Anisotropic Elastic Materials Research Articles

Solid Wood Modification toward Anisotropic Elastic and Insulative Foam-Like Materials.

The methods used to date to produce compressible wood foam by top-down approaches generally involve the removal of lignin and hemicelluloses. Herein, we introduce a route to convert solid wood into a super elastic and insulative foam-like material. The process uses sequential oxidation and reduction with partial removal of lignin but high hemicellulose retention (process yield of 72.8%), revealing fibril nanostructures from the wood's cell walls. The elasticity of the material is shown to result from a lamellar structure, which provides reversible shape recovery along the transverse direction at compression strains of up to 60% with no significant axial deformation. The compressibility is readily modulated by the oxidation degree, which changes the crystallinity and mobility of the solid phase around the lumina. The performance of the highly resilient foam-like material is also ascribed to the amorphization of cellulosic fibrils, confirmed by experimental and computational (molecular dynamics) methods that highlight the role of secondary interactions. The foam-like wood is optionally hydrophobized by chemical vapor deposition of short-chained organosilanes, which also provides flame retardancy. Overall, we introduce a foam-like material derived from wood based on multifunctional nanostructures (anisotropically compressible, thermally insulative, hydrophobic, and flame retardant) that are relevant to cushioning, protection, and packaging.

Adhesive contact between two-dimensional anisotropic elastic bodies

Adhesion plays a vital role in the design of smart and intelligent high-tech devices such as modern optical, microelectromechanical, and biomedical systems. However, in the literature, adhesive contact is mostly considered for contact of rigid substrates and transversely isotropic and isotropic elastic materials. The composite materials are increasingly used in the mart and intelligent high-tech devices. Since the composite materials are generally anisotropic and contact bodies are all deformable, it is more practical to consider the adhesive contact of two anisotropic elastic materials. In this paper, an adhesive contact model of anisotropic elastic bodies is established, and the closed-form solutions for two-dimensional adhesive contact of two anisotropic elastic bodies are derived. The full-field solutions and the relation for the contact region and applied force are developed using the Stroh complex variable formalism, the analytical continuation method, and concepts of the JKR adhesive model. We will show that the frictionless contact of two anisotropic elastic materials is just a special case of the present contact problem, and its solutions can be obtained by setting the work of adhesion equal to zero. In addition, we also show that our present solutions are valid for the problems of indentation by a rigid punch on an elastic half-space through a proper placement of the contact radius and the corresponding material constant. Numerical results are provided to demonstrate the accuracy, applicability, and versatility of the developed solutions.

Effective Macroscopic Thermomechanical Characterization of Multilayer Circuit Laminates for Advanced Electronic Packaging

Laminate substrates in advanced IC packages serve as not only the principal heat dissipation pathway but also the critical component governing the thermomechanical performance of advanced packaging technologies. A solid and profound grasp of their thermomechanical properties is of crucial importance to better understand IC packages’ thermomechanical behavior. This study attempts to introduce a subregion homogenization modeling framework for effectively and efficiently modeling and characterizing the equivalent thermomechanical behavior of large-scale and high-density laminate substrates comprising the non-uniform distribution and non-unidirectional orientation of tiny metal traces. This framework incorporates subregion modeling, trace mapping and modeling, and finite element analysis (FEA)-based effective modeling. In addition, the laminates are macroscopically described as elastic orthotropic or elastic anisotropic material. This framework is first validated with simple uniaxial tensile and thermomechanical test simulations, and the calculation results associated with these two effective material models are compared with each other, as well as with those of two existing mixture models, and direct the detailed FEA. This framework is further tested on the prediction of the process-induced warpage of a flip chip chip-scale package, and the results are compared against the measurement data and the results of the whole-domain modeling-based effective approach and two existing mixture models.

