Theory of space-time dissipative elasticity and scale effects

2013 ◽  
Vol 2 (1) ◽  
Author(s):  
S.A. Lurie ◽  
P.A. Belov
Keyword(s):  
Scale Effects ◽  
Displacement Vector ◽  
Kinematic Model ◽  
Transversely Isotropic ◽  
Thermomechanical Properties ◽  
Space Time ◽  
Force Model ◽  
Conductivity Equation ◽  
Dynamic Thermoelasticity ◽  
Covariant Model

AbstractIn this article a model of irreversible dynamic thermoelasticity of an ideal continuua is constructed from an elasticity theory of asymmetrical, transversely isotropic in time direction, dissipative defectless 4D-continuum. In the model the fourth component of the 4D-displacement vector is locally irregular time R. The kinematic model comprises 3D-tensor of distortion, 3Dvector of velocity, 3D-gradient vector of local irregular time and entropy in unified tensor object which is an asymmetrical 4D-tensor of distortion of second rank. Consequently, the force model comprises 3D-tensor of stress, 3D-vector of impulses, 3D-vector of heat flow and temperature in unified tensor object which is an asymmetrical 4D-stress tensor of second rank. Hooke’s law equations have been formulated which connect components of asymmetrical 4D-tensors of stress and distortion. Physical interpretations have been given to the tensors’ components of thermomechanical properties of formulated continuum. Therefore, the article formulate an irreversible dynamic thermoelasticity covariant model of ideal (defectless) continua in which basic kinematic and force variables are components of unified tensor objects and theory is represented by 4D-vector equation. Sedov’s equation has been derived and resulted into Euler’s equations, space projections of which determine motion equations, and time projection determines heat conductivity equation as well as the whole spectrum of the space-time boundary value problems. The proposed theory allows one to describe the scale effects in the thermal processes and opens prospects for studying the scale effects of the coupled dynamic thermoelasticity and its nanoscience applications. A temperature-scale refinement can also broaden the range of applicability of the law of heat conduction in solids to allow for design of small-sized components, devices and nano-systems.

scholarly journals Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions

Materials ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 758 ◽  
Author(s):  
Lorenzo Leonetti ◽  
Nicholas Fantuzzi ◽  
Patrizia Trovalusci ◽  
Francesco Tornabene
Keyword(s):  
Finite Element ◽  
Scale Effects ◽  
Kinematic Model ◽  
Elastic Response ◽  
Actual Behavior ◽  
Orthotropic Composite ◽  
Additional Degree ◽  
Micropolar Continua ◽  
Orthotropic Composites ◽  
Micropolar Materials

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted.

Dynamic Modeling and Response Analysis of a Planar Rigid-Body Mechanism With Clearance

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Chen Xiulong ◽  
Jiang Shuai ◽  
Deng Yu ◽  
Wang Qing
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Contact Force ◽  
Kinematic Model ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Prototype Model ◽  
Force Model ◽  
Normal Contact

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

COSMIC DEFECT COSMOLOGY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1620-1624
Author(s):  
A. TARTAGLIA
Keyword(s):  
Phase Space ◽  
Cold Dark Matter ◽  
Displacement Vector ◽  
Empty Space ◽  
Space Time ◽  
Point Particle ◽  
Accelerated Expansion ◽  
Displacement Vector Field ◽  
Type Ia ◽  
Ia Supernovae

The accelerated expansion of the universe is interpreted as an effect of a defect in space-time treated as a four-dimensional continuum endowed with physical properties. The analogy is with texture defects in material continua, like dislocations and disclinations, described in terms of a singular displacement vector field. A Lagrangian for empty space-time is proposed exploiting one further analogy between the phase space of a Robertson-Walker universe and the phase space of a point particle moving across an homogeneous isotropic medium. The model, named Cosmic Defect theory, produces, as a byproduct, also inflation near the initial singularity. The theory has been applied to fit the luminosity data of 192 type Ia supernovae. The results are satisfying and comparable with the ones obtained by means of the Λ Cold Dark Matter standard model.

