Fundamental Deformations Research Articles

Examining lung mechanical strains as influenced by breathing volumes and rates using experimental digital image correlation

BackgroundMechanical ventilation is often employed to facilitate breathing in patients suffering from respiratory illnesses and disabilities. Despite the benefits, there are risks associated with ventilator-induced lung injuries and death, driving investigations for alternative ventilation techniques to improve mechanical ventilation, such as multi-oscillatory and high-frequency ventilation; however, few studies have evaluated fundamental lung mechanical local deformations under variable loading.MethodsPorcine whole lung samples were analyzed using a novel application of digital image correlation interfaced with an electromechanical ventilation system to associate the local behavior to the global volume and pressure loading in response to various inflation volumes and breathing rates. Strains, anisotropy, tissue compliance, and the evolutionary response of the inflating lung were analyzed.ResultsExperiments demonstrated a direct and near one-to-one linear relationship between applied lung volumes and resulting local mean strain, and a nonlinear relationship between lung pressures and strains. As the applied air delivery volume was doubled, the tissue surface mean strains approximately increased from 20 to 40%, and average maximum strains measured 70–110%. The tissue strain anisotropic ratio ranged from 0.81 to 0.86 and decreased with greater inflation volumes. Local tissue compliance during the inflation cycle, associating evolutionary strains in response to inflation pressures, was also quantified.ConclusionVentilation frequencies were not found to influence the local stretch response. Strain measures significantly increased and the anisotropic ratio decreased between the smallest and greatest tidal volumes. Tissue compliance did not exhibit a unifying trend. The insights provided by the real-time continuous measures, and the kinetics to kinematics pulmonary linkage established by this study offers valuable characterizations for computational models and establishes a framework for future studies to compare healthy and diseased lung mechanics to further consider alternatives for effective ventilation strategies.

YIELD STRESS UNDER REPEATED LOADING AFTER APPLYING DIFFERENT DEFORMATION PATH FOR LARGE TENSION AND SHEAR

This paper describes the yield phenomenon when a repeated loading is applied to the structure after giving a large pre-strain on it. In the series of our previous research, focusing on the fundamental deformations such as tension or shear, changes of yield stress as the number of repetition increases have been investigated experimentally by using test specimens of annealed pure copper. In the determination of yield stress value, the method by using slope of stress-strain curve at yield has been used instead of proof stress. As a consequence, it has been found that if the type of pre-deformation and the type of deformation in repeated load are the same, yield stress at the pre-deformation side has a declining tendency as compared with opposite side. Therefore, it is predicted that the yield stress under repeated loading after applying a large deformation is closely related to the loading history in large deformation previously applied. Thus, in this study, in order to clarify the influence of pre-deformation on the yield behavior under repeated loading, the experiments are performed by changing the order of tension and shear in pre-deformation. Consequentially, it is clarified that the declining tendency of yield stress under repeated loading is closely related to the yield surface anisotropy, which is formed during the second half of the pre-deformation.

Geometrizing non-relativistic bilinear deformations

We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the mathrm{T}overline{mathrm{T}} deformation and the recently introduced hard rod deformation. We show that all three deformations can be interpreted as coupling the non-relativistic QFT to a specific Newton-Cartan geometry, similar to the Jackiw-Teitelboim-like gravity in the relativistic case. Using the gravity formulations, we derive closed-form deformed classical Lagrangians of the Schrödinger model with a generic potential. We also extend the dynamical change of coordinate interpretation to the non-relativistic case for all three deformations. The dynamical coordinates are then used to derive the deformed classical Lagrangians and deformed quantum S-matrices.

Application of generalized Bloch method: Strain engineering of low dimensional materials through inhomogeneous strains

