Anisotropic Stiffness Research Articles

Structural control on the directional amplification of seismic noise (Campo Imperatore, central Italy)

Seismic signals propagating across a fault may yield information on the internal structure of the fault zone. Here we have assessed the amplification of seismic noise (i.e., ambient vibrations generated by natural or anthropogenic disturbances) across the Vado di Corno Fault (Campo Imperatore, central Italy). The fault zone is considered as an exhumed analogue of the normal faults activated during the L'Aquila 2009 earthquake sequence. Detailed structural geological survey of the footwall block revealed that the fault zone is highly anisotropic and is affected by a complex network of faults and fractures with dominant WNW–ESE strike. We measured seismic noise with portable seismometers along a ∼500 m long transect perpendicular to the average fault strike. Seismic signals were processed calculating the horizontal-to-vertical spectral ratios and performing wavefield polarization analyses. We found a predominant NE–SW to NNE–SSW (i.e., ca. perpendicular to the average strike of the fault-fracture network) amplification of the horizontal component of the seismic waves. Numerical simulations of earthquake-induced ground motions ruled out the role of topography in controlling the polarization and the amplitude of the waves. Therefore, the higher seismic noise amplitude observed in the fault-perpendicular direction was related to the measured fracture network and the resulting stiffness anisotropy of the rock mass. These observations open new perspectives in using measures of ambient seismic noise, which are fast and inexpensive, to estimate the dominant orientation of fracture networks within fault zones.

A multiple anisotropic material finite element and its application to stiffness tensor predictions for woven composite lamina

The effective anisotropic stiffness tensor Cijkl of a woven composite lamina can be calculated by performing a finite element analysis (FEA) of the representative volume element (RVE); however, the complex geometry of heterogeneous RVEs makes meshing tedious. This paper develops two unique multiphase voxel elements (MVEs) that account for multiple materials within an elemental domain by utilizing the material properties at each integration point to develop local strain corrections. Studies performed on simple cuboid geometries show exceptional agreement with standard FEA results, and results from the new voxel elements are more accurate than previous MVEs presented in literature. The application for these new MVEs is demonstrated on plain and twill weave composite laminae, and the results generated are in exceptional agreement with experimental results available in the literature and computationally expensive studies using standard finite elements.

Anisotropy of elasticity and fabric of granular soils

Anisotropy of elasticity is a very important feature of granular soils. In this paper, numerical experiments using discrete element method were performed to emulate drained triaxial tests and simple shear tests at different stress levels. From these numerical experiments the macroscopic elasticity parameters were determined. The results show that at isotropic stress states the stiffness of the numerical specimen increases, while the Poisson’s ratio decreases with increasing confining pressure. The small strain shear modulus of the numerical specimen agrees well with the laboratory experimental results on a specimen with similar conditions. At anisotropic stress states, there is a threshold stress ratio ( $${ SR}_{\mathrm{th}}$$ ), which characterizes the degrees of stiffness change and fabric change during the shearing. When the stress ratio (SR) is less than $${ SR}_{\mathrm{th}}$$ , the microscopic contact number does not change and its distribution remains nearly isotropic, while the distribution of contact forces change and become anisotropic to resist the applied anisotropic stress. Therefore the stiffness anisotropy of the specimen mainly results from the anisotropy of contact forces. When SR is larger than $${ SR}_{\mathrm{th}}$$ , however, the contact number decreases significantly in the minor principal stress direction resulting in the fabric anisotropy, along with the adjustments of contact forces. The stiffness anisotropy of the specimen results from both the fabric anisotropy and the contact force anisotropy. It also indicates that the stress normalized stiffness may be used as an index of the degree of fabric anisotropy. Moreover, the Poisson’s ratio of the specimen increases continuously with increasing stress ratio and its anisotropy can be approximately related to the stiffness anisotropy.

Crack driving force in twisted plywood structures.

Twisted plywood-like structures exist in many natural fiber composites, such as bone or insect carapaces, and are known to be very fracture resistant. The crack driving force in such materials is analyzed quantitatively for the first time, using the concept of configurational forces. This tool, well established in the mechanics of materials, is introduced to the modeling of biological material systems with inhomogeneous and anisotropic material behavior. Based on this analysis, it is shown that the system can be approximated by an appropriately chosen inhomogeneous but isotropic material for the calculation of the crack driving force. The spatial variation of the crack driving force and, especially, its local minima are essential to describe the fracture properties of twisted plywood structures.