Phase-field study of the solutes-interstitial loops interaction in Fe–Cr alloys

Interstitial dislocation loops are typically formed in post-irradiated materials, such as Ferritic-Martensitic Fe–Cr alloys. These loops demonstrate solute segregation along their perimeters, effectively pinning the dislocation climb and resulting in high-density, small-sized loops that cause embrittlement. Phase-field simulations were conducted to investigate the behavior of Cr segregation in the stress field of a<100> type and various a/2<111> type interstitial dislocation loops in post-irradiated Fe–10Cr alloy. The study considers the long-range elastic interaction of solute Cr within the stress field of dislocation loops in a cubic elastic anisotropic material. The findings reveal a nonuniform stress distribution along the loop's perimeter depending on the included angle of habit plane normal n and Burgers vector b; the nonuniformity becomes more pronounced as the Burgers vector deviates from the normal direction. Furthermore, this nonuniform stress induces Cr segregation within regions experiencing tensile stress and Cr depletion in compression stress regions. Furthermore, a comprehensive analytical solution has been developed to characterize the diverse stress fields and solute segregation induced by interstitial dislocation loops with varying habit planes and Burgers vectors. The proposed analytical model effectively depicts the stress distribution of various dislocation loops, resulting in a Cr segregation profile that closely approximates those obtained through phase-field simulations. A thorough analysis of solute segregation mechanisms also elucidates the dispersed fine-scale nature and high density observed in experimental investigations of dislocation loops.

INFLUENCE OF HIGH-ORDER TERMS IN THE SOLUTION GENERALIZING THE APPROACH OF M. WILLIAMS, TAKING INTO ACCOUNT THE ANISOTROPY OF THE MATERIAL

The research is devoted to the study of the stress field at the crack tip in an anisotropic material with three mutually orthogonal axes of symmetry of the fourth order (with cubic symmetry). A plane case is considered when one of the axes of symmetry is orthogonal to the cracked plate, and the remaining two axes lie in the plane of the plate. The paper presents an asymptotic analysis of the contribution of higher approximations in the generalized asymptotic decomposition of mechanical fields near the crack tip in a linearly elastic anisotropic material with cubic symmetry of its elastic properties. In the article, based on the obtained solution of M. Nejati and co-authors for an infinite anisotropic plate with a central crack, circumferential apportionments of the stress tensor components at the crack tip at various distances fromthe crack tip are constructed, which makes it possible to estimate the contribution of non-singular (regular)terms to the general asymptotic representation of mechanical fields generated by an acute crack. In the work of M. Nejati, the contribution of exclusively T-stresses is analyzed, then, as shown in this work, the terms following the T-stress play a significant role in describing the fields induced by the crack. A comparison of the angular distributions of the stress tensor components constructed at different distances from the crack tip indicates that with the increase of distances from the crack tip, it is required to preserve in asymptotic series representing stresses, displacements and strains near the tip of the crack, the terms of high order of smallness. The preservation of the terms of high order of smallness can be used to expand the domain in which the asymptotic solution in the series is valid.

Generalized dynamic domain-independent interaction integral in the transient fracture investigation of magneto-electro-elastic composites

The domain-independent interaction integral (DII-integral) is a powerful tool for dealing with crack issues of nonhomogeneous materials, due to its feature of being independent of the scale of integration domain, regardless of the nonhomogeneous properties and complex material interfaces. As an important part of the interaction integral (I-integral), the auxiliary field conditions required to establish the dynamic DII-integral have not been clearly clarified so far. For the first time, this work rigorously proves and gives the requirements of the auxiliary fields for building the dynamic DII-integral in anisotropic linear elastic, piezoelectric (PE), piezomagnetic (PM) and MEE materials, respectively, and a theoretical framework is derived for designing the dynamic DII-integral for new functional materials in the future. This proof guarantees the successful utilization of DII-integral to investigate the transient response in cracked composites without employing homogenized material parameters, while considering internal microstructure and complex interfaces. Using the extended finite element method (XFEM) as a pre-processing technique, the accuracy of the DII-integral is verified by comparing available references. Then, the domain-independence is confirmed with multiple integration domains, especially for those containing interfaces. Finally, the arrangements of PE/PM layers, locations and distributions of PE/PM particles affecting dynamic IFs are systematically investigated. Simultaneously, illustrations of elastic wave in cracked MEE composites are depicted to better understand the dynamic fracture response.

