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Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = −1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress–strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels. [ABSTRACT FROM AUTHOR]

The thermal vibration and buckling behavior of a functionally graded nanoplate are examined in this study. The nanoplate is made up of a silicon nitride/stainless steel core plate and two cobalt-ferrite/barium-titanate face plates. Four alternative porosity models were used to simulate the porosity of the nanoplate, and numerous variables that can affect the nanoplate's behavior were taken into account. The study found that the thermomechanical behavior of nanoplates with magneto-electro-elastic face layers and a functionally graded porous core plate is affected by material gradation indices, porosity ratios, nonlocal variables, and different core plate material porosity models. [ABSTRACT FROM AUTHOR]

This article discusses the development of optically clear adhesives (OCAs) derived from biomass for use in foldable displays. The OCAs are synthesized using eco-friendly visible-light-driven polymerization and possess low modulus and excellent creep and recovery properties, making them suitable for foldable devices. The authors synthesized new monomers from terpenes and combined them with established monomers to formulate OCAs with low glass transition temperature (Tg) and good adhesion properties. The properties of the OCAs were confirmed through rheological analysis, and their potential for enhancing the eco-friendliness of foldable devices was demonstrated. The authors also explored a sustainable visible-light-driven polymerization method for synthesizing the OCAs and found that the properties of the OCAs produced using this method were comparable to those produced using conventional UV methods. The authors concluded that the terpenoid-based acrylates used in their study offer advantageous attributes for eco-friendly foldable electronic devices. [Extracted from the article]

A size-dependent post buckling analysis of functionally graded (FG) microbeams is conducted by using an analytical solution based on a reformulated strain gradient elasticity theory (RSGET). The nonlinear behavior of post buckling is considered by employing the von-Karman nonlinear strain–displacement relation. The microstructure-dependent behavior of the microbeam is captured by the RSGET which incorporated both couple stress and strain gradient effects using one size-dependent parameter for each. The material properties of the FG microbeam changed along the thickness direction, which are described using a power law relation. Based on the principle of minimum potential energy, the equations of equilibrium and boundary conditions of the Euler–Bernoulli microbeam are obtained. The post buckling response of FG mcirobeams with different boundary conditions are analytically derived. Moreover, the effects of the length scale parameter, material gradient index, length-thickness ratio and Poisson's ratio on the post buckling responses are studied. In addition, the total critical pressure for the FG array structures is estimated. These results are helpful for designing FG-MEMS devices. [ABSTRACT FROM AUTHOR]

This study delves into the investigation of exact analytical solutions for the plane stress and displacement fields within linear homogeneous anisotropic nano-beam models of gradient elasticity. It focuses on solving the Helmholtz equation, which encompasses a second-order non-homogeneous linear partial differential equation in plane gradient elasticity theory, utilizing polynomial series-type solutions. The analysis centers on the utilization of gradient Airy stress functions to derive stress fields in the gradient theory. The research yields closed-form analytical solutions for Airy stress functions, stress, and strain fields in both classical and gradient theories. The study considers five distinct types of two-dimensional functionally graded cantilever beams with various boundary conditions: a cantilever anisotropic nano-beam subjected to a concentrated force at the free end, a cantilever anisotropic nano-beam under a uniform load, a simple anisotropic nano-beam under a uniform load, a propped cantilever anisotropic nano-beam under a uniform load, and a fixed end cantilever anisotropic nano-beam under a uniform load. General analytical solutions for the gradient stress and displacement fields of two-dimensional and one-dimensional anisotropic nano-beams under different boundary conditions are provided. The study showcases significant strain gradient size effects at the nano-scale through the derived analytical solutions for anisotropic beams. Additionally, it demonstrates that the strain gradient theory results for the limit case of the gradient coefficient c precisely align with results for isotropic and anisotropic materials in elasticity theory and classical theory. Furthermore, real-world applications are discussed, considering stress and displacement fields in real anisotropic materials such as TiSi 2 single crystals and orthotropic materials, which are special cases of anisotropic materials like wood and epoxy as documented in the literature. • Exact solutions for stress/displacement in gradient elasticity models for anisotropic functionally graded nano-beams. • Analysis focuses on constructing stress fields using "gradient Airy stress function" notation. • Solutions reveal significant strain gradient effects in anisotropic nano-beams. • Literature solutions for CT beams match findings by taking gradient coefficient c to zero. • Gradient stress fields vanish except in y-direction as c approaches infinity. [ABSTRACT FROM AUTHOR]

