Effects Of Material Anisotropy Research Articles

The impact of initial fabric anisotropy on cyclic liquefaction behavior with polygonal particles using the discrete element method (DEM)

Liquefaction is one of the most significant phenomena that can occur in soil during an earthquake. The destructive effects of this phenomenon on earth structures have captured the attention of many geotechnical engineers. Additionally, the gradual increase in pore water pressure during the cyclic loading induced by the propagation of earthquake waves, known as cyclic liquefaction, is a crucial factor that might lead to the complete loss of shear strength in soils. A better understanding of cyclic liquefaction is essential for improving earthquake hazard analysis and mitigating structural damage. Factors influencing liquefaction behavior include particle size, particle grading, and soil fabric. By “soil fabric,” we refer to the arrangement and positioning of particles with each other, particle shape, and the shape of voids among particles. This research aims to focus on the effects of fabric anisotropy on cyclic liquefaction of granular soils with angular particles. To carry out this investigation, the discrete element method has been employed. In the discrete element method, the geometry of particles and, generally, the soil fabric can be considered. In this research, specimens with varying particle orientation angles were produced and subjected to cyclic loading tests under undrained conditions. By examining the stress paths of specimens during cyclic loading, it is observed that the initial fabric and inherent anisotropy significantly influence the behavior of the specimens. Inherent anisotropy leads to varying numbers of cycles required for the initial liquefaction of each specimen. Furthermore, it is observed that as the particle orientation angle increases, the localization of axial strains shifts from tensile to compressive directions. The effect of inherent anisotropy plays a substantial role in the initial liquefaction (ru = 1). If the liquefaction of specimens is of interest at lower values of ru, the effect of inherent anisotropy can be disregarded.

Improved modeling of anisotropic effects on seismic waves in layered transversely isotropic half-spaces: Implications for velocity profile inversion challenges

In this paper, we first derive the dynamic solution in a transversely isotropic (TI) elastic and layered half-space, induced by a time-harmonic vertical load on its surface. The solution is obtained via the efficient and unconditionally stable dual variable and position (DVP) matrix method along with the fast Fourier-Bessel series (FBS) expansion approach. In order to study the effect of material anisotropy, the degree of anisotropy, namely the ratio of the horizontal Young's modulus over vertical Young's modulus, is introduced as the key parameter, with a very reasonable assumption on other involved elastic constants in the layered TI half-space. This enables us to investigate the effect of material anisotropy on the wave Green's functions, dispersion curves, ellipticity, and polarity. By comparing with the effect of Poisson's ratio in the corresponding layered isotropic (ISO) half-space, we observe that nearly all the wave features with varying degrees of anisotropy in the TI layered half-space are similar to those with varying Poisson's ratio in the corresponding ISO half-space. This indicates the challenge or non-uniqueness in the inversion of TI velocity profiles using vertical surface loading only.

Influence of material anisotropy on the mechanics of surface damage

The problem of multiple cracks originating at free surface (surface damage) in an anisotropic material is considered. We focus on the effect of material anisotropy on the mechanics of crack interactions – in particular, on the suppressing effect of interactions on crack nucleation and growth under the tensile loading (stress shielding). Importantly, this effect may change to the opposite one of enhancement, under the shear loading. These effects strongly depend on the material anisotropy. Calculations were performed for the orthotropic materials and the effect of anisotropy was examined by case studies of specific configurations that included comparison with the case of the isotropic material.

Energy harvesting using magnetostrictive materials: Effects of material anisotropy and stress multiaxiality

Low-frequency vibrations are common as background noise in urban and industrial environments. They originate from natural or artificial sources: road vehicles, industrial machinery, wind, etc., and constitute a ubiquitous energy source. In the framework of energy harvesting, magnetostrictive materials are an attractive alternative solution to the brittleness and geometrical limitations of piezoelectric materials. While numerous previous works dealt with uniaxial stress on selected materials, the exploration of the effects of multiaxial loadings and material anisotropy has not yet been investigated as a way to improve the performance of low-frequency vibration energy harvesting systems. In this work, we investigated the capability of grain-oriented electrical steel in an energy-harvesting context. This material has been selected as a model material, notably as it is abundant and cost-effective. It shows limited magnetostriction but significant elastic, magnetic, and magnetostrictive anisotropy. We combined experimental and predictive simulation results to discuss the possibility of increasing the levels of harvested energy by playing with the orientation of magnetic and mechanical stimuli. Various orientations of magnetic field and mechanical stress were considered with regard to the rolling direction of the material. Unexpectedly high energy density amounts, up to 10 mJ·cm−3, were obtained, competing with giant magnetostrictive materials like Terfenol-D or Galfenol.

