Continuum Mechanics of Space Seen from the Aspect of General Relativity An Interpretation of the Gravity Mechanism

A mechanical structure of space is suggested. On the supposition that a space as vacuum has a physical fine structure like continuum, it enables us to apply a continuum mechanics to the so-called ＂vacuum＂ of space. A space is an infinite continuum and its structure is determined by Riemannian geometry. Assuming that space is an infmite continuum, the pressure field derived from the geometrical structure of space is newly obtained by applying both continuum mechanics and General Relativity to space. A fundamental concept of space-time is described that focuses on theoretically innate properties of space including strain and curvature. As a trial consideration, gravity can be explained as a pressure field induced by the curvature of space.

Trans-scale mechanics: looking for the missing links between continuum and micro/nanoscopic reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frame-works of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of trans-scale problems （problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/ molecules and a finite size body at micro/nano-level） and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.

New approach based on continuum damage mechanics with simple parameter identification to fretting fatigue life prediction

A new continuum damage mechanics model for fretting fatigue life prediction is established. In this model, the damage evolution rate is described by two kinds of quantities. One is associated with the cyclic stress characteristics obtained by the finite element （FE） analysis, and the other is associated with the material fatigue property identified from the fatigue test data of standard specimens. The wear is modeled by the energy wear law to simulate the contact geometry evolution. A two-dimensional （2D） plane strain FE implementation of the damage mechanics model and the energy wear model is presented in the platform of ABAQUS to simulate the evolutions of the fatigue damage and the wear scar. The effect of the specimen thickness is also investigated. The predicted results of the crack initiation site and the fretting fatigue life agree well with available experimental data. Comparisons are made with the critical plane Smith- Watson-Topper （SWT） method.

Lie symmetry and Mei continuum conservation law of system＊

Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper. The equation of motion of continuum system is established by using variational principle of continuous coordinates. The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric. The condition of obtaining Mei conservation theorem from Lie symmetry is also presented. An example is discussed for applications of the results.

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.

A Hybrid Local/Nonlocal Continuum Mechanics Modeling of Damage and Fracture in Concrete Structure at High Temperatures

This paper proposes a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures.In this model,we introduce the thermal expansion into peridynamics and then couple it with the thermoelasticity based on the Morphing method.In addition,a thermomechanical constitutive model of peridynamic bond is presented inspired by the classic Mazars model for the quasi