An active radial compliance method with anisotropic stiffness learning for precision assembly

Compliance is essential for precision assembly, which provides motion guidance and damage avoidance. Force control can offer flexible implementation of active compliance for manipulators. In this paper, an active radial compliance method is developed for the insertion task of thin walled millimeter-sized cylinders. A radial force controller is designed to satisfy the contact force constraint in the component’s radial directions, which integrates the explicit force control with the high precision attitude measurement based on microscopic vision. An anisotropic stiffness learning method is proposed based on clustering and support vector machines. It can obtain the hidden anisotropic stiffness characteristics of the mechanical system from experience data. Experimental results verify the effectiveness of the proposed methods.

A study of the effects of weathering on soils derived from decomposed volcanic rocks

A comprehensive investigation was made of the effects of weathering on the nature and mechanics of volcanic saprolites from Hong Kong. Few such studies have been conducted in volcanic weathered soils and the application of a critical state type of framework that accounts for the effects of structure, as has been used here, is especially novel. The investigation examined the effects of spatial variations of the effects of weathering both vertically as the weathering degree alters, and horizontally through comparing data from different sites. In addition to index tests, SEM and XRD, an extensive series of oedometer, triaxial and multi-directional bender elements tests was carried out, comparing the behaviour of samples from different locations and depths in both intact and reconstituted states. This meant that the changes to the intrinsic (reconstituted) behaviour could be traced throughout different degrees of weathering along with the effects of changing structure on the mechanical behaviour of the intact soils. The intrinsic properties changed in a manner that was broadly consistent with the increasing of fines content and plasticity due to weathering. The effects of meso-structure were small to medium in compression, and in shearing they were generally even less evident, both at small strains and failure. The degrees of anisotropy of stiffness for both intact and reconstituted samples were mostly quite small.

Fracture-Induced Anisotropy of the Stress–Strain Response of Shale at Multiple Scales

Author(s): Xu, H; Busetti, S; Arson, C | Abstract: This paper investigates deformation and stiffness anisotropy induced by damage propagation in a rock brittle deformation regime. Specifically, a finite-element-based Continuum damage mechanics model is used to capture sample size effects and the influence of intrinsic anisotropy on the stress-strain response of shale. The differential stress-induced damage (DSID) model previously proposed by the authors is calibrated against triaxial compression tests performed on North Dakota Bakken shale samples. Laboratory tests simulated with the FEM reproduce deformation and damage localization phenomena and capture the increase of boundary effects expected in larger samples. Simulations performed for various initial states of damage are used to investigate the role of the dominant fabric anisotropy of the rock: bedding planes in shale are modeled by a smeared damage zone with the DSID model and by a discrete crack plane. The continuum approach successfully captures the development of microcrack propagation and energy dissipation at the early stage of the strain hardening process observed in triaxial compression tests. Additionally, using initial anisotropic damage can effectively account for various types of mechanical anisotropy in shale.

Comparison of grain to grain orientation and stiffness mapping by spatially resolved acoustic spectroscopy and EBSD.

Our aim was to establish the capability of spatially resolved acoustic spectroscopy (SRAS) to map grain orientations and the anisotropy in stiffness at the sub-mm to micron scale by comparing the method with electron backscatter diffraction (EBSD) undertaken within a scanning electron microscope. In the former the grain orientations are deduced by measuring the spatial variation in elastic modulus; conversely, in EBSD the elastic anisotropy is deduced from direct measurements of the crystal orientations. The two test-cases comprise mapping the fusion zones for large TIG and MMA welds in thick power plant austenitic and ferritic steels, respectively; these are technologically important because, among other things, elastic anisotropy can cause ultrasonic weld inspection methods to become inaccurate because it causes bending in the paths of sound waves. The spatial resolution of SRAS is not as good as that for EBSD (∼100 μm vs. ∼a few nm), nor is the angular resolution (∼1.5° vs. ∼0.5°). However the method can be applied to much larger areas (currently on the order of 300 mm square), is much faster (∼5 times), is cheaper and easier to perform, and it could be undertaken on the manufacturing floor. Given these advantages, particularly to industrial users, and the on-going improvements to the method, SRAS has the potential to become a standard method for orientation mapping, particularly in cases where the elastic anisotropy is important over macroscopic/component length scales.

Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores

The vibration performance of sandwich beams with honeycomb-corrugation hybrid cores was investigated in this paper. The method of homogenization was employed to obtain the equivalent macroscopic stiffness of honeycomb-corrugation hybrid cores. Finite element methods and modal analysis techniques have been used to predict their vibration characteristics (i.e. their natural frequencies and mode shapes). It is shown that in most cases the predictions by using the equivalent homogenization model (2D model) agree well with the experimental and three-dimensional finite element calculated results. For sandwich beams with corrugated cores, the filling honeycomb not only enhances their flexural rigidity and increases their natural frequency of higher orders, but also more or less eliminates the anisotropy of the structural stiffness and suppresses the local modes of vibration. In addition, considering mass efficiency, a dimensionless frequency parameter was proposed. It was found that the frequency parameter has different sensitivity to the geometry parameters, i.e. the slenderness ratio of corrugated member, the face sheet thickness ratio and the relative density of filling honeycomb.

Programmable snapping composites with bio-inspired architecture

The development of programmable self-shaping materials enables the onset of new and innovative functionalities in many application fields. Commonly, shape adaptation is achieved by exploiting diffusion-driven swelling or nano-scale phase transition, limiting the change of shape to slow motion predominantly determined by the environmental conditions and/or the materials specificity. To address these shortcomings, we report shape adaptable programmable shells that undergo morphing via a snap-through mechanism inspired by the Dionaea muscipula leaf, known as the Venus fly trap. The presented shells are composite materials made of epoxy reinforced by stiff anisotropic alumina micro-platelets oriented in specific directions. By tailoring the microstructure via magnetically-driven alignment of the platelets, we locally tune the pre-strain and stiffness anisotropy of the composite. This novel approach enables the fabrication of complex shapes showing non-orthotropic curvatures and stiffness gradients, radically extending the design space when compared to conventional long-fibre reinforced multi-stable composites. The rare combination of large stresses, short actuation times and complex shapes, results in hinge-free artificial shape adaptable systems with large design freedom for a variety of morphing applications.

Undrained stiffness anisotropy from hollow cylinder experiments on four Eocene-to-Jurassic UK stiff clays

The paper describes the anisotropic undrained stiffness behaviour of four medium-plasticity heavily overconsolidated UK stiff marine clays as revealed through hollow cylinder testing. The experiments contributed to two broader studies on stiff-to-hard London, Gault, Kimmeridge, and Oxford clay strata. They involved static and dynamic testing of multiple high-quality natural specimens sampled at similar depths from inland sites. This paper explores the directional dependency of the clays’ highly nonlinear undrained stiffness characteristics. New data-analysis approaches are outlined that allow the stiffnesses associated with one-dimensional vertical, horizontal, or pure horizontal shear modes to be isolated in complex undrained stress paths. In the presented experiments, loading progressed from in situ stresses to reach ultimate failure at a range of final major principal stress orientation angles α (defined in the vertical plane) while keeping fixed values of the intermediate principal stress ratio, b. The tests reveal strong undrained stiffness anisotropy that can impact significantly on the prediction and understanding of ground deformation patterns in numerous geotechnical engineering applications.

The interplay of stiffness and force anisotropies drives embryo elongation.

The morphogenesis of tissues, like the deformation of an object, results from the interplay between their material properties and the mechanical forces exerted on them. The importance of mechanical forces in influencing cell behaviour is widely recognized, whereas the importance of tissue material properties, in particular stiffness, has received much less attention. Using Caenorhabditis elegans as a model, we examine how both aspects contribute to embryonic elongation. Measuring the opening shape of the epidermal actin cortex after laser nano-ablation, we assess the spatiotemporal changes of actomyosin-dependent force and stiffness along the antero-posterior and dorso-ventral axis. Experimental data and analytical modelling show that myosin-II-dependent force anisotropy within the lateral epidermis, and stiffness anisotropy within the fiber-reinforced dorso-ventral epidermis are critical in driving embryonic elongation. Together, our results establish a quantitative link between cortical tension, material properties and morphogenesis of an entire embryo.

Interfacial free energy and stiffness of aluminum during rapid solidification

Using molecular dynamics simulations and the capillary fluctuation method, we have calculated the anisotropic crystal-melt interfacial free energy and stiffness of aluminum in a rapid solidification system where a temperature gradient is applied to enforce thermal non-equilibrium. To calculate these material properties, the standard capillary fluctuation method typically used for systems in equilibrium has been modified to incorporate a second-order Taylor expansion of the interfacial free energy term. The result is a robust method for calculating interfacial energy, stiffness and anisotropy as a function of temperature gradient using the fluctuations in the defined interface height. This work includes the calculation of interface characteristics for temperature gradients ranging from 11 to 34 K/nm. The captured results are compared to a thermal equilibrium case using the same model and simulation technique with a zero gradient definition. We define the temperature gradient as the change in temperature over height perpendicular to the crystal-melt interface. The gradients are applied in MD simulations using defined thermostat regions on a stable solid-liquid interface initially in thermal equilibrium. The results of this work show that the interfacial stiffness and free energy for aluminum are dependent on the magnitude of the temperature gradient, however the anisotropic parameters remain independent of the non-equilibrium conditions applied in this analysis. The relationships of the interfacial free energy/stiffness are determined to be linearly related to the thermal gradient, and can be interpolated to find material characteristics at additional temperature gradients.