Numerical evaluation of spinal reconstruction using a 3D printed vertebral body replacement implant: effects of material anisotropy.

Artificial vertebral implants have been widely used for functional reconstruction of vertebral defects caused by tumors or trauma. However, the evaluation of their biomechanical properties often neglects the influence of material anisotropy derived from the host bone and implant's microstructures. Hence, this study aims to investigate the effect of material anisotropy on the safety and stability of vertebral reconstruction. Two finite element models were developed to reflect the difference of material properties between linear elastic isotropy and nonlinear anisotropy. Their biomechanical evaluation was carried out under different load conditions including flexion, extension, lateral bending and axial rotation. These performances of two models with respect to safety and stability were analyzed and compared quantitatively based on the predicted von Mises stress, displacement and effective strain. The maximum von Mises stress of each component in both models was lower than the yield strength of respective material, while the predicted results of nonlinear anisotropic model were generally below to those of the linear elastic isotropic model. Furthermore, the maximum von Mises stress of natural vertebra and reconstructed system was decreased by 2-37MPa and 20-61MPa, respectively. The maximum reductions for the translation displacement of the artificial vertebral body implant and motion range of whole model were reached to 0.26mm and 0.77°. The percentage of effective strain elements on the superior and inferior endplates adjacent to implant was diminished by up to 19.7% and 23.1%, respectively. After comprehensive comparison, these results indicated that the finite element model with the assumption of linear elastic isotropy may underestimate the safety of the reconstruction system, while misdiagnose higher stability by overestimating the range of motion and bone growth capability.

Linking sand permeability anisotropy to fabric anisotropy via numerical simulation

Characterisation of the permeability of soils is of practical importance and, for cohesionless or granular soils, it can be predicted from the void ratio and the particle size distribution (PSD). However, the effect of fabric anisotropy on the permeability is rarely discussed. Restricting consideration to granular (cohesionless) soil, this study combines a variety of numerical methods to investigate (1) how the anisotropy of the permeability evolves as the soil fabric anisotropy evolves in triaxial deformation and (2) establish a link between the anisotropy of the permeability and the fabric anisotropy. The Discrete Element Method (DEM) was employed to create linearly graded virtual samples of spheres (Cu of 1 to 2). Initially isotropic sphere packings were subjected to triaxial compression or triaxial extension up to 30% of absolute axial strain to induce an anisotropic fabric. Pore Network Models (PNMs) present a computationally efficient option for simulation of flow through the pore space. A PNM models fluid flow between pores (nodes) connected by pipes (edges) whose geometry is defined by the topology of the connected pores and the mass balance equation is solved at each pore. After demonstrating the accuracy of the PNM framework adopted here, this contribution presents data from PNM simulations that used the positions of individual particles in the sheared spherical packings as input data. The fabric and permeability anisotropies during triaxial shear deformation were compared at axial strain intervals of 1%. Detailed microscale analyses suggest that the anisotropy in the permeability can be attributed to an increase in the local conductance of fluid pipes in the direction of the major principal stress, which is related to the evolution of the pore topologies during the shear deformation.