The analysis of plane stress problems has long been a topic of interest in linear elasticity. The corresponding problem for non-linearly elastic materials is considered here within the context of homogeneous incompressible isotropic elasticity. It is shown that when the problem is posed in terms of the Cauchy stress, a semi-inverse approach must be employed to obtain the displacement of a typical particle. If however the general plane stress problem is formulated in terms of the Piola-Kirchhoff stress, the deformation of a particle requires the solution of a non-linear partial differential equation for both simple tension and simple shear, the trivial solution of which yields a homogeneous deformation. It is also shown that the general plane stress problem can be solved for the special case of the neo-Hookean material. [ABSTRACT FROM AUTHOR]

This article is concerned with the minimization of peak stresses occurring in linear elasticity. We propose to minimize the maximal von Mises stress of the elastic body. This leads to a non-smooth shape functional. We derive the shape derivative and associate it with the Clarke sub-differential. Using a steepest descent algorithm, we present numerical simulations. We compare our results to the usual p -norm regularization and show that our algorithm performs better in the presented tests. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [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]

This study focused on evaluating the sensitivity and limitations of the simplified equipment used in the Digital Image Correlation (DIC) technique, comparing them with the analog extensometer, based on the mechanical property data of a composite made of fiberglass and epoxy resin. The objectives included establishing a methodology based on the literature, fabricating samples through manual lamination, conducting mechanical tests according to the ASTM D3039 and D3518 standards, comparing DIC with the analog extensometer of the testing machine, and contrasting the experimental results with classical laminate theory. Three composite plates with specific stacking sequences ( [ 0 ] 3 , [ 90 ] 4 , and [ ± 45 ] 3 ) were fabricated, and samples were extracted for testing to determine tensile strength, modulus of elasticity, and other properties. DIC was used to capture deformation fields during testing. Comparisons between data obtained from the analog extensometer and DIC revealed differences of 11.1% for the longitudinal modulus of elasticity E 1 and 5.6% for E 2 . Under low deformation conditions, DIC showed lower efficiency due to equipment limitations. Finally, a theoretical analysis based on classical laminate theory, conducted using a Python script, estimated the longitudinal modulus of elasticity E x and the shear strength of the [ ± 45 ] 3 laminate, highlighting a relative difference of 31.2% between the theoretical value of 7136 MPa and the experimental value of 5208 MPa for E x . [ABSTRACT FROM AUTHOR]

By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures. [ABSTRACT FROM AUTHOR]

This study investigated the effects of intercalation and exfoliation of the graphite flake particles on the mechanical properties of elastomeric composites using analytical, computational, and experimental techniques. Relying on the modified Eshelby and incremental Mori–Tanaka approach, a new micromechanics model was proposed to estimate Young's modulus and develop a constitutive model for expanded graphite (EG)-filled elastomer in finite strain deformation. It was found that when the initial graphite flakes expanded, the actual volume fraction and ultimate aspect ratio of the dispersed particles significantly affected the mechanical properties of the EG-reinforced composites. The present model and subsequent predictions reflect the initial flake diameter, actual volume fraction, ultimate aspect ratio of the particles, and other convenient physical properties of the composite constituents. In addition, molecular dynamics simulations were performed to evaluate the elastic properties of the EG-Matrix interphase region using the COMPASS force field function. The MD results showed that Young's modulus of the interphase region increased significantly as the quantity of the graphene layer increased. The micromechanics-constitutive model results were validated using the experimentally determined stress–strain relation of the composites. EG- and CB-elastomer nanocomposite specimens were fabricated and tested in the experimental program. Field emission scanning electron microscopy (FESEM) analysis of the cryo-fractured surfaces of the elastomer compounds showed good interactions between the constituents. Numerical computations indicated that the proposed model incorporating the new parameters could accurately predict the experiment at a small particle concentration. [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]

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]

This research investigates the synergistic impact of Trinidad Lake Asphalt (TLA) and Crumb Rubber Modifier (CRM) on the performance characteristics of PG 64-22 asphalt binder. Employing Superpave test analysis and Multiple Stress Creep Recovery (MSCR) testing, our study reveals that the incorporation of TLA significantly elevates the viscosity of the binder due to its high asphaltene content. This viscosity enhancement translates to increased stiffness and durability of the asphalt binder. Furthermore, CRM contributes to improved elasticity and deformation resistance, counterbalancing the stiffness induced by TLA. Our results indicate that the combined use of TLA and CRM not only boosts viscosity but also mitigates stiffness, thereby enhancing the binder's resistance to rutting, especially post-aging. However, an elevated concentration of TLA increases the risk of fatigue cracking, a concern effectively alleviated through the integration of CRM. At a critical temperature of −12 °C, Bending Beam Rheometer (BBR) tests demonstrate that TLA augments stiffness while CRM enhances low-temperature flexibility. This study underscores the necessity of optimizing TLA and CRM ratios to achieve a balance between enhanced performance and practical feasibility. The findings highlight the potential of TLA and CRM to substantially improve asphalt binder performance, contributing to the longevity and resilience of pavement structures. [ABSTRACT FROM AUTHOR]

