Class Of Deformations Research Articles

Non-degenerate metrics, hypersurface deformation algebra, non-anomalous representations and density weights in quantum gravity

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions.

Design and development of a flexible-rigid Triglide sorting manipulator

Flexible manipulators have been widely applied in various tasks involving grasping and manipulation, and their unique characteristics in terms of lightweight design and adaptability make them particularly suitable for tackling complex spatial pick-and-place operations. In this work, a Triglide flexible manipulator is presented and developed, based on the parallel Biglide mechanism and dual leaf springs in parallelogram structure, which features adjustable stiffness by changing the transverse configuration of the leaf springs. To analyze the deflections of the leaf springs efficiently, a segmented approach is deployed, to calculate large deflection within the plane of the leaf-springs parallelogram structure. The adopted approach uses classical bending deformation formulas from mechanics of materials. Consequently, the static models of the manipulator are derived for analyzing bending deformation and workspace by means of numerical calculations. Finite element analysis is adopted to investigate the mechanical characteristics of the manipulator. A prototype of the variable stiffness manipulator is built, and an experimental setup is established for static testing. The obtained results align with the previously observed mechanical characteristics. The main advantages of the flexible robotic manipulator lie in its simple structure, small footprint, and simple kinematic model for control.

Measure-Valued Structured Deformations

Measure-valued structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure-valued structured deformation is defined via relaxation departing either from energies associated with classical deformations or from energies associated with structured deformations. A concise integral representation of the energy functional is provided both in the unconstrained case and under Dirichlet conditions on a part of the boundary.

Exact solution for free vibration analysis of non-uniform thickness functionally graded porous nanosheet with surface effect based on variable nonlocal and length-scale parameters

In this article, the analytical solution for free oscillation of non-uniform thickness functionally graded porous (FGP) rectangular nanosheets resting on a Pasternak foundation with various boundary conditions (BCs) based on the nonlocal strain gradient theory and surface effect are discovered. The nonlocal stress and strain effects are captured on the nonlocal strain gradient hypothesis, while the surface energy effects are based on the surface elasticity hypothesis. The FGP nanosheet has a nonlinear thickness change in both x and y directions and is placed on the Pasternak elastic foundation. The unique point of this study is to investigate the change of nonlocal and length-scale coefficients along the thickness as mechanical properties of the material. Applying classical shear deformation theory (ignore the effect of shear deformation) combined with Hamilton’s principle, the motion balance equation of non-uniform thickness nanosheets is established. The accuracy of the proposed method is verified through reliable publications. A set of results of natural vibration frequencies of variable thickness FGP nanosheets under the influence of factors are discovered and discussed. The results of this study can be used in design calculations of MEM and NEMs systems in mechanics.

Effect of Sinusoidal Fiber Waviness on Non-Linear Dynamic Performance of Laminated Composite Plates with Variable Fiber Spacing

This study investigated influence of varying waviness characteristics of fiber, represented by path amplitude Δ and different numbers of half sine waves k , on the elastic-plastic dynamic behaviour of laminated composite plates with variable fiber spacing. The analysis was based on the equations for action of constant axial dynamic loading and two-dimensional layered approach with classical first order shear deformation theory with five degrees of freedom per node, and it was performed with FORTRAN 94 programming language. Von-Karman’s assumptions were used for the discretization of the laminated plates to include geometric nonlinearity for nine-node Lagrangian isoperimetric quadrilateral elements. Complete bond between the layers was assumed with no delamination, which was based on first-order shear deformation theory. The Newmark implicit time integration method and Newton-Raphson iteration were simultaneously used to solve the nonlinear governing equation in conjunction. It was proven in the research that the nonlinear performance of the laminated composite plate was affected by the studied waviness parameters Δ and k , and also by the variable distribution pattern selected for this study.

TSDT vs CPT and FSDT for Free Vibration Analysis of Functionally Graded Incompressible Plates