Analysis of effects of material anisotropy on ductile damage using microscopic unit‐cell model

AbstractIt is experimentally observed that the failure in ductile metals is mainly due to the nucleation, growth, and coalescence of micro‐voids as well as micro‐shear‐cracks. Furthermore, plastic anisotropy has significant role in damage and failure behavior of ductile metals. Finite element simulations of unit cell provide a basis to understand different mechanisms on micro‐scale, for example, changes in shape and size of single voids and defects as well as localization of plastic strains. This contribution deals with the numerical analysis of unit cell containing spherical void subjected to symmetrical boundary conditions taking material anisotropy into account. Elastic isotropic behavior is described by Hooke's law while Hoffman yield criterion considering the strength‐differential effect is used to model the anisotropic plastic behavior. Generalized anisotropic stress invariants, generalized stress triaxiality, and generalized Lode parameter are introduced to characterize the stress state in the anisotropic ductile metal. The effect of plastic anisotropy on the damage behavior of the aluminum alloy EN AW‐2017A is studied in detail by performing a series of numerical simulations covering a wide range of stress triaxialites and Lode parameters. Stress triaxility and Lode parameter are controlled and kept constant during the entire loading process. The numerical results are then used to discuss general mechanisms of damage and failure process in ductile metals.

Non-stationary anisotropy-dependent critical state for clays

In this paper, the effect of fabric anisotropy on the critical state behaviour of clays is investigated. An original concept of moving critical state is elaborated by a novel state parameter-based rotational hardening rule that is subsequently used to formulate a complete anisotropic elastoplastic constitutive model for clays. It is shown that some of the distinctive pre-failure and critical state responses of clays can be explained by adopting a non-stationary critical state line. Furthermore, an enhanced definition for the state of the soil is proposed that provides a more realistic correspondence between the shearing behaviour of an overconsolidated clay and its initial consolidation state. The proposed model is validated by simulating the experimental data from triaxial tests on a number of clays.

Investigation of acoustoelastic surface acoustic waves in prestressed media

Dispersion of broadband surface acoustic waves (SAWs) is often used for the nondestructive evaluation of near-surface elastic properties of materials. The accurate forward model of SAW propagation is essential for inversion. In this paper, we present a combining semi-analytical finite element (SAFE) and perfectly matched layer method for accurately predicting the phase velocity dispersion, attenuation and polarization modes of SAWs in any prestressed anisotropic layered half-space. Equations of motion are formulated based on the Biot's theory of small deformations influenced by initial stress, so it does not matter whether the residual stress results from hyperelastic transformations. The simulated results are firstly validated by the solutions from the exact three-dimensional elasticity theory-based method. The SAFE method is then used to discuss the effect of material anisotropy and residual stress on the SAWs. Finally, the method is applied to two practical examples. The differences and similarities of two common types of acoustoelastic theories are also discussed.

Experimental study on wire and arc additively manufactured steel double-shear bolted connections

Wire and arc additive manufacturing (WAAM) has emerged as a highly promising technique for manufacturing large-scale steel structural elements. However, the distinct mechanical properties of WAAM steel could potentially lead to different performance of WAAM steel bolted connections compared to the traditional steel bolted connections. This study aims to investigate the material properties of WAAM steel and the structural behaviours of WAAM steel bolted connections, focusing on the effects of print layer orientation and connection plate geometrical dimensions. A total number of 24 WAAM steel coupon specimens with three different print layer orientations and 36 WAAM double-shear bolted connections with two print layer orientations and different geometric dimensions were designed, fabricated and tested under monotonic tension. These specimens were measured using a 3D laser scanner and Digital Image Correlation (DIC) was adopted to measure the structural response during testing. The impact of print layer orientations on WAAM material properties and the effects of WAAM material properties on bolted connections were analysed and discussed. The current design codes for traditional steel bolted connections were evaluated against the test results of WAAM steel bolted connections. The study found that the print layer orientations of WAAM steel plates initiated an anisotropic material property of the coupon specimens, demonstrated by the differences in ultimate tensile strength and strain of specimens with different print layer orientations. Five failure modes, including net section tension, shear-out, bearing, end-splitting, and block shear failure were observed for the bolted connections. The material anisotropy further affects the performance of the bolted connections, though in the same dimensions, 28% of the specimens presented different failure modes due to the different print layer orientations. The effectiveness of current steel design standards was compromised by inaccurate predictions of failure modes due to the distinct end-splitting failure mode and the effects of material anisotropy, though the predictions of the ultimate capacities of the WAAM lap shear specimens were relatively accurate.