Due to their special structural morphologies, low dimensional materials are in nanometer scale in zero, one or two dimensions. This feature offers them superior structural flexibility. This characteristic, together with their excellent electronic property response to mechanical deformation, makes strain engineering an important way to optimize the physical properties of materials. Because in low dimension, structural deformations are usually inhomogeneous, the standard electronic and phonon calculation methods formulated via translation under the periodic boundary conditions encounter fundamental difficulties. A fresh approach in this aspect is called for rapidly. In this paper, the essential idea of the generalized Bloch method is introduced, in the context of a tight-binding treatment of electrons. This special method makes use of the helical symmetry and rotational symmetry to deal with the two fundamental non-uniform structural deformations, i.e., torsion and bending. In this way, the atomistic simulation of the deformed structures can still be carried out through a relatively small repeating cell. Such treatment enables the realistic atomistic quantum mechanical simulations in a viable manner. In practice, this new method is implemented into the so-called density-functional tight-binding (DFTB) calculation, an approach widely used in the material computation today. We note that the utility of DFTB brings us several benefits. First of all, the self-consistent field improves the calculation accuracy to be compatible with first-principles calculations. Next, the capability to deal with spin freedoms of DFTB enables us to study the strain tunable properties of spin-polarized electronic states. We illustrate the application of the generalized Bloch method with several examples that can be categorized into “strain tunable electronic properties”, “spatial manipulation of dopants in semiconductor nanowires”, and “strain engineering of phonon properties”. We also have a vision that the generalized Bloch method shall have important application in more areas. Studies of twist bilayers of two-dimensional materials are one of the focuses of the current condensed matter physics research. However, due to the twist induced lattice mismatch, a twisted bilayer is often of a unit cell containing a huge number of atoms. This makes direct realistic atomistic simulations difficult. We indicate that the calculation can be simplified by using the generalized Bloch method where the helical symmetry and possible rotational symmetry of the twisted bilayer would be used. Exploring giant flexoelectricity is a growing area of materials science. Different from piezoelectricity, flexoelectricity is by definition the linear response of polarization to the strain gradient. Usually, in the actual experimental studies, the strain gradient of materials is generated by applying the bending deformation to the slab. This fact indicates that the generalized Bloch method can be used to simulate such systems. In today’s semiconductor technology, the design of flexible electronic devices is an important development field. The low dimensional materials are natural candidates of flexible systems. Obviously, the generalized Bloch method will also play an important role in this aspect. Our recent work has realized the phonon calculation for low-dimensional structures of helical and rotational symmetries based on the electronic structure calculation with the generalized Bloch method. This functionality will expand the application scope of the generalized Bloch method, making it possible to study the strain modulation of thermal properties in low-dimensional systems with inhomogeneous strain patterns.

Yield Curve of Mg-Y Alloy based on Fundamental Plastic Deformations by Micropillar Testing

Yield Curve of Mg-Y Alloy based on Fundamental Plastic Deformations by Micropillar Testing

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

ABSTRACTWe propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.

Effective Zeeman splitting in bent lateral heterojunctions of graphene and hexagonal boron nitride: A new mechanism towards half-metallicity

Low-dimensional half-metallic (HM) systems are invaluable for future spintronics. Yet a definitive experimental demonstration of HM characteristic in two-dimensional (2D) materials remains elusive. Here, we reveal that in recently synthesized graphene/hexagonal boron nitride ($\mathrm{G}\text{/}h\mathrm{BN}$) lateral heterojunctions, pronounced HM can be achieved by applying an in-plane bending. We demonstrate with generalized Bloch theorem that bending has strong influence on interfacial spin states, mimicking the Zeeman effect, which consequently leads to the desired HM phase with a sizable HM gap and excellent magnetic stability. Given recent experimental advances in fabrication of $\mathrm{G}\text{/}h\mathrm{BN}$ heterostructures, this strain-driven HM phase may be practically accessible. The generalized Bloch theorem coupled with self-consistent charge density-functional tight binding is useful to model 2D structures under fundamental deformations, thus may boost the study of strain tunable electronic property of low-dimensional materials with inhomogeneous strain patterns.

The Analogy Study Method in Engineering Mechanics

The course ‘Engineering Mechanics’ plays an essential role as a bridge and bond between fundamental and specialized knowledge, and it has become a basic class for most engineering students. However, there are many complex concepts and formulas to be covered, and this makes it difficult for students to grasp the spirit of engineering mechanics. One way to solve this problem is to use the analogy study method in learning. Following this new route, students can find the linear quantities and angular quantities in theoretical mechanics, and some analogous relations between stress and deformation for fundamental deformations in mechanics of materials. Through these analogy relations, students can appreciate the essence of different physical phenomena. Indeed, it seems that twice as much is accomplished with half the effort.