This article studies vibrational behavior of incompressible functionally graded plates through utilizing classical, first-order shear, and third-order shear deformation plate theories. Plate material properties are presumed to differ continuously in the thickness direction concurringto a power law function. The motion and continuity equations are produced using three different plate theories, and then they are analytically solved for rectangular plates with simple supports utilizingNavier's method. The results are verified by obtaining the plate natural frequency for the power law index value equals zero and comparing them to those reported in previous works. It is shown that transverse vibrational analysis of the classical and first-order shear deformationplate theories for incompressible plates are not as precise as thecompressible ones. It is shown that this issue is due to the fact that according to those theories, unlike the higher order theories, the hydrostatic pressure cannot participate in carrying the bending loads. Consequently, the equivalent flexural stiffness and as a result flexural frequencies decrease. So, to analyze the vibrational behavior of functionally graded incompressibleplates, whether the plate is either thin or thick, higher order theories should be adopted. Also, it is demonstrated that TSDT is the simplest shear deformation plate theory for which the hydrostatic pressure can contribute to withstandig the bending moments. So, it can be a practical theory for free vibration analysis of functionally graded incompressible plates. Finally, this theory has been taken into consideration to analyze the vibrational behavior of rectangular plates made of functionally graded incompressible materials Also detailed parametric studies have been carried out.

Finite deformation micropolar peridynamic theory: Variational consistency of wryness measure

This paper concerns developments in both classical and peridynamic (PD) finite deformation micropolar elasticity theory. The first part presents an alternative proof of a theorem that demonstrates variational consistency of the wryness measure in classical finite deformation micropolar elasticity which is one of the novel contributions of this work. The linearized version of the proposed wryness measure is compared with the wryness measure of small deformation micropolar elasticity. In the second part of this work, a finite deformation micropolar PD theory is presented. After proposing an additional integro-differential equation along with the standard PD equation of motion, the global balance of angular momentum is proved to be satisfied. The balance of virtual work is derived for the micropolar PD theory. Next, constitutive correspondence approach is used to relate PD force and moment states with their classical counterparts. The nonlocal versions of the strain and the proposed wryness measure are used in the constitutive correspondence. The constitutive equations of the classical micropolar theory are presented and how they can be incorporated in PD framework is discussed. We introduce a new bond breaking criterion for PD micropolar materials based on critical stretch and critical relative rotation. Quasi-static numerical simulations on deformations of plate with a hole and fracture of a double notched sheet are presented. Dynamic simulations concern wave propagation through a solid specimen and plate with a hole. Validation of the simulation results with the finite element solutions, boundary element solutions, and experimental observations demonstrate the potential of our approach.

Effects of crustal rheology and fault strength on the formation of the Qaidam Basin: Results from 2-D mechanical modeling

The Cenozoic Qaidam Basin on the northern Tibetan Plateau is bounded by the foreland thrust belts of the East Kunlun Mountains to the south and Qilian Mountains to the north. In this basin, the maximum thickness of the accumulated sedimentary strata is ∼17 km near the geographic center of the basin. Such a basin architecture challenges the classic foreland-basin deformation model, wherein substantial sediments should be localized near the basin margins owing to thrust loads on a bending plate. Based on the available geological and geophysical constraints, we built a two-dimensional viscoelastoplastic finite element model to investigate whether the unique pattern of the Qaidam Basin was mechanically related to the rheological structure of the crust and frictional strength of the basin-bounding thrust fault. By testing reasonable bounds on the viscosity of the ductile crust and effective frictional coefficient of the thrust faults, we modeled a basin framework that fits well with that of Qaidam Basin. The model parameters include a layered rheological structure, with the viscosity of the ductile crust of the basin being two orders of magnitude greater than that of the adjacent mountain belts and an effective frictional coefficient of >0.2. Furthermore, the initial width of the basin significantly affected its deformation style. Therefore, the layered rheological structure of the crust and frictional strength of the basin-bounding thrust faults played important roles in the formation of the Qaidam Basin. Our findings suggest that the inelastic behavior of the crust affects foreland deformation, highlighting that the classic foreland basin model must be revised for some tectonic settings.

Investigation of the effect of morphological and crystallographic textures on the ductility limits of thin metal sheets using a CPFEM-based approach

The current contribution investigates the effect of some relevant microstructural parameters (specifically, morphological and crystallographic textures) on the ductility limits of polycrystalline aggregates using the Crystal Plasticity Finite Element Method (CPFEM). The polycrystalline aggregates are assumed to be representative of thin metal sheets and their macroscopic behavior is determined from that of their constituent single crystals on the basis of the periodic homogenization technique. The single crystal behavior is described by a finite strain elastoplastic framework in which the plastic flow rule obeys the classical Schmid law and plastic deformation is solely attributed to the slip on the crystallographic slip systems. The CPFEM is implemented within and in connection with ABAQUS/Standard finite element code. The ductility limits are predicted by the Rice bifurcation theory where strain localization is detected when the macroscopic acoustic tensor becomes singular. Three grain morphologies (namely, cube, random, and elongated morphology) and three initial crystallographic textures (namely, cube, random, and copper orientation) are considered to investigate the effect of morphological and crystallographic textures on the onset of plastic strain localization. The numerical results indicate that the effect of initial crystallographic texture is much more pronounced than that of grain morphology on the predicted ductility limits. In addition, the impact of grain size and sheet thickness are thoroughly analyzed. The research reveals that the trends of the predicted ductility limits are strongly dependent on the size effects.