Numerical analysis of hydro-thermal fracturing in saturated rocks by considering material anisotropy and micro-structural heterogeneity

This study is devoted to numerical modeling of cracking process induced by temperature change in saturated porous rocks in the context of geological disposal of radioactive waste. Effects of material anisotropy and heterogeneity are taken into account. The macroscopic elastic properties are determined from two steps of homogenization by considering pores and mineral inclusions at two different scales. An extended phase-field model is proposed to describe the initiation and propagation of localized cracks. Two damage variables are introduced to conveniently represent both tensile and shear cracks. New damage evolution criteria are defined by incorporating the pore pressure effect. Three application examples are presented. By assuming a random distribution of pores and inclusions, the efficiency of the proposed model for capturing the progressive cracking process is first verified in a triaxial compression test. The thermal cracking process in an anisotropic and heterogeneous sample is then investigated. The respective influences of elastic anisotropy and spatial variability of pores and inclusions are outlined. Finally, the proposed model is applied to a series of real laboratory thermal cracking tests. Both hydromechanical responses and cracking evolution patterns are investigated. Numerical results are compared with experimental measurements. The main mechanisms involved in the thermal cracking process are highlighted.

Three-dimensional axisymmetric transient response of an unsaturated poroelastic transversely isotropic half-space

This paper investigates the three-dimensional (3D) axisymmetric dynamic response of an unsaturated poroelastic transversely isotropic half-space subjected to different vertical transient loading types. Taking into account the compression deformation of soil particles, pore fluid, the viscous and inertial coupling between different phases, as well as the material anisotropy of soil skeleton, the dynamic governing equations of unsaturated poroelastic transversely isotropic half-space medium in cylindrical coordinate system are established. Then, the general solutions for the soil skeleton’s displacement and stress, as well as the relative displacements and pressures of pore-water and pore-air, are obtained by using Laplace-Hankel transform. Finally, the Durbin numerical inversion method and Gauss-Kronod algorithm are applied to solve the transient Lamb’s problem in time domain. After validating the correctness of the proposed solution, the numerical examples focused on the effect of material anisotropy, transient loading type, the degree of saturation and distance from the loading source on the vertical and radial surface displacements of an unsaturated transversely isotropic poroelastic half-space are investigated.

Propagation of plane waves in a nonlocal transversely isotropic thermoelastic medium with voids and rotation

AbstractThe objective of present research work is to investigate the propagation of time harmonic plane waves in a rotating, nonlocal, transversely isotropic thermoelastic half‐space having void pores in the context of Lord–Shulman theory. It has been observed that four coupled plane waves travel in such type of medium with distinct speeds. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are presented. Numerical computations for a magnesium crystal‐like material are performed with the help of MATLAB software to study the effects of material anisotropy, nonlocal, void and rotation parameters on the amplitude ratios. The computational results are displayed and explained through graphs. The phase velocities of plane waves in transversely isotropic medium are found to depend upon the incident angle, whereas these attain constant values in an isotropic medium. The energy conservation law is also justified during the reflection phenomena.

Critical velocities of a two-layer composite tube under a moving internal pressure

Critical velocities of a two-layer composite tube under a uniform internal pressure moving at a constant velocity are analytically determined. The formulation is based on a Love–Kirchhoff thin shell theory that incorporates the rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar materials, which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form expressions for the critical velocities and radial displacement of the two-layer composite tube are first derived for the general case by including the effects of material anisotropy, rotary inertia and radial stress. The formulas for composite tubes without the rotary inertia effect and/or the radial stress effect and with various types of material symmetry for each layer are then obtained as special cases. In addition, it is shown that the model for single-layer, homogeneous tubes can be recovered from the current model as a special case. To illustrate the new model, a composite tube with an isotropic inner layer and an orthotropic outer layer is analyzed as an example. All four critical velocities of the composite tube are calculated using the newly derived closed-form formulas. Six values of the lowest critical velocity of the two-layer composite tube are computed using three sets of the new formulas, which compare fairly well with existing results.

