHOR]

A novel higher-order multi-scale computational approach for efficient nonlocal gradient elasticity simulation of composite materials is proposed in this paper. Based on the use of decoupling technique, raw fourth-order nonlocal gradient equations with periodically oscillatory coefficients are decoupled as the new second-order multi-scale equations for reducing the continuity requirements when implementing multi-scale simulation. Next, a novel macro-micro coupled multi-scale computational model with higher-order corrected terms is rigorously devised for high-resolution multi-scale and nonlocal analysis of composite materials via multi-scale asymptotic analysis. Then, the local error analysis of higher-order multi-scale solutions in the point-wise sense illustrates that establishing higher-order asymptotic corrected terms plays a vital role in investigating the micromechanical mechanisms. Moreover, a rigorous global error estimation with an explicit rate of higher-order multi-scale solutions is first derived in the energy norm sense. In addition, an efficient multi-scale numerical algorithm is presented to effectively simulate nonlocal gradient elasticity problems of composite materials based on finite element method (FEM). And we also derive the convergence estimation of the proposed numerical algorithm. Finally, numerical experiments are conducted to gauge the efficiency and accuracy of the proposed higher-order multi-scale method. This paper offers a unified higher-order two-scale computational framework for enabling nonlocal gradient elasticity behavior simulation of composite materials. [ABSTRACT FROM AUTHOR]

Heavy mechanized bridge is utilized to be rapidly deployed as a temporary bridge to facilitate the movement of vehicles and personnel across obstacles. This paper presents a dynamic model of the TMM-3M heavy mechanized bridge during the span-lowering process, including considerations of cable deformation, rear outriggers, elasticity of tire, and front suspension system. Based on the dynamic model, the authors establish a system of differential equations describing the oscillation of the system using Lagrangian equations of the second kind. The article provides a fundamental basis for studying the entire process of deploying the TMM-3M bridge and aims to improve the rear outriggers and cable winding system to reduce bridge deployment time. [ABSTRACT FROM AUTHOR]