In this study, we conducted in-situ tensile deformation tests using synchrotron X-ray and neutron diffraction techniques on Nb-bearing AISI 201 austenitic stainless steel specimens with varying grain sizes, including ultrafine (UFG, 0.28 μm), fine (FG, 1.75 μm), and coarse (CG, 110 μm) grains. The primary objective was to investigate the effect of grain size on the evolution of lattice strains and deformation mechanisms. Our findings reveal that grain size significantly impacts the evolution of lattice strains, peak broadening, and the distribution of load between the austenite and martensite phases. Notably, the average lattice strain and peak broadening were found to be higher in the CG specimen compared to the UFG and FG counterparts. While the lattice strains in the UFG and FG steels are all compressive, a tensile manner can be seen for the CG steel as deformation proceeds. The strain-induced martensite transformation kinetics for the reversion-annealed UFG and FG steels was higher than that of the solution-annealed CG one. A soft behavior from reflection (200) was found compared to other reflections in all UFG, FG, and CG specimens, showing anisotropic elastic properties. The analysis of lattice strain and peak broadening evolutions indicated that dislocation slip predominantly governs the deformation mechanism in the CG steel, while strain-induced martensitic transformation and twinning are more prominent in the UFG and FG specimens. [ABSTRACT FROM AUTHOR]

We report on the elastic and photodynamic properties of (E)‐1,2‐bis(pyridinium‐4‐yl)ethene dinitrate [H2Ebpe](NO3)2, whose needle‐like crystals can be reversibly deformed by applying external mechanical stress. The macro‐scale mechanical properties of [H2Ebpe](NO3)2 crystals were quantified by a three‐point bending test, which gave a stress‐strain curve with an elastic modulus of 1.18 GPa, and its values are lower than those of other flexible elastic organic crystals. It can also be reversibly bent through the [2+2] cycloaddition reaction of the olefin moiety, depending on the direction of UV irradiation. [ABSTRACT FROM AUTHOR]

The dispersion and reflection characteristics of coupled waves in the piezomagnetic solid with flexomagnetic microstructure effect are studied in this paper. The flexomagnetic effect, strain gradient effect and micro-inertia effect are introduced into the constitutive equation and the governing equation to establish the wave propagation theory in the piezomagnetic solid with flexomagnetic microstructure effect. The secular equation of wave propagation is derived, and the properties of five coupled waves are analyzed. The dispersion characteristics of coupled waves and the reflection properties of coupled waves at the free boundary are solved numerically and checked by the energy conservation law. The influences of the flexomagnetic effect, strain gradient effect and micro-inertia effect on the wave propagation are discussed. It is found that the flexomagnetic effect mainly enhances the mechanical-magnetic coupled property, strain gradient effect mainly enhances the elastic property, and micro-inertia effect not only enhances the inertia property, but also essentially changes the dispersion characteristics of coupled waves. [ABSTRACT FROM AUTHOR]

We combine flow visualisation techniques and particle image velocimetry to experimentally investigate the higher-order transition to elastoinertial turbulence of Boger fluids ($El = 0.11\unicode{x2013}0.34$) in Taylor–Couette flows. The observed route to turbulence is associated with the appearance of chaotic inflow jets, termed flame patterns, for increasing inertia, and stable structures of solitons, known as diwhirls, for decreasing inertia. We also report for the first time spatially and temporally resolved flow fields in the meridional plane for the three characteristic viscoelastic flow regimes (diwhirls, flame patterns and elastoinertial turbulence). We observe in all cases coherent structures of dynamically independent solitary vortex pairs. The stability of these coherent structures is jet-dominated and can be mainly ascribed to the high extension of the polymer chains in the inflow boundaries in the $r$ – $z$ plane. Solitary pairs are self-sustained when created through random events and do not split; instead, they merge when moving sufficiently close and annihilate when hoop stresses are not sufficient to sustain them. The highly localised and random events result in highly fluctuating, chaotic flow states. We estimate the decay exponent of spatial power spectral density, illustrating a universal scaling of $-2.5$ for elastoinertial turbulence. Based on our observations and in an effort to unify and combine precedent theories with our results, we suggest a mechanism for the origins of elastoinertial instabilities, accounting for both the effect of elasticity on the vortex formation and the effect of increasing/decreasing inertia on the flow dynamics. [ABSTRACT FROM AUTHOR]

A complete closed-form solution is derived to the finite plane elasticity problem associated with an elliptical incompressible liquid inclusion embedded in an infinite compressible hyperelastic matrix of harmonic type subjected to uniform remote in-plane Piola stresses. The internal uniform hydrostatic Piola stresses and deformation gradients within the elliptical incompressible liquid inclusion are obtained. The internal uniform hydrostatic tension and hoop stress on the matrix side along the liquid-solid interface for various shapes of the elliptical liquid inclusion and different elastic constants of the matrix under various remote loadings are calculated. [ABSTRACT FROM AUTHOR]

We consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods. However, current numerical methods omit important details of the microscopic structure and dynamics of the fluid, which can modulate the magnitudes and directions of viscoelastic restoring forces. To address this issue, we develop a simulation platform for modeling viscoelastic media with tensorial elasticity. We build on the lattice Boltzmann algorithm and incorporate viscoelastic forces, elastic immersed objects, a microscopic orientation field, and coupling between viscoelasticity and the orientation field. We demonstrate our method by characterizing how the viscoelastic restoring force on a driven immersed object depends on various key parameters as well as the tensorial character of the elastic response. We find that the restoring force depends non-monotonically on the rate of diffusion of the stress and the size of the object. We further show how the restoring force depends on the relative orientation of the microscopic structure and the pulling direction. These results imply that accounting for previously neglected physical features, such as stress diffusion and the microscopic orientation field, can improve the realism of viscoelastic simulations. We discuss possible applications and extensions to the method. [ABSTRACT FROM AUTHOR]

Curved nanobeams are one of the essential components in manufacturing nano-electromechanical systems needing nonlinear stability design. In the current investigation, the nonlinear buckling characteristics of functionally graded porous reinforced curved (FGPRC) nanobeams having different degrees of curvature are analyzed by counting the higher-order gradients of the classical strain tensor as well as nonlocal-type interatomic interactions. In this regard, two independent length-scale constants within the framework of the nonlocal strain gradient theory (NSGT) of continuum elasticity are taken into account. Via employing the promising low computational cost and geometrically adaptable method of isogeometric collocation, various branches of NSGT-based equilibrium graphs of FGPRC nanobeams are plotted relevant to each considered degree of curvature. It is extrapolated that the quantity of graphene platelet (GPL) weight fraction has a negligible influence on the significance of nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect in the value of the maximum deflections or lateral loads at the detected limit points, especially attributed to a higher degree of curvature. Besides, it can be remarked that, in the FGPRC nanobeam owning a small degree of curvature, lessening the quantity of porosity index results in an increment in the significance of the nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect on the maximum deflection at both upper and lower limit points. However, in the FGPRC nanobeams owning medium and large degrees of curvature, it gets lesser at the upper limit point, but becomes higher at the lower limit one. [ABSTRACT FROM AUTHOR]

The aim of this study is to understand the influence of the membrane electrode assembly (or MEA) interfaces properties on the mechanical behavior of PEMFCs, using the development of a numerical model. The in-plane elastic orthotropic properties and nonlinear out-of-plane properties of the gas diffusion layers will be considered in the numerical model. Numerical results suggest that it is possible to limit the plastic deformation of the PEM by controlling its assembly mode, as well as the properties at the MEA interfaces, considered as bonded or free. Different recommendations are then proposed to increase the durability of PEMFCs by limiting the amplitude of mechanical strains or stresses in their core. [Display omitted] [ABSTRACT FROM AUTHOR]

Thin-walled cylindrical shell structures are revisited with the objective of increasing the axial load-carrying capacity. By using the postbuckling reserve of rectangular plates, polygonal shells are studied, which combines the response of a plate-like structure with a shell-like structure. These "plate-shells" are shown to be imperfection insensitive for a range of polygonal shell designs. Furthermore, their collapse load exceeds the corresponding load for a circular cylindrical shell. These results are a significant departure from the well-known imperfection sensitivity in the axial compressive response of cylindrical shells. [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]

For the last 20 years, researchers have been looking for ways to modify asphalt binders to improve their rheological and thermophysical properties. The application of composite modifiers to enhance the rheological properties of asphalt binders offers a potential remedy for this significant issue. Because of this, this study looked at how composite modifiers affected the plain binder's rheological characteristics. This study examined the rheological properties of unmodified and modified binders using a variety of formulations to blend modifiers including linear styrene-butadiene-styrene (SBS), radial SBS, Elvaloy, and polyphosphoric acid (PPA). The effect of PPA on the properties of polymer-added binders at low temperatures was investigated. Additionally, modifications using PPA aim to reduce the polymer content. Based on traditional performance classification (PG) and multiple stress creep recovery (MSCR) systems, original, rolling thin film oven–aged, and pressure aging vessel–aged binders were divided into three groups using a dynamic shear rheometer (DSR). The performance of binders at low temperatures was also assessed using the bending beam rheometer (BBR). All of the study's additions were discovered to have enhanced the neat binder's high-temperature capabilities. The elastic property of the neat binder was increased by the addition of Elvaloy and PPA. Results showed that, although the PPA modifier reduced the hardness of neat asphalt binder at low temperatures, other additives did not show significant effects on the hardness of the binder. The MSCR procedure was successfully utilized to grade all of the binders, but it appears that some binders and conditions do not fit the MSCR protocol's "percent difference" criterion. According to the study's findings, SBS can be replaced by 611 elastomer to enhance the performance of binders at high and moderate temperatures. [ABSTRACT FROM AUTHOR]