Mixed boundary-value problems and dynamic impedance functions due to vibrations of a rigid disc on a thermoelastic transversely isotropic half-space

The mixed boundary-value problems and impedance functions due to forced vibrations of a rigid disc on a thermoelastic transversely isotropic half-space are presented analytically and numerically for the first time. Dynamic interaction problems of the disc with the thermoelastic half-space are solved by utilizing an indirect boundary-element method (BEM) which uses the dynamic Green's functions for uniform circular disc loads acting on the surface of a thermoelastic transversely isotropic half-space. The horizontal, vertical, rocking, and torsional vibrations of the disc are investigated and the results are presented in terms of several dual- and Fredholm- integral equations. For the four vibration modes, the related thermo-elastodynamic mixed boundary-value problems are solved and the contact normal and shear stresses, the resultant forces and moments acting on the disc as well as the impedance and compliance functions are derived analytically. By zeroing some parameters, we proved that the obtained analytical thermo-elastodynamic solutions are reduced to the corresponding elastodynamic results reported in the literature. The numerical procedures for the involved semi-infinite integrals of the kernel functions as well as the numerical quadrature methods for evaluating the impedance functions are further presented. The discretization method is required to be applied only to the interface of the rigid disc with the thermoelastic half-space. A computer program is coded in Mathematica where the singularities due to some branch points and the Rayleigh pole were treated. The Gauss-Legendre quadrature method is used for numerical evaluation of impedance functions, and its advantages are presented and compared with other methods. Some graphical results are presented for the dimensionless impedance functions versus the dimensionless frequency. Effects of thermal and anisotropic properties of the thermoelastic materials; and frequency of excitation on the impedance functions are presented and compared with the elastic materials. Numerical results indicate the significant effects of material anisotropy on the impedance functions.

Dynamic interactions, impedance functions and elastic wave propagation due to horizontal and vertical vibrations of a rigid foundation in a transversely isotropic elastic ground

The analytical and numerical treatments of horizontal and vertical forced time-harmonic vibrations of a rigid circular foundation in a transversely isotropic elastic half-space ground are presented. A complete discussion on the boundary conditions and elastic wave propagation due to horizontal and vertical vibrations of the foundation on the half-space is presented and a comparison is made with the full-space problem. With the aid of appropriate dynamic Green’s functions reported in the literature, the horizontal and vertical vibrations of the foundation are treated analytically, and the results are expressed in terms of the solutions of several Fredholm integral equations. For these two vibration modes, the relations for the contact normal and shear stresses, the resultant forces acting on the foundation, and the dimensionless impedance and compliance functions are given. To validate the analytical formulations, the results obtained in this paper are reduced to static responses for transversely isotropic half-space, and to dynamic responses for isotropic half-space; and compared with the results reported in the literature. An efficient numerical procedure is presented to evaluate the semi-infinite integrals appeared in the analytical solutions utilizing some features of the Mathematica software. The Fredholm integral equations and impedance and compliance functions are solved and evaluated numerically using the Gaussian quadrature method. Some graphical results are provided to present the impedance and compliance functions for different transversely isotropic materials. The effects of material anisotropy, as well as the frequency of excitation on the responses are discussed. The differences between vibrations of rigid foundations in the half-space and full-space mediums are emphasized in view of the Rayleigh wave propagation. Moreover, the difficulties related to numerical procedures needed for handling the strong singularities due to propagation of Rayleigh waves in the half-space media are presented.

Modeling anisotropic ductile fracture of AA7075-T6 sheet for sheet metal forming considering anisotropic stress state

Anisotropic ductile fracture is one of the critical issues in the precision plastic forming of lightweight sheet metals. In this work, a new anisotropic ductile fracture model is developed by introducing the anisotropic stress triaxiality into the weight equation of the shear-controlled ductile fracture criterion. In an attempt to consider the effect of material anisotropy on stress state, the proposed fracture model is constructed in the anisotropic stress state form. The proposed anisotropic fracture model is used to characterize the anisotropic ductile fracture behavior of the AA7075-T6 sheet with a thickness of 2.0 mm under various stress states at room temperature. A series of uniaxial tensile tests are conducted using the in-plane shear specimen, the specimen with a central hole, and the plane strain grooved specimen to experimentally investigate the ductile fracture of AA7075-T6 along rolling, diagonal, and transverse directions. The proposed fracture model is calibrated by fracture strains determined from the hybrid experimental–numerical approach. With the calibrated fracture model, the anisotropic ductile fracture behaviors of AA7075-T6 over a wide range of stress states are predicted and compared with experimental measurements. The results show that the proposed fracture model successfully captures the anisotropic ductile fracture behavior of AA7075-T6 under various stress states at room temperature. Furthermore, to further illustrate the fracture predictive capability of the proposed fracture model, the predicted anisotropic fracture forming limit diagram is compared with the experimental forming limit strains obtained from the literature. Reasonable agreement is shown between literature data points and predicted fracture forming limit diagram. Accordingly, the proposed model has a great advantage in quantitative characterizing the anisotropic ductile fracture of high-strength aluminum alloy sheets under various loading conditions.