The influence of pore geometry and orientation on the strength and stiffness of porous rock

The geometry of voids in porous rock falls between two end-members: very low aspect ratio (the ratio of the minor to the major axis) microcracks and perfectly spherical pores with an aspect ratio of unity. Although the effect of these end-member geometries on the mechanical behaviour of porous rock has received considerable attention, our understanding of the influence of voids with an intermediate aspect ratio is much less robust. Here we perform two-dimensional numerical simulations (Rock Failure Process Analysis, RFPA2D) to better understand the influence of pore aspect ratio (from 0.2 to 1.0) and the angle between the pore major axis and the applied stress (from 0 to 90°) on the mechanical behaviour of porous rock under uniaxial compression. Our numerical simulations show that, for a fixed aspect ratio (0.5) the uniaxial compressive strength and Young's modulus of porous rock can be reduced by a factor of ∼2.4 and ∼1.3, respectively, as the angle between the major axis of the elliptical pores and the applied stress is rotated from 0 to 90°. The influence of pore aspect ratio on strength and Young's modulus depends on the pore angle. At low angles (∼0–10°) an increase in aspect ratio reduces the strength and Young's modulus. At higher angles (∼40–90°), however, strength and Young's modulus increase as aspect ratio is increased. At intermediate angles (∼20–30°), strength and Young's modulus first increase and then decrease as pore aspect ratio approaches unity. These simulations also highlight that the influence of pore angle on compressive strength and Young's modulus decreases as the pore aspect ratio approaches unity. We find that the analytical solution for the stress concentration around a single elliptical pore, and its contribution to elasticity, are in excellent qualitative agreement with our numerical simulations. The results of our numerical modelling are also in agreement with recent experimental data for porous basalt, but fail to capture the strength anisotropy observed in experiments on sandstone. We conclude that the alignment of grains or platy minerals such as clays exerts a greater influence on strength anisotropy in porous sandstones than pore geometry. Finally, we show that the strength anisotropy that arises as a result of preferentially aligned elliptical pores is of a similar magnitude to that generated by bedding in porous sandstones and foliation in low-porosity metamorphic rocks. The modelling presented herein shows that porous rocks containing elliptical pores can display a strength and stiffness anisotropy, with implications for the preservation and destruction of porosity and permeability, as well as the distribution of stress and strain within the Earth's crust.

Uniaxial Negative Thermal Expansion and Mechanical Properties of a Zinc-Formate Framework.

The thermal expansion behavior of a metal-formate framework, Zn(HCOO)2·2(H2O) (1), has been systematically studied via variable temperature single-crystal X-ray diffraction. Our results demonstrate that this formate exhibits significant negative thermal expansion (NTE, −26(2) MK−1) along its c-axis. Detailed structural analyses reveal that the large NTE response is attributed to the ‘hinge-strut’ like framework motion. In addition, the fundamental mechanical properties of framework 1 have been explored via nanoindentation experiments. The measured elastic modulus and hardness properties on the (00-2)/(100)/(110) facets are 35.5/35.0/27.1 and 2.04/1.83/0.47 GPa, respectively. The stiffness and hardness anisotropy can be correlated well with the underlying framework structure, like its thermoelastic behavior.

A Compliant Telescopic Limb with Anisotropic Stiffness

Soft limbs with anisotropic stiffness are common in nature and enable animals to solve a variety of tasks, including locomotion and manipulation. This mixture of hardness and softness enables animals to efficiently control the unpredictable contact forces that occur while performing such tasks. A challenge for soft robotics is to create artificial limbs that mimic natural mixtures of hardness and softness for use as a building block for soft, adaptable robots. This article presents the design of a novel pneumatic limb module with adjustable length and anisotropic stiffness. The artificial limb is designed with a rigid telescopic endoskeleton inside a rubber bellow, which we show is able to resist buckling, while remaining externally soft. Finally, we present the design of a hexapod walker based on the limb units.