Shear strength of damage zone, representing the stress threshold for rupture initiation, is a critical parameter in faulting mechanics. Despite its significance, the damage‐zone's shear strength has not been estimated in natural earthquake ruptures. Here we employed coseismic deformation and strain, kinematic slip model, and finite element modeling to determine the elastic properties and peak shear stress of coseismic damage zones along the 2021 Mw 7.4 Maduo earthquake. Through the analysis of the lowest shear stress resulting in surface ruptures and the highest stress without surface rupture, we constrained the strength within a range of 7–17 MPa. Our result is consistent with strength (5–16 MPa) of sandstone samples from laboratory tests, demonstrating the validity of this estimation. Although factors such as fault maturity and confining pressure influence strength variation, the strength can directly reflect the stress threshold required for macroscopic surface rupture formation in fault damage zones dominated by sandstone. Plain Language Summary: Shear strength of a fault damage zone inform us its ability to withstand shear stress before surface rupture occurs. This information often provides insights into the earthquakes rupture hazards near the Earth's surface. Natural earthquakes provide a perfect opportunity for us to address the question of "what is the shear strength of a fault damage zone." To this end, we require a set of comparative references: the utmost shear stress that a damage zone can withstand without surface rupture and the minimal one necessary for the zone to generate surface rupture. In this investigation, we studied the 2021 Maduo earthquake because it had multiple distinct surface rupture segments in some places but not in others. By comparing shear stress in these segments, we could figure out how strong the damage zones were. We used real observations and numerical simulations to estimate how much stress these damage zones can withstand. Our results indicate that, for damage zones embedded in intact sandstone with a Young's modulus of 15 GPa, its strength ranges from 7 to 17 MPa. Significantly, our study is the first to reveal the shear strength of damage zone from a nutural earthquake using geodetic data. Key Points: Shear modulus and shear stress for coseismic damage zone were determined using coseismic deformation and finite element modelEstimated shear strength from overlap range of coseismic stress between surface rupture and non‐rupture parts ranges from 7 to 17 MPaShear strength exhibits positive and negative correlations with confining pressure and fault maturity, respectively [ABSTRACT FROM AUTHOR]

This study investigates the room- and high-temperature (650 °C) tensile and low-cycle-fatigue behavior of Inconel 718 produced by laser powder bed fusion (PBF-LB/M) with a four-step heat treatment and compares the results to the conventional wrought material. The microstructure after heat treatment is characterized on different length scales. Compared to the wrought variant, the elastic and yield properties are comparable at both test temperatures while tensile strength, ductility, and strain hardening capacity are lower. The fatigue life of the PBF-LB/M variant at room temperature is slightly lower than that of the wrought material, while at 650 °C, it is vice versa. The cyclic stress response for both material variants is characterized by cyclic softening, which is more pronounced at the higher test temperature. High strain amplitudes (≥0.7%) at room temperature and especially a high testing temperature result in the formation of multiple secondary cracks at the transitions of regions comprising predominantly elongated grain morphology and columns of stacked grains with ripple patterns in the PBF-LB/M material. This observation and pronounced crack branching and deflection indicate that the cracks are controlled by sharp micromechanical gradients and local <001> crystallite clusters. [ABSTRACT FROM AUTHOR]

The study of thermal stresses in crystals grown from a melt is of great importance for optimizing growth regimes. The emergence of new promising materials, such as gallium oxide, requires stress calculations taking into account the anisotropy of the thermal and elastic properties of the material. A study was carried out of the influence of anisotropy on the distribution of thermoelastic stresses in thin crystalline rods of gallium oxide. Approximate formulas for the components of the stress tensor are given, obtained using the asymptotic integration of the thermoelasticity equations taking into account rectilinear anisotropy of a general form. A comparison of stress values for two growth directions was carried out. It is shown that choosing the orientation of the growth direction makes it possible to control the magnitude and distribution of thermoelastic stresses that arise in gallium oxide crystals when they are grown from a melt. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach to analyze the stress and displacement fields around blunt notches in bi-material media, focusing on mode III loading conditions. The eigenfunction expansion method is used to derive a simplified yet accurate solution, satisfying the boundary conditions for bi-material blunt V-notches. The robustness of the proposed asymptotic solution is validated through several finite element analyses, encompassing a range of notched geometries such as blunt V-notches, VO-notches, and circular holes. Notably, it is demonstrated that when the notch tip radius approaches zero, the solution coincides with the existing sharp V-notch model. [ABSTRACT FROM AUTHOR]