An analytical solution for dynamics of cyclic thermomechanically loaded multi-layered filament-wound composite pipes in hygrothermal environment

In this study, an analytical solution is provided to present the stress and strain analyses of the multi-layered filament-wound composite (MLF-WC) pipes subjected to the cyclic internal pressure and cyclic thermal loading in hygrothermal environment. The MLF-WC pipe is made of anisotropic, homogeneous and linear elastic materials. It is assumed that the material properties are temperature-independent. Also, applied cyclic loadings are independent of the tangential and axial coordinates. Using the three-dimensional anisotropic elasticity, time-dependent analytical expressions are provided for the stresses, strains and displacements. The accuracy of present analytical approach and numerical results is verified by comparison with those given in literature. It is remarked that the developed analytical solution can be used for the dynamic analysis of functionally graded pipes and pressure vessels under the cyclic loadings. Moreover, through the numerical results, it is found that stacking sequence has a considerable effect on the distributions of shear strain and stress. Furthermore, for the MLF-WC pipe under simultaneous cyclic internal pressure and cyclic thermal loading, the mean amplitudes of the cyclic loadings have a significant effect on the sign of axial strain.

Similarity laws of geometric and material distortion for anisotropic elastic plate subjected to impact loads

Although the similarity laws were widely used in impact fields, the scaling relations of anisotropic elastic structures often were broken when the geometric distortion (not equal scaling in different spatial directions) and the material distortion (different materials used for scaled model and full-size prototype) were considered. To overcome the difficulty of geometric and material distortion, a directional framework of similarity laws, termed as oriented-density-length-velocity (ODLV) system, is proposed for the anisotropic elastic structure under impact loads. Different from previous similarity law systems using scalar dimensional analysis, the directional similarity law framework mainly considers spatial anisotropy for structural geometry and material parameters. Based on the oriented dimensional analysis and the orthotropic Hooke's law, directional dimensionless numbers and directional scaling relations with geometric power properties for the elastic modulus and the Poisson's ratio are presented systematically. By selecting the dominant material parameters controlling similarity, three important scaling techniques with correction of geometric width and thickness are proposed to compensate for the difficulty of distortion. A clamped square plate with different anisotropic and isotropic elastic materials subjected to dynamic pressure pulse is verified numerically and discussed in detail. The results show that the thin square plate prototype must be scaled to be the thinner/thicker rectangular plate, and the components of displacement, stress and strain of the scaled model presented consistency with the corresponding prototype in both spatial and temporal fields.

Calculation of Mechanical Properties, Electronic Properties, and Thermodynamic Properties of AuAl Crystal: First‐Principles Calculation

AbstractThe structural stability, elastic properties, electronic properties, and thermodynamic property (Debye temperature) of AuAl intermetallic compound (IMC) are systematically investigated using first‐principles calculations based on density functional theory. The elastic constants, elastic moduli (including bulk modulus, shear modulus, Young's modulus, and Poisson's ratio) and Vickers hardness, the density of states, and Debye temperature of AuAl under hydrostatic pressure are calculated. The calculation results show that AuAl is an elastic anisotropic material with low rigidity and high toughness under zero pressure. Under hydrostatic pressure, the anisotropy index decreases while the hardness and Debye temperature increase. The research in this paper provides a theoretical basis for the study of the properties of bonding gold wire intermetallics.

Homogenization of an Anisotropic Elastic Material Reinforced by a Small Volume Fraction of Very Stiff Anisotropic Fibers. Non Local Effects. Bending Effects. Torsional Effects

Homogenization of an Anisotropic Elastic Material Reinforced by a Small Volume Fraction of Very Stiff Anisotropic Fibers. Non Local Effects. Bending Effects. Torsional Effects

A theoretical framework for mechanics of diaphragm

A theoretical framework is developed for mechanics of the diaphragm. The diaphragm is modeled as an anisotropic elastic material surface with activation functionality. A constitutive function is formulated that relates the stresses in the diaphragm to the surface deformation gradient, the anisotropy vector, and the muscle activation parameter. The equilibrium equations for the diaphragm are derived to determine the deformed shape of the diaphragm in the process of respiration with the associated transdiaphragmatic pressures. A numerical solution is presented, that demonstrates the capability of the model to recover the experimental observations and to predict the shape and stresses of the diaphragm.

Crack propagation induced by a plane stress wave in a general anisotropic elastic material

Abstract The stress intensity factors of a semi-infinite crack propagating with constant speed in an anisotropic elastic solid under a uniform stress wave loading are considered. The crack is assumed to start propagating at some arbitrary time after an obliquely incident plane stress wave strikes the crack tip. It is shown that the stress intensity factor of the propagating crack has the form of the product of a universal matrix function of the crack speed and an equivalent stationary crack stress intensity factor of t*, which is the time that would have elapsed since the incident wavestruck the crack tip if the crack tip had been always at its instantaneous position. The present result is a generalization of that obtained by Freund for isotropic materials.