McCune-Albright syndrome: Beyond classical craniofacial deformities

McCune-Albright syndrome: Beyond classical craniofacial deformities

The impact of pre-compression and temperature on perfluoroalkoxy alkane springs: Insights into spring relaxation.

A predictive model was proposed for determining the high-temperature free height of perfluoroalkoxy alkane springs in air-operated double-bellow pumps with the aim of investigating their relaxation. The model incorporates classical spring deformation theory and considers the material, structure, and real-world operating conditions of the perfluoroalkoxy alkane springs. Experimental validation of the model is also conducted. This study examines the effects of varying temperatures and pre-compression values on the relaxation of perfluoroalkoxy alkane springs' free height. It collects relaxation curves under different temperatures and various pre-compression conditions. The results indicate that spring relaxation increases with higher temperatures when there is no pre-compression. Furthermore, increasing pre-compression at the same temperatures leads to greater spring relaxation. Pre-compression has a more significant impact on spring relaxation. By comparing the experimental data with the simulated curve generated by the model, it is evident that the predicted spring free height relaxation closely aligns with the actual measurements. This verification demonstrates the effectiveness and accuracy of the proposed model in evaluating the relaxation of perfluoroalkoxy alkane springs' free height. Moreover, the model provides a valuable tool for predicting the lifespan of similar perfluoroalkoxy alkane springs in engineering applications.

The Artin component and simultaneous resolution via reconstruction algebras of type $A$

This paper uses noncommutative resolutions of non-Gorenstein singularities to construct classical deformation spaces by recovering the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. The relations of the reconstruction algebra are then deformed, and the deformed relations together with variation of the GIT quotient achieve the simultaneous resolution. This extends the work of Brieskorn, Kronheimer, Grothendieck, Cassens–Slodowy, and Crawley-Boevey–Holland into the setting of singularities \mathbb{C}^{2}/H with H \leq \mathrm{GL}(2, \mathbb{C}) and furthermore gives a prediction for what is true more generally.

Evolution of the Deformation‐ and Flow‐Induced Crystallization and Characterization of the Microstructure of a Single Spherulite, Lamella, and Chain of Isotactic Polypropylene

AbstractIsotactic polypropylene (iPP) is a frequently used polymer in industrial processing and scientific research, used as a model material. This review highlights some current and forefront issues in polymer science and engineering. This review alludes to classical deformation schemes to interpret the complicated deformation in isotactic polypropylene as a semicrystalline polymer. Also, due to the complex hierarchical structures of crystallized polymers, the progress on the multiscale and multistage microstructural evolution covering each deformation stage from the initiation of plasticity until failure is mainly concerned, particularly in terms of crystalline morphology changes. Specifically, the characterization of the microstructure evolution of a single spherulite, lamella, and chain of isotactic polypropylene will be emphasized and mentioned. Here, the authors are most interested in the results obtained from stretching (strain‐induced) orientation and crystallization studies accompanied by the in situ scattering and spectroscopy techniques offering a detection window from nano to micrometer scale, which should be able to reflect the microstructural changes at different length scales of interest. During polymer processing, the melts are frequently subjected to shear or/and elongation flow fields, producing flow‐induced molecular chain orientation in the melt. The oriented molecular chains crystallize differently than those encountered under quiescent conditions. Thus, orientation‐induced crystallization has long been an object of intense interest. A vast body of research is reported about the effects of preorientation on the crystallization of various polymers. Among them, iPP is most frequently studied since its diversified structure and morphology are very sensitive to changes in processing conditions and molecular parameters.