Stretchable inorganic electronics have been of growing interest over the past decades due to their various attractive potential applications. The island-bridge structure is the most widely used structural design, where rigid inorganic devices (islands) and interconnects (bridges) are attached to an elastomer substrate, and large deformations in the structure are accommodated by the large stretchability of the interconnects and the elastomer underneath them. Due to the large modulus mismatch of more than five orders of magnitude between the rigid island and elastomer substrate, there is a severe stress and strain concentration at the interface between the island and the substrate during large deformations, which may cause the interface fracture and delamination. In this work, the analytical solution of the interfacial shear and peel stress between the island and the substrate is derived to reveal the mechanism of interface fracture and agrees well with finite element analysis (FEA) results. A simple porous partition substrate design strategy is proposed to alleviate this stress and strain concentration at the boundary of the interface, where the porous region can undergo larger deformation due to the reduced stiffness of the material. FEA obtains the key parameters affecting the pore layout. The digital image correlation (DIC) experiment verifies the design strategy. The results show that, compared to the solid substrate, the porous partition substrate strategy can significantly reduce the maximum normal strain of the substrate around the island, thus effectively reducing the risk of structural interface failure. [ABSTRACT FROM AUTHOR]

Existing studies on wrinkling, an instability phenomenon commonly observed on electro-active polymers (EAP), have largely ignored the unequal-biaxial taut states, focusing instead on the equal-biaxial deformations of such a material class. EAP-based soft actuators, primarily used in soft robotics, frequently exhibit a variety of instabilities, which may adversely affect their functioning and trigger device failure. Conversely, wrinkles can be utilized proactively in specific applications that necessitate an intentional transformation in surface morphology along with functional particle reinforcement on EAP composites. The dielectric elastomer is a promising EAP material class for the same, often filled with functional particles to improve its electromechanical performance. This paper theoretically develops a continuum physics-based unequal-biaxial deformation model incorporating the classical tension field theory to predict the thresholds on the taut domains in the plane of principal stretches. The model solution ties an unanswered ideal remark on the deviations of taut states with the biaxiality ratio of unequal-biaxially deformed wrinkle appearance in EAP composites. The proposed model solution may aid in designing next-generation soft robotic systems by offering guidelines for the wrinkling control of EAP composites. [ABSTRACT FROM AUTHOR]

We study the flexoelectric effect induced in an infinite strip of a dielectric material, due to an applied shear deformation at the upper surface, while the lower surface is fixed. The model incorporates dynamic spontaneous polarization, flexocoupling deformation, and microinertia effects to evaluate these effects combined. The variation of the Hamiltonian functional in the medium, and of the external forces yields the governing equations and the boundary conditions. There are many types of applied boundary conditions besides the initial conditions, where the initial conditions are imposed due to the dynamics of many effects in the mathematical modelling formulation. In addition to that, the boundary conditions are divided into two groups, where the first group contains mechanical boundary conditions such as traction boundary conditions and displacement boundary conditions for the classical treatment as in the theory of elasticity while for the strain gradient theory of elasticity, conditions for higher-order traction vector should be imposed and cannot be neglected. The proposed technique depends on applying Laplace’s transform to the field equations to obtain the characteristic equation, the roots of which are expressed in terms of the s;-transform parameter and other parameters related to the elastic and electric properties of the material. Those roots which produce a bounded solution are then approximated using Taylor’s expansion, then the boundary conditions are applied to complete the solution. This technique enables to obtain the solution in terms of simple analytical functions that are easily inverted from the s-domain to the time domain. This technique is applied to a simple shear deformation problem to study the dynamical flexoelectric effect in dielectric materials due to shear displacement and external electric potential. A suitable material, such as Strontium Titanate material, SrTiO3, is used for numerical simulation, and the results are analyzed, discussed, and represented graphically. [ABSTRACT FROM AUTHOR]

In this paper, we study the long-time dynamics of a pullback exponential attractors for non-autonomous one dimensional system in nonlocal Mindlin's strain gradient porous elastic theory recently developed by Aouadi [Well-posedness, lack of analyticity and exponential stability in nonlocal Mindlin's strain gradient porous elasticity. Z Angew Math Phys. 2022;73:111]. In this theory, the second gradient of deformation and the second gradient of volume fraction field are added to the set of independent constitutive variables by taking into account the nonlocal length scale parameters effect. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of global solution. Then we establish a Lipschitz stability result. We also prove the existence of pullback exponential attractors which as a consequence, implies the existence of a minimal pullback attractor with finite fractal dimension. Finally, we prove the upper-semicontinuity of minimal pullback attractors with respect to the perturbations parameter in natural energy space. [ABSTRACT FROM AUTHOR]