A powerful matrix formalism for stress singularities in anisotropic multi-material corners. Homogeneous (orthogonal) boundary and interface conditions

A computational code based on a semianalytic procedure for the determination of the characteristic exponents and the singular stress and displacement fields in multi-material corners is developed. Linear elastic anisotropic materials under generalized plane strain state are considered. This code is a universal computational tool able to analyze both open and closed (periodic) corners, composed of one or multiple materials with isotropic, transversely isotropic or orthotropic constitutive laws, covering both mathematically non-degenerate and degenerate materials in the framework of Stroh formalism. In multi-material corners, material junctions with perfectly bonded or frictionless sliding interfaces can be studied. The considered homogeneous boundary conditions cover stress free and fixed faces, or faces with some restricted or allowed direction of displacements, defined either in the reference frame aligned with the cylindrical coordinate system or in an inclined reference frame. The code is developed in MATLAB and it is based on the Stroh matrix formalism for anisotropic elasticity, the concept of transfer matrix for single material wedges, and on the matrix formalism for homogeneous (orthogonal) boundary conditions. The comparison of the characteristic exponents obtained by the present code and by the solution of closed-form eigenequations available in the literature, has a two-fold objective, first to exhaustively check the general computational implementation of the matrix formalism presented, and second to check the closed-form expressions of eigenequations for relevant specific cases published in the literature.

深層学習を用いた異方性弾性体中の欠陥形状再構成

In this study, the shape reconstruction method of a cavity is developed for 2-D pure antiplane anisotropic elastodynamics. Elastic wave scattering by a cavity is implemented by using the convolution quadrature time-domain boundary element method. Scattered waves obtained at receiver points are prepared and utilized for the deep learning. The created deep learning model estimates position and size of a cavity in 2-D pure antiplane anisotropic solids. Numerical example shows that deep learning can be useful for inverse analysis of a defect in anisotropic elastic materials.

Micro-cantilever beam experiments and modeling in porous polycrystalline UO2

Understanding the impact of microstructure on the thermo-mechanical behavior of oxide nuclear fuels is vital to predicting their performance through multiscale models . Evaluating the mechanical properties at the sub-grain length scale is key to developing these multiscale models. In this work, 3D finite element (FE) models were constructed to simulate the micrometer-scale bending of micro-cantilever beams fabricated using porous polycrystalline uranium dioxide (UO 2 ) and tested at room temperature. The results showed that the porosity and elastic anisotropy of individual grains can play a significant role in determining the effective mechanical properties of the material deduced from the tests. Specifically, the porosity had a non-negligible effect, given that the pore size was of the same order of magnitude as the dimensions of the micro-beams. Correlations between load-deflection data, pore location, and elastic properties (effective Young's modulus) were investigated using UO 2 micro-beam FE models, where pore clusters were included and placed at different locations along the length of the beam. Results indicated that the presence of pore clusters near the substrate, i.e., the clamp of the micro-cantilever beam, has the strongest effect on the load-deflection behavior, with the porosity leading to a reduction of stiffness that is the largest for any location of the pore clusters. Furthermore, it was also found that pore clusters located towards the middle of the span and close to the end of the beam have a comparatively small effect on the load-deflection behavior. Therefore, it is concluded that accurate estimates of Young's modulus can be obtained from micro-cantilever experiments after accounting for porosity on the one third of the beam length close to the clamp. This, in turn, provides an avenue to improve microscale experiments and their analysis in porous, anisotropic elastic materials.