The constitutive modelling of London Clay

Advances in understanding real soil behaviour, achieved over the past twenty years, and subsequent developments of relevant soil constitutive models, have greatly enhanced the predictive ability of numerical analyses of geotechnical structures. Of particular relevance, especially for serviceability limit state (SLS) design, has been the understanding of soils' small strain behaviour. For the behaviour of London Clay, initially developed models were simple curve-fitting techniques that reproduce stiffness dependence on stress and strain level, which has shown some successes in predicting SLS behaviours. Modelling failure of London Clay is significantly more complex due to its overconsolidated and fissured nature. More recent developments in soil constitutive modelling have therefore tried to encompass most important aspects of clay behaviour within the unified framework of critical state. However, even these advanced models have insufficient features to simulate the behaviour of overconsolidated clays. In this paper, a study has been made, comparing high quality laboratory triaxial data on London Clay with the predictions of two constitutive models, highlighting these deficiencies. It is shown how relatively simple modifications of advanced models, to capture the anisotropy of small strain stiffness and to impose a strength curtailment to represent strain localisation, can significantly improve the predictions of laboratory experiments.

Spatial anisotropy of topological domain structure in hexagonal manganites

The domain structure of hexagonal manganites is simulated based on the phenomenological Ginzburg-Landau theory, and special attention is paid to the evolution of a topological vortex-antivortex pattern with the varying out-of-plane anisotropies of two stiffness parameters for the in-plane ($xy$-plane) trimerization amplitude $Q$ and out-of-plane ($z$-axis) polarization $P$. It is revealed that the topological domain structure can be remarkably modulated by the stiffness anisotropies. A larger stiffness for $Q$ along the $z$ axis causes the trajectory lines of the vortex nodes and antivortex nodes to be seriously stretched along the $z$ axis, eventually leading to the topological stripelike domain pattern. The larger stiffness for either $Q$ or $P$ along the $z$ axis makes the domain walls perpendicular to the $z$ axis wider, while the domain walls parallel to the $z$ axis remain less affected. The present work suggests that the topological domain structure may be controlled by some approaches (e.g., lattice strain) which can change the trimerization stiffness and polarization stiffness in hexagonal manganites.

Stability analysis of an open cracked rotor with the anisotropic rotational damping in rotating operation

The damping effects with the distinction of stationary damping and the anisotropic rotating damping on the dynamic stability of the rotating rotor with an open crack on the surface of the shaft is studied. The motion equations of the cracked rotor system are formed by Lagranges principal. Different from previous studies, the anisotropic system with the multi periodical varied coefficients is simplified by the moving frame method such that the stability analysis based on the root locus method can be applied. The corresponding Campbell diagram, decay rate plot and roots locus plot are derived to prove the destabilizing influence of both the rotational damping and the varied anisotropy ratio of the rotating damping. The effects of anisotropy of stiffness on the decisions of the critical range are also presented. The result with theoretical precision would not only generally provide practical applicability to crack detection and instability control of the heavy loading turbo-machinery system, but also give the suggestion that, the increased proportion and the aggravated anisotropy of the rotational damping due to the crack of the fatigue rotor should been taken into consideration on the modeling of cracked rotor system.

Artificial Slanted Nanocilia Array as a Mechanotransducer for Controlling Cell Polarity.

We present a method to induce cell directional behavior using slanted nanocilia arrays. NIH-3T3 fibroblasts demonstrated bidirectional polarization in a rectangular arrangement on vertical nanocilia arrays and exhibited a transition from a bidirectional to a unidirectional polarization pattern when the angle of the nanocilia was decreased from 90° to 30°. The slanted nanocilia guided and facilitated spreading by allowing the cells to contact the sidewalls of the nanocilia, and the directional migration of the cells opposed the direction of the slant due to the anisotropic bending stiffness of the slanted nanocilia. Although the cells recognized the underlying anisotropic geometry when the nanocilia were coated with fibronectin, collagen type I, and Matrigel, the cells lost their directionality when the nanocilia were coated with poly-d-lysine and poly-l-lysine. Furthermore, although the cells recognized geometrical anisotropy on fibronectin coatings, pharmacological perturbation of PI3K-Rac signaling hindered the directional elongation of the cells on both the slanted and vertical nanocilia. Furthermore, myosin light chain II was required for the cells to obtain polarized morphologies. These results indicated that the slanted nanocilia array provided anisotropic contact guidance cues to the interacting cells. The polarization of cells was controlled through two steps: the recognition of underlying geometrical anisotropy and the subsequent directional spreading according to the guidance cues.