This article discusses a method for estimating residual stresses in metal samples produced by additive manufacturing, specifically focusing on steel cylindrical bars produced by laser powder bed fusion (LPBF). The method involves making a partial longitudinal cut in the bar using electrical discharge machining (EDM) and measuring the resulting deflection to assess the contribution of residual stresses. The study combines experimental analysis with numerical simulation using finite element modeling (FEM). The proposed method allows for the estimation of residual stresses in the laboratory without the need for special equipment. The article also provides a list of references that cover various topics related to residual stresses and mechanical properties of additively manufactured stainless steel, which can be useful for further research. [Extracted from the article]

The parameterization of machine learning potentials (MLP) for precise characterization of the interaction between carbon atoms in graphite and diamond phases is described. The training set consisted of various allotropic forms of carbon and their compounds. The MLPs are trained using forces, energies, and stress tensors obtained from ab initio simulations. It is shown that the MLPs can accurately reproduce elastic properties and structural parameters of carbon phases. However, the MLPs also predict some unphysical behavior due to the training set limitations and the lack of long-range interactions in the MLPs. In spite of these limitations, MLPs are a promising tool for the accurate characterization of diamond nucleation in graphite. [ABSTRACT FROM AUTHOR]

We develop randomized neural networks (RNNs) with Petrov–Galerkin (RNN-PG) methods to solve linear elasticity and Navier–Stokes equations. RNN-PGs use the Petrov–Galerkin variational framework, where the solution is approximated by randomized neural networks and the test functions are piecewise polynomials. Unlike conventional neural networks, the parameters of the hidden layers of randomized neural networks are fixed randomly while the parameters of the output layer are determined by the least-squares method, which can effectively approximate the solution. We also develop mixed RNN-PG (M-RNN-PG) methods for linear elasticity problems to ensure symmetry of the stress tensor and avoid locking effects. For the Stokes problem, we present various M-RNN-PG methods that enforce the divergence-free constraint by different techniques. For the Navier–Stokes equations, we propose a space-time M-RNN-PG that uses Picard or Newton iteration to deal with the nonlinear term. Using several examples, we compare RNN-PG methods with the finite-element method, the mixed discontinuous Galerkin method, and the physics-informed neural network. The numerical results demonstrate that RNN-PG methods achieve higher accuracy and efficiency. [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]

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The apparatus of holomorphic functions of many complex variables is applied to solving spatial boundary value problems of the linear theory of elasticity. The construction of the solution of the boundary value problem is based on the representation of the displacement vector in the form of J. Dougall through spatial harmonic potentials. The transition from spatial harmonic potentials to holomorphic functions of two complex variables z1, z2 was carried out and a boundary value problem for the above functions was formulated. By presenting these holomorphic functions in the form of homogeneous polynomials of order k relative to complex variables z1, z2, solutions were constructed by the method of development of the complex tensor of stresses by basic states. The application of this technique is illustrated in the examples of marginal problems, the real components of solutions that correspond to the solutions of Grashof's problem for an elastic beam. Imaginary components of exact analytical solutions are obtained and corresponding structures of external load vectors for elastic beams of complex cross-section are constructed. [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]

Most shell or beam models of anisotropic tubes under bending have no validity for thick-walled structures. As a result, the need to develop three-dimensional formulations which allow a change in the stress, strain and displacement distributions across the radial component arises. Basic formulations on three-dimensional anisotropic elasticity were made either stress- or displacement-based by Lekhnitskii or Stroh on plates. Lekhnitskii also was the first to expand these analytical formulations to tubes under various loading conditions. This paper presents a review of the stress and strain analysis of tube models using three-dimensional anisotropic elasticity. The focus lies on layered structures, like fiber-reinforced plastics, under various bending loads, although the basic formulations and models regarding axisymmetric loads are briefly discussed. One section is also dedicated to the determination of an equivalent bending stiffness of tubes. [ABSTRACT FROM AUTHOR]

In this work, closed-form expressions of shear correction factor (SCF) have been derived for beams with functionally graded material (FGM), through variational asymptotic method (VAM). An energy equivalence approach has been adopted between VAM and Timoshenko model, for estimating the SCF. A planar FGM beam has been considered and the calculation for SCF has been carried out. The formulation has been derived in a functional form that permits solutions for a large class of gradation models of FGM. In the limiting case when the material becomes homogeneous the estimated SCF matches exactly with that of the literature, thus validating the solution. A detailed discussion has been carried out on the results and conclusions have been drawn. [ABSTRACT FROM AUTHOR]

We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly valid in the incompressible limit. A posteriori estimates are derived for both the compressible and incompressible cases. The results are verified by numerical examples. [ABSTRACT FROM AUTHOR]