Transient thermal stress analysis of temperature-dependent anisotropic viscoelastic solids

Consider the transient thermal stress analysis for a material that is anisotropic (direction-dependent), viscoelastic (time-dependent), and thermorheologically simple (temperature-dependent). To solve this problem, three fundamental theories are employed: (1) complex variable Stroh formalism for anisotropic elasticity, (2) elastic-viscoelastic correspondence principle (EVCP) or time-stepping method (TSM) for viscoelasticity, and (3) time-temperature superposition principle (TTSP) for thermorheologically simple materials. By using the Stroh formalism, all different kinds of anisotropic elastic materials can be analyzed by using the same formulae. With EVCP and TSM, the problem of viscoelasticity can be solved via its corresponding problem of elasticity. By TTSP, the temperature-dependent constitutive relation can be expressed by using the reference temperature and the reduced time defined through shift factor. Thus, through the combined use of these theories, the complicated problems of transient anisotropic thermo-viscoelasticity can be solved by using the available solution tool for anisotropic elasticity such as the boundary element method (BEM). Based upon this concept, two novel BEMs are developed for the transient thermal stress analysis of temperature-dependent anisotropic viscoelastic solids. One is BEM-EVCP, and the other is BEM-TSM. The final results show that both of them can provide accurate solutions, and BEM-TSM is much more efficient than BEM-EVCP.

Многокритериальная оптимизация композитного крыла беспилотного летательного аппарата

The article considers the results of multicriteria optimization of the unmanned aircraft composite wing. Minimum deflection, mass and normal stresses acting along the reinforcement directions are taken as optimization criteria. The thicknesses of the load-bearing frame elements and wing skin elements were selected as optimization parameters for three types of composites: carbon fiber reinforced plastic (CFRP) based on unidirectional carbon layers, CFRP based on carbon fabric layers, and fiberglass laminate based on E-glass fiberglass. A checking calculation of the optimal composite wing stability was performed using a geometrically nonlinear model. The calculation of the stress-strain state of the wing was performed using an anisotropic linear elastic material model. Calculations were carried out using finite element software packages ANSYS and FEMAP.

Mixed Mode Crack Propagation in Iliac Bone

Abstract Bone is a complex material that can be regarded as an anisotropic elastic composite material. The problem of crack propagation in human bone is analyzed by using a generalization of the maximum tensile stress criterion (MTS). The results concern the critical stress for crack propagation and the direction of the crack path in Iliac bone.

Influence of residual stress on the free vibrations of an elastic solid; application to resonant ultrasound spectroscopy (RUS)

Resonant ultrasound spectroscopy (RUS) is a standard technique for experimentally measuring the elastic constants of anisotropic elastic materials. Traditionally, the influence of internal or residual stresses on the measurement of elastic constants is not taken into consideration. However, it is well-known that residual stress can impart a small variation in the phase velocity of ultrasonic bulk waves, which is known as the acoustoelastic effect. Thus, it is plausible that residual stress will influence the resonances of samples measured during RUS. In this presentation, the elastodynamic theory for describing free vibrations is reformulated by using a stress-dependent constitutive relationship. The model culminates in an eigenvalue problem with a stiffness matrix being dependent on the spatially varying residual stress field within the domain of the sample. The model is evaluated by considering a realistic residual stress distribution. Results show the degree at which frequencies of resonance depend on the residual stress. While accounting for residual stress is expected to improve the estimates of elastic constants, there is also potential to use RUS as a tool to assess and characterize the residual stress present in samples.

Computational investigation for endocytosis of CoVID-19 virus SARS-CoV-2 in cell membrane

CoVID-19 virus SARS-CoV-2 follows the endocytosis process to enter inside a cell to infect it. It is important to study the endocytosis of SARS-CoV-2 in cell membrane to prevent the pandemic of CoVID-19. In this paper we develop a finite element based computational model for endocytosis of SARS-CoV-2 in cell membrane and determine curvature generation on it during the process. The virus SARS-CoV-2 is modeled as a rigid spherical particle and cell membrane as an anisotropic elastic material, while its fluidic nature due to lipid exchange with infinite reservoir is preserved using suitable conditions. With the help of a contact pair created between the virus particle and cell membrane, endocytosis process is computationally studied and the curvature of membrane is evaluated as the time progresses during the endocytosis process. At the tip of the virus particle and half-radius distance from it, the membrane follows the curvature of virus very quickly. However, it takes more time for the membrane point located at a distance equal to the radius of the virus particle. This is compensated by the cytoplasmic peripheral proteins binding onto the inside surface of the cell membrane. The role of cytoplasmic peripheral BAR proteins is investigated by using a linear curvature-coupling model with protein concentrations. It is observed that F-BAR protein is more sensitive to the curvature of virus particle in comparison to the other BAR proteins. The sensitiveness deteriorates as the curvature is increased.