Variable caster steering in vehicle dynamics

2017 ◽  
Vol 232 (9) ◽  
pp. 1270-1284 ◽  
Author(s):  
Dai Q Vo ◽  
Hormoz Marzbani ◽  
Mohammad Fard ◽  
Reza N Jazar
Keyword(s):  
Kinematic Model ◽  
Lateral Force ◽  
Lateral Acceleration ◽  
Steering Wheel ◽  
Force Model ◽  
Front Suspension ◽  
The Road ◽  
Handling Characteristics ◽  
Centre Of Rotation ◽  
Vehicle Dynamic Model

When a car is cornering, its wheels usually lean away from the centre of rotation. This phenomenon decreases lateral force, limits tyre performance and eventually reduces the vehicle lateral grip capacity. This paper proposes a strategy for varying caster in the front suspension, thereby altering the wheel camber to counteract this outward inclination. The homogeneous transformation was utilised to develop the road steering wheel kinematics which includes the wheel camber with respect to the ground during a cornering manoeuvre. A variable caster scheme was proposed based on the kinematic analysis of the camber. A rollable vehicle model, along with a camber-included tyre force model, was constructed. MATLAB/Simulink was used to simulate the dynamic behaviour of the vehicle with and without the variable caster scheme. The results from step steer, ramp steer, and sinusoidal steer inputs simulations show that the outward leaning phenomenon of the steering wheels equipped with the variable caster, is reduced significantly. The corresponding lateral acceleration and yaw rate increase without compromising other handling characteristics. The actively controlled car, therefore, provides better lateral stability compared to the passive car. The tyre kinematic model and the vehicle dynamic model were validated using multibody and experimental data.

The propagation of elastic waves in a certain class of inhomogeneous anisotropic materials. I. The refraction of a horizontally polarized shear wave source

1992 ◽  
Vol 436 (1898) ◽  
pp. 449-478 ◽  
Keyword(s):  
Shear Wave ◽  
Isotropic Material ◽  
Displacement Vector ◽  
Transversely Isotropic ◽  
Constitutive Law ◽  
Coarse Grained ◽  
Wave Source ◽  
Uniform Asymptotic Expansion ◽  
Wide Range ◽  
Steel Welds

This paper is the first in a series of articles describing the refraction and propagation of infinitesimal disturbances in a 'coarse grained’ inhomogeneous anisotropic material which is fused to an isotropic substrate. Here, the basic constitutive law for the material is motivated by applications to the non-destructive evaluation of austenitic steel welds, although it is clear that the phenomena described and the mathematical analysis used is also of interest in geophysics, the study of composite materials and several other areas of continuum mechanics. This work is concerned with the refraction of a horizontally polarized shear wave source at the fusion interface between a homogeneous isotropic material and transversely isotropic material. The latter is inhomogeneous by virtue of the fact that the zonal axis or axis of symmetry of the crystals varies in direction with the distance from the interface. The mathematical boundary-value problem is solved exactly, and, in the highfrequency limit, a uniform asymptotic expansion for the displacement vector is found. It is shown that in this limit, and for a wide range of material constants, the refracted energy which penetrates certain regions of the ‘weld material’ is totally internally reflected. This conclusion is highly significant in the design of inspection procedures for structurally important welds.

Nonvibrating energy strings as fundamental building blocks of space and particles

2019 ◽  
Vol 32 (3) ◽  
pp. 338-352
Author(s):  
Albert Zur (Albo)
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Displacement Vector ◽  
Building Blocks ◽  
Space Time ◽  
Accelerated Expansion ◽  
Absolute Space ◽  
Position Space ◽  
3D Space ◽  
The Universe

In the proposed Energy String (ES) theory, we assume the existence of fundamental energy strings forming a generally Euclidean four-dimensional fabric of empty space as well as forming all types of particles in the universe. The 4D space fabric is composed of space energy strings bearing dark-energy as well as a newly described dark-momentum. Particles are composed of particle energy strings which interact with space energy strings inducing three-dimensional space curvatures embedded in a flat fourth-space dimension. The induced space curvatures are responsible for gravity of particles and assign a longitudinal and a transverse direction to particles. The proposed ES theory yields an adapted model of the universe with remarkable teachings as follows: (1) The fabric of space and related dark-energy are associated with a newly defined dark-momentum. This dark momentum is the sole contributor to the cosmological constant Λ in Einstein's field equations which describes the accelerated expansion of the universe. The energy of the quantum vacuum becomes nonrelevant to the cosmological constant Λ, enabling a solution to the “Cosmological Constant Problem”; (2) All particles perform an equal distance of translatory displacement in 4D-space, reflecting a universal displacement rate of particles relative to an absolute generally Euclidean 4D-space. This universal principle is equivalent to Lorentz transformation of a fundamental four-displacement vector, representing a new model of Special Relativity with superior compatibility to quantum theories. (3) Time is a displacement property of mass particles in 4D-space. Frames of 3D-space+time are the perspective by which mass particles experience 4D-space. In this perspective, absolute space longitudinally displaces over mass particles experienced as proper time elapse. Temporal momentum is an inherent invariant property of mass particles. Frames of 3D-space+time are mixed domains: three spatial coordinates of position-space and a temporal coordinate of momentum-space, meaning the position-space in the temporal coordinate is totally inaccessible.