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

This study analyzes the nonlinear dynamic stability of carbon nanotube reinforced composite (CNTRC) piezoelectric viscoelastic nano/micro plate under time dependent harmonic compressive biaxial mechanical loading. The nano/micro plate is single-layer with a uniform and rectangular cross section. Polyvinylidene fluoride (PVDF) is the material used for the nano/micro plate. Also, it is located on a nonlinear viscoelastic piezoelectric foundation made of Zinc Oxide (ZnO). Single-walled carbon nanotubes (SWCNTs) have been used to strengthen nano/micro plate. Using Kelvin-Voigt model, the material properties of the system are assumed to be viscoelastic. Nano/micro plate is subjected to 2D magnetic field and electric potential. Magnetic field effects are incorporated using Maxwell’s relations. An alternating and direct voltage is applied to the nano/micro plate and also smart foundation in thickness direction. Eshelby-Mori-Tanaka approach is used to estimate the effective elastic properties. Additionally, follower force and uniform thermal gradient is applied to nano/micro plate in this study. The nonlinear strain–displacement relations are based on the Von-Kármán theory. According to classical, first order, third order, sinusoidal, parabolic, hyperbolic and exponential shear deformation plate theories, a new formulation is proposed incorporating surface stress effects through the Gurtin-Murdoch elasticity theory. In order to consider small scale parameters, this research is based on modified strain gradient theory (MSGT). Using the energy method and Hamilton’s principle, the non classical governing equations are derived. For nano/micro plate, simply supported boundary conditions are considered. For the purpose of solving differential equations, an analysis based on Galerkin procedure and finally the Bolotin method will be used to obtain the dynamic instability region (DIR). It is the objective of this study to investigate the impact of such parameters as small-scale parameters, alternating and direct applied voltage, intensity of magnetic field, surface effects, thermal environment and static load factor on the DIR. This study revealed that taking into account the smart foundation reduces the area of dynamic instability region by more than 60% for a constant intensity of magnetic field. The stability responses are also more convergent with the smart foundation. Additionally, the range is moved toward higher excitation frequencies and greater system stability. Validation of answers based on reliable scientific articles is one of the final stages of this research. These results can be used to design nano/micro electromechanical systems.

A generalisation of the Pucci–Saccomandi model of rubber elasticity

The Pucci–Saccomandi model of rubber elasticity, also known as the Gent–Gent model, is generalised in this manuscript for a more enhanced applicability to a wider range of finite deformation behaviours, rubber-like material types, and an increased modelling accuracy. The generalising of interest is developed by devising a higher order rational approximant, i.e., of order [1/1], of the response functions. The proposed model is shown to be a parent to some of the celebrated limiting chain extensibility, classical WI1,I2 and generalised neo-Hookean models. The application of the proposed generalised model to the finite deformation of various isotropic incompressible rubber-like materials is demonstrated, including natural unfilled and filled rubbers, commercial polymers and biomaterials. The considered datasets exhibit various deformation behaviours from the classical large deformation of natural rubbers to the downward concavity of filled rubbers, strain/shear softening behaviours of polymers and the softening behaviour of biomaterials up to the onset of failure. The modelling results are directly compared with those of the Gent–Gent model, where the higher accuracy of the proposed model and its capability to favourably capture the aforementioned challenging and varied behaviours is established. In particular, the Gent–Gent model is shown unsuitable for capturing such downward concavity, shear/strain softening and continuous softening to failure behaviours. Given the improved modelling predictions, simplicity of the functional form of the devised model, and its relatively low number of model parameters, the proposed model is presented as a more general, comprehensive and versatile modelling tool for application to the finite deformation of various isotropic incompressible soft materials.

Semi-Analytical Prediction of Ground Surface Heave Induced by Shield Tunneling Considering Three-Dimensional Space Effect

The ground surface deformation induced by shield tunnels passing through enclosure structures of existing tunnels is a particular underground construction scenario that has been encountered in Wuhan Metro Line 12 engineering cases in China. Timely ground deformation prediction is important to keep shield tunneling safe. However, the classic ground deformation theory is difficult to accurately predict for this ground deformation. This paper develops a semi-analytical method to predict ground heave considering the space effect in this engineering condition. Based on the improved ground deformation theory, a novel deformation prediction method for the ground and enclosure structure is derived and combined with Kirchhoff plate theory. Comparing with field deformation measurements, the maximum difference between the measured and calculated deformation is 14.6%, which demonstrates that the proposed method can be used to predict the ground heave induced by shield tunnels passing through the enclosure structure of existing tunnels. The parameters of the underground diaphragm wall used in Wuhan Metro Line 12 are further studied in detail. The results show that the ground heaves have a positive correlation with the embedded ratio of the diaphragm wall, but a negative correlation with its elastic modulus and thickness. However, the thickness and embedded ratio have a limited effect on ground heaves. This study provides a technical reference for optimizing the setting of enclosure structures in order to protect existing buildings.