Effect of steel anisotropy on contact pressure and stress distribution in dry and lubricated point contacts: A case study with measured material properties

On a macroscopic level, bearing steel behaves isotropic all due to the aggregate effect of many anisotropic grains. However, the effects of material anisotropy on the local scale of a contact zone between rolling element and raceway may be significant for the pressure at the surface, the subsurface stresses, and for the lubricant film, particularly in extreme conditions of heavily starved contacts. Multigrid techniques were shown to allow numerical simulation with the dense grids needed to represent 3D material consisting of grains with varying crystallographic orientation. In earlier work, this was shown for grains generated by Voronoi tessellation with randomly varying orientation. Here, we demonstrate the capability of computational diagnostics using local orientation angles and phase composition of 100Cr6 (ASTM 52100) bearing steel, obtained from electron back scatter diffraction (EBSD) analysis of a ring near-raceway sample. For a circular contact under dry and elasto-hydrodynamically lubricated conditions, it is shown that the variation of the crystallographic orientation, effectively forming a variation of stiffness of the grain in load direction, leads to stress concentrations between grains with the larger differences in orientation angles. The developed algorithm can be used for criticality evaluation of measured subsurface topological/crystallographic structures and optimization.

Prediction of Forming Limit Diagram Using the Marciniak-Kuczynski Method for Ti-6Al-4V Using Different Material Models

The forming limit diagram (FLD) is a widely used tool to assess the formability of a metal sheet [1]. The current study aims to investigate the influence of strain rate, material anisotropy and hardening on the FLD of Ti-6Al-4V predicted by the well-known Marciniak-Kuczynski (M-K) method. The tensile data of quasi-static (8 10-5 s-1), intermediate (0.5 s-1) and dynamic experiments (approximately 1000 s-1) on Ti-6Al-4V sheet are available at three different orientations, with respect to the rolling direction: 0°, 45° and 90°. Different hardening models are taken into account. Also, von Mises and Hill yield criterion are considered. The results show that the influence of the hardening law on FLD is significant. In particular, the most conservative limit strains are predicted by the Voce law because of its saturation characteristic. The yield criterion is found to only affect the right part of the FLD. Regarding the strain rate influence, the left part of the FLD is mainly dominated by the amount of uniform elongation, while the right part is strongly dependent on the yield function used. Therefore, for this region the effects of strain rate and yield function are difficult to distinguish. Finally, the effect of material anisotropy on the FLD is significant. Under quasi-static conditions, the Lankford coefficient seems to be the driving factor in uniaxial and equibiaxial deformation. However, in plane strain conditions the effect of the strain hardening exponent is dominant.

A transient simulation of thermomechanical instability in metal-free friction materials with anisotropic properties

A two-dimensional non-linear transient thermomechanical model is developed to incorporate the anisotropic properties of a metal-free friction material sliding against a steel disc using a finite element approach. The main focus of the study is the effect of material anisotropy on thermomechanical instability (TMI) of friction linings used in automotive disc clutches or brakes. The model is validated by comparing the result to an existing eigenvalue solution. A parametric study on the material anisotropy revealed that for contact with the separation effect, an increase in elastic modulus E11 in the sliding direction and thermal conductivity K22 in the thickness direction discourage TMI formation. Conversely, a higher thermal conductivity K11 in the sliding direction and elastic modulus E22 in the thickness direction make the friction material more susceptible to TMI formation for a full-contact regime and contact with the separation effect. In addition, the effect of the thermal expansion coefficient was considered in this work.