This work deals with the modeling of solid continua undergoing incompatible deformations due to the presence of microscopic defects like dislocations. Our approach relies on a geometrical description of the medium by the strain tensor and the representation of internal efforts using zeroth- and second-order strain gradients in an infinitesimal framework. At the same time, energetic arguments allow to monitor the corresponding moduli. We provide mathematical and numerical results to support these ideas in the framework of isotropic constitutive laws. [ABSTRACT FROM AUTHOR]

In this work, we report on a comparative study of the structural, optical, and elastic properties of SrTiSe3 and SrZrSe3 compounds using the DFT method. The lattice constants of the compounds are calculated using the GGA-PBE approximation and the hybrid functional Heyd, Scuseria, and Ernzerhof (HSE). The properties of the SrTiSe3 and SrZrSe3 materials in relation to electronic composition, elastic constants, and optical characteristics are deduced and analyzed. Both compounds display magnetic behavior, according to electronic calculations. SrTiSe3 shows metallic behavior, as the calculated bandgap value is zero. SrZrSe3, on the other hand, has a bandgap of 0.347 eV, which demonstrates its semiconducting nature. We have demonstrated that the plasma frequency of SrTiSe3 is around 1.77836. Using density functional theory, we report on the electronic characteristics of the compounds under mechanical stress. For SrZrSe3, the gap energy values rise with compressive stress and decrease with increasing tensile stress to zero. In addition, the study includes the extinction coefficient, optical conductivity, dielectric tensor, electron energy loss, and refractive index. [ABSTRACT FROM AUTHOR]

This work analyses a high-order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG solution can be computed. The introduction of the rotation as one of the unknowns allows us to use the gradient of the displacements to obtain an explicit representation of the boundary data in the computational domain. The boundary data is transferred from the true boundary to the computational boundary by line integrals, where the integrand depends on the Cauchy stress tensor and the rotation. Under closeness assumptions between the computational and true boundaries, the scheme is shown to be well-posed and optimal error estimates are provided even in the nearly incompressible case. Numerical experiments in two dimensions are presented. [ABSTRACT FROM AUTHOR]

The thermal and mechanical properties of materials show differences depending on the temperature change, which necessitates consideration of the dependence of the properties of these materials on this change in the analysis of thermal stress and deformation of the material. As a result, in the present work, a mathematical framework for thermal conductivity was formulated to describe the behavior of non-simple elastic materials whose properties depend on temperature changes. This derived model includes generalized fractional differential operators with non-singular kernels and two-stage delay operators. The fractional derivative operators under consideration include both the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative, in addition to the traditional fractional operator. Not only that, but the system of governing equations includes the concept of two temperatures. Based on the proposed model, the thermodynamic response of an unlimited, constrained thermoelastic medium subjected to laser pulses was considered. It was taken into account that the thermal elastic properties of the medium, such as the conductivity coefficient and specific heat, depend on the temperature. The governing equations of the problem were formulated and then solved using the Laplace transform method, followed by the numerical inverse. By presenting the numerical results in graphical form, a detailed analysis and discussion of the effects of fractional factors and the dependence of properties on temperature are presented. The results indicate that the fractional order coefficient, discrepancy index, and temperature-dependent properties significantly affect the behavior fluctuations of all physical domains under consideration. [ABSTRACT FROM AUTHOR]

Boron carbide plays a crucial role in various extreme environment applications, including thermal barrier coatings, aerospace applications, and neutron absorbers, because of its high thermal and chemical stability. In this study, the temperature-dependent elastic stiffness constants, thermal expansion coefficient, Helmholtz free energy, entropy, and heat capacity at a constant volume ( C v ) of rhombohedral B4C have been predicted using a quasi-harmonic approach. A combination of volume-dependent first-principles calculations (density functional theory) and first-principles phonon calculations in the supercell framework has been performed. Good agreement between the elastic constants and structural parameters from static calculations is observed. The calculated thermodynamic properties from phonon calculations show trends that align with the literature. As the temperature rises, the predicted free energy follows a decreasing trend, while entropy and C v follow increasing trends with temperature. Comparisons between the predicted room temperature thermal expansion coefficient (TEC) ( 7.54 × 10 − 6 K−1) and bulk modulus (228 GPa) from the quasi-harmonic approach and literature results from experiments and models are performed, revealing that the calculated TEC and bulk modulus fall within the established range from the limited set of data from the literature (TEC = 5.73–9.50 × 10 − 6 K−1, B = 221–246 GPa). Temperature-dependent C i j s are predicted, enabling stress analysis at elevated temperatures. Overall, the outcomes of this study can be used when performing mechanical and thermal stress analysis (e.g., space shielding applications) and optimizing the design of boron carbide materials for elevated temperature applications. [ABSTRACT FROM AUTHOR]