A perturbation analysis of pure torsion of incompressible hyperelastic cylinders

The stretch-based formulation of basic problems for incompressible isotropic hyperelastic materials has been the subject of renewed recent attention largely motivated by application to modelling the mechanical response of soft tissues. Here we are concerned with the classical problem of simple torsion of a circular cylinder which has in the past been primarily investigated by employing the classical approach of Rivlin in terms of invariants of the Cauchy–Green deformation tensors. Here we propose a perturbation approach to the pure torsion problem for thin (but not necessarily infinitesimally thin) cylindrical specimens motivated by potential applications to rubber-like or biological filaments and for the infinitesimal twisting of thick cylinders. The advantage of this approach is that the results are valid for all strain–energy functions whether based in terms of the principal stretches or in terms of the classical deformation invariants. The asymptotic results obtained for the resultant force and moment are applied to the special case of the one-term stretch-based Ogden model. In particular, a prediction of a transition in the Poynting effect for values of the Ogden parameter α>6 is obtained. Other illustrative examples for both invariant and stretch-based strain energies are described. In view of the complexity of a general analysis of torsion for arbitrary strain energies, the perturbation approach provides a viable alternative for assessing the resultant force and moment.

Mechanical behaviors of metallic alloys dominated by thermo-kinetic synergistic effects upon materials processing

For most metallic alloys, improving strength is usually accompanied by losing ductility (and via versa) even if the work hardening rate keeps unchanged, however, the behind reasons still remain elusive to date. In the present work, we explore the underlying physics for such mechanical performance paradox from the perspective of synergistic effects between thermodynamics and kinetics of phase transition and deformation involved in materials processing. With age-hardenable aluminum alloys as typical examples, the hardening and softening effects are analyzed in terms of system energy accumulation and dissipation during precipitation nucleation and growth along with dislocation multiplication and annihilation. The key thermo-kinetic parameters of driving force and energy barrier are determined by performing relevant atomistic calculations. Analytical models for bridging mechanical performances and thermo-kinetics in terms of microstructural characteristics, which derive from classical phase transition and deformation theories, endow connotation for directing precipitation design, as confirmed by a 6xxx series alloy at the pre-determined aging temperature with ideal strength and ductility. Our work offers an insightful perspective toward understanding the strength and ductility paradox, which can benefit to further establish quantitative connections among processing routes, microstructures and mechanical performances of metallic alloys.

HDHumans

Photo-real digital human avatars are of enormous importance in graphics, as they enable immersive communication over the globe, improve gaming and entertainment experiences, and can be particularly beneficial for AR and VR settings. However, current avatar generation approaches either fall short in high-fidelity novel view synthesis, generalization to novel motions, reproduction of loose clothing, or they cannot render characters at the high resolution offered by modern displays. To this end, we propose HDHumans, which is the first method for HD human character synthesis that jointly produces an accurate and temporally coherent 3D deforming surface and highly photo-realistic images of arbitrary novel views and of motions not seen at training time. At the technical core, our method tightly integrates a classical deforming character template with neural radiance fields (NeRF). Our method is carefully designed to achieve a synergy between classical surface deformation and a NeRF. First, the template guides the NeRF, which allows synthesizing novel views of a highly dynamic and articulated character and even enables the synthesis of novel motions. Second, we also leverage the dense pointclouds resulting from the NeRF to further improve the deforming surface via 3D-to-3D supervision. We outperform the state of the art quantitatively and qualitatively in terms of synthesis quality and resolution, as well as the quality of 3D surface reconstruction.

Modelling and experimental validation of burr control in micro milling of metals

Classical deformation theories are limited to predicting microscopic deformation when the machining parameters are comparable to the dimension of a single grain. Micro-cutting is one such process where the physical phenomenon is significantly influenced by the microstructure characteristics and initial state of stress. The micro-features such as burrs caused owing to these cutting processes, are undesired and affect the quality of the product. In this study, an analytical methodology is proposed, supported by FEM pre-processing, to determine the burr morphology during the micro-milling process for Ti-6Al-4V, Al-6061 and OFHC-Cu. At first, the flow stress is calculated with the help of strain gradient and dynamic recrystallization methods; contact pressure on the cutting edge and minimum chip thickness are introduced through an FE simulation, this assists to find out the axial and radial plastic strain which eventually yields the dimensions of individual burrs. Peening of the material surface prior to micro-milling provided 67 % less formation of top burr. The average burr width and height are measured and validated with predicted results. The grain structure and dynamic recrystallization of the micro-milled surface are revealed by electron backscatter diffraction. Further, the burr distribution from FE modelling is verified with an SEM image.