Experimental Investigation on Brazilian Tensile Strength of Organic-Rich Gas Shale

SPE Journal ◽  
2016 ◽  
Vol 22 (01) ◽  
pp. 148-161 ◽  
Author(s):  
Hui Li ◽  
Bitao Lai ◽  
Hui-Hai Liu ◽  
Jilin Zhang ◽  
Daniel Georgi
Keyword(s):  
Tensile Strength ◽  
Water Content ◽  
Scale Effects ◽  
Transversely Isotropic ◽  
Fracture Initiation ◽  
Bedding Plane ◽  
Organic Content ◽  
Eagle Ford ◽  
X Ray ◽  
Mancos Shale

Summary Tensile strength is a critical parameter for hydraulic fracturing, predicting fracture initiation and propagation in reservoirs, especially in shale reservoirs with complex natural fractures and fissures. The tensile strength of conventional rocks, such as sandstone and limestone, has been well-studied and -documented. There are many studies of the tensile strength of laminated shale, which focus on scale effects, loading direction, and temperature effects; however, the studies on effects of mineralogy and the water content on tensile strength of organic-rich shales are very limited. The objectives of this paper are to (1) critically review the key parameters that affect the tensile strength of shale and 2) experimentally examine the effects of water content, mineralogy, and lamination on tensile strength. To do so, a rigorous workflow is followed: 1) Each 1-in.-long shale sample is cut into two subsamples, A and B, of similar length; (2) X-ray computed-tomography (CT) scan is performed to diagnose pre-existing cracks and defects inside the core plugs; (3) nuclear magnetic resonance (NMR) is then used to measure the air dry samples’ water content; (4) Sample A is placed on a load frame to measure the tensile strength; (5) Sample B is vacuumed and then saturated; (6) NMR is used to measure the water content after saturation; (7) tensile strength of the saturated Sample B is measured; and (8) after the sample fails, the pieces are used for X-ray diffraction (XRD), scanning electron microscopy (SEM), and pyrolysis to estimate the mineralogy and total organic content (TOC). A total of 70 Mancos and 48 Eagle Ford shale samples have been tested. The experimental results show that (1) bedding plane/lamination has a significant effect on Eagle Ford tensile strength, but no pronounced impact is observed for the Mancos shale; (2) the imbibed water significantly reduces the tensile strength by 4.4 to 51.7% as water content increases from 4.45 to 11.7%; (3) pre-existing detectable microfractures can significantly reduce the tensile strength by up to 66%; (4) Eagle Ford exhibits typical brittle hard-rock failure configuration, with primary fractures and secondary fractures being observed, whereas for the Mancos shale, only primary fractures are observed; (5) acoustic velocity-test results confirm that Eagle Ford is mechanically transversely isotropic, and Mancos is likely mechanically isotropic.

scholarly journals On axially symmetric space–times admitting homothetic vector fields in Lyra’s geometry

2016 ◽  
Vol 94 (11) ◽  
pp. 1148-1152
Author(s):  
Ragab M. Gad ◽  
A.E. Al Mazrooei
Keyword(s):  
Vector Field ◽  
Symmetric Space ◽  
Vector Fields ◽  
Displacement Vector ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Homothetic Vector ◽  
Lyra’S Geometry

This paper investigates axially symmetric space–times that admit a homothetic vector field based on Lyra’s geometry. The cases when the displacement vector is a function of t and when it is constant are studied. In the context of this geometry, we find and classify the solutions of the Einstein’s field equations for the space–time under consideration, which display a homothetic symmetry.

Modeling and Simulation of Aligning Process for Alignment Mechanism of Large Aircraft Component

2012 ◽  
Vol 160 ◽  
pp. 351-355
Author(s):  
Zheng Ying ◽  
Ying Lin Ke
Keyword(s):  
Dynamic Models ◽  
Dynamic Performance ◽  
Kinematic Model ◽  
Force Model ◽  
Continuous Contact ◽  
Contact Force Model ◽  
Aircraft Component ◽  
Alignment Mechanism ◽  
Kinematic Joint ◽  
Large Aircraft

The dynamic performance of alignment mechanism of large aircraft component is directly associated with the structure and clearance of spherical joints. To accurately evaluate this influence, kinematic and dynamic models of spherical joints are developed. Firstly, a kinematic model of spherical joints is established. Secondly, a dynamic model of spherical joints is derived from the kinematic model and continuous contact force model. Finally, simulations of alignment mechanism of large aircraft component are carried out for typical moving trajectories. The influences of moving trajectory on the dynamic performance of mechanism are analysed. The simulation results are also applicable to similar mechanism design, moving trajectory planning and kinematic joint wear forecasting.

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