Earthquake fragmentation and slip processes: Spin and shear-twist wave mosaic

We follow our former considerations on rotational processes and emission of rotation and shear-twist waves as occurring in earthquake source zones. A concise presentation of the motion and constitutive relations is given for each type of the four fundamental point deformations: displacements, rotations, point stretch/squeeze, and string-string point deformations (shear nuclei).

Coset for Hopf fibration and squashing

We provide a simple derivation of metrics for fundamental geometrical deformations such as Hopf fibration, squashing and the Zk quotient which play essential roles in recent studies on the AdS4/CFT3. A general metric formula of Hopf fibrations for complex and quaternion cosets is presented. Squashing is given by a similarity transformation which changes the metric preserving the isometric symmetry of the projective space. On the other hand, the Zk quotient is given as a lens space which changes the topology preserving the ‘local’ metric.

Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

A nonlinear vibration analysis of laminated cylindrical shells is presented in which the effect of the specified boundary conditions at the shell edges, including nonlinear fundamental state deformations, can be accurately taken into account. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections, and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Furthermore, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

Lateral tension increases the line tension between two domains in a lipid bilayer membrane

The effect of an external applied lateral tension on the line tension between two domains of different thickness in a lipid bilayer membrane is calculated. The thick domain is treated as a liquid-ordered phase in order to model a raft in a biological membrane; the thin domain is considered a liquid-disordered phase to model the surrounding region. In our model, the monolayers elastically distort at the boundary to create a smooth rather than steplike boundary to avoid exposure of the hydrophobic interior of the thick raft to water. The energy of this distortion is described by the fundamental deformations of splay and tilt. This energy per unit length of boundary yields the line tension of the raft. Applying lateral tension alters the fundamental deformations such that line tension increases. This increase in line tension is larger when the spontaneous curvature of a raft is greater than that of the surround; if the spontaneous curvature of the raft is less than that of the surround, the increase of the line tension due to application of the lateral tension is more modest.

Boundary eigensolutions in elasticity II. Application to computational mechanics

The theory of fundamental boundary eigensolutions for elastostatic problems, developed in Part I, is applied to formulate methods for computational mechanics. This theory shows that every elastic solution can be written as a linear combination of some fundamental boundary orthogonal deformations, thus providing a generalized Fourier expansion. One finds that traditional boundary element and finite element methods are largely consistent with this theory, but do not harness its full power. This theory shows that these computational methods are indirectly a generalized discrete Fourier analysis. Furthermore, by utilizing suitable boundary weight functions, boundary element and finite element formulations may be written exclusively in terms of bounded quantities, even for non-smooth problems involving notches, cracks, mixed boundary conditions and bi-material interfaces. The close relationship between the resulting boundary element and finite element methods also becomes evident. Both use displacement and surface traction as primary variables. A new degree-of-freedom concept is introduced, along with a stiffness tensor that enables one to visualize a finite element method via a boundary discretization process, just as in a boundary element approach. Global convergence characteristics of the traction-oriented finite element method are also developed. Comparisons with closed-form fundamental boundary eigensolutions for a circular elastic disc are presented in order to provide a means for assessing the numerical methods. Several other numerical examples are solved efficiently by using the concept of boundary eigensolutions in an indirect fashion. The results indicate that the algorithms follow the underlying theory and that solutions to non-smooth problems can be obtained in a systematic manner. Beyond this, the concept of boundary eigensolutions provides an alternative view of computational continuum mechanics that may lead to the development of other non-traditional approaches.

Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation

The equivalence of the finite-element formulations used inflexible multibody dynamics is the focus of this investigation. Thisequivalence will be used to address several fundamental issues related tothe deformations, flexible body coordinate systems, and the geometriccentrifugal stiffening effect. Two conceptually different finite-elementformulations that lead to exact modeling of the rigid body dynamics will beused. The first one is the absolute nodal coordinateformulation in which beams and plates can be treated as isoparametricelements. This formulation leads to a constant and symmetric mass matrix andhighly nonlinear elastic forces. In this study, it is demonstrated thatdifferent element coordinate systems which are used for the convenience ofdescribing the element deformations lead to similar results as the elementsize is reduced. In particular, two element frames are used;the pinned and the tangent frames. The pinned frame has one ofits axes passing through two nodes of the element, while the tangent frame isrigidly attached to one of the ends of the element. Numerical resultsobtained using these two different frames are found tobe in good agreement as the element size decreases. The relationshipbetween the coordinates used in the absolute nodal coordinate formulationand the floating frame of reference formulation is presented. Thisrelationship can be used to obtain the highly nonlinear expression of thestrain energy used in the absolute nodal coordinate formulation from thesimple energy expression used in the floating frame of referenceformulation. It is also shown that the source of the nonlinearityis due to the finite rotation of the element. The result of the analysispresented clearly demonstrates that the instability observedin high-speed rotor analytical models due to the neglect of the geometriccentrifugal stiffening is not a problem inherent to a particular finite-element formulation. Such a problem can only be avoided by considering the known linear effect of the geometric centrifugal stiffening or by using a nonlinear elastic model as recently demonstrated. Fourier analysis of the solutions obtained in this investigation also sheds new light on the fundamental problem of the choice of the deformable body coordinate system in the floating frame of reference formulation. Another method forformulating the elastic forces in the absolute nodal coordinate formulationbased on a continuum mechanics approach is also presented.

Automatic analysis of cerebral atrophy

3D MR data obtained for 10 healthy control subjects have been used to build a brain atlas. The atlas is built in four stages. First, a set of features that are unambiguously definable and anatomically relevant need to be computed for each item in the database. The chosen features are crest lines along which the maximal principal curvature of the surface of the brain is maximal in its associated principal direction. Second, a nonrigid registration algorithm is used to determine the common crest lines among the subjects in the database. These crest lines form the structure of the atlas. Third, a set of crest lines is taken as a reference set and a modal analysis is performed to determine the fundamental deformations that are necessary to bring the individual data in line with the reference set. The deformations are averaged and the set of mean crest lines becomes the atlas. Finally, the standard deviation of the deformations between the atlas and the items in the database defines the normal variation in the relative positions of the crest lines in a healthy population. In a fully automatic procedure, the crest lines on the surface of the brain adjacent to the cerebral ventricles in a patient with primary progressive aphasia were compared to the atlas; confirmation that the brain of this patient demonstrates atrophy was provided by stereological analysis that showed that the volume of the left cerebral hemisphere is 48.8 ml (CE 2.8%) less than the volume of the right cerebral hemisphere in the region of the temporal and frontal lobes. When the amplitude of the deformations necessary to register the crest lines obtained for the patient with the atlas were greater than three standard deviations beyond the variability inherent in the atlas, the deformation was considered significant. Four of the five main deformation modes of the longest crest line of the surface of the brain adjacent to the cerebral ventricles were significantly different in the patient with primary progressive aphasia compared to the atlas. The ventricles are preferentially enlarged in the left cerebral hemisphere. Furthermore, they are closer together posteriorly and further apart anteriorly than in the atlas. These observations may be indicative of the atrophy of the temporal and frontal lobes of the left cerebral hemisphere noted in the patient. Ultimately, the approach may provide a useful screening technique for identifying brain diseases involving cerebral atrophy. Serial studies of individual patients may provide insights into the processes controlling or affected by particular diseases.

A dynamic deformation model of an elastoplastic porous medium

A closed system of equations is obtained for dynamic deformation of an elastoplastic Prandtl-Reiss porous medium. The heterogeneous approach makes it possible to describe the properties of such media in a wide range of loading rates within the theory of plastic flow with the kinematic simplification. The hydrodynamic deformation theory of porous media [1, 2] has been first correctly generalized to the case of including the deviator components of the stress tensor of the medium. The well-known functions of the model are determined from analyzing the fundamental deformations of the corresponding spherical cells.

Some improvements of J2F/J2D and their applications to large elastic-plastic deformation analyses by FEM.

The procedure to introduce J2G (or MG-constitutive equation), which was previously proposed by the author, into a FEM program is presented. Another constitutive equation, J2N, is newly proposed which is a kind of non-normality plasticity theory involving J2F and J2D as its special forms without the difficulty of discontinuous transition from plastic state to elastic state during plastic deformation unlike J2D and other non-normality theories commonly used. A few fundamental large elastic-plastic deformations are analyzed by FEM using J2G, J2G-II (or MG-II), J2N and J2F and the results are discussed. It is found that J2G-II gives results close to those by J2G, and that J2N is less sensitive to strain localization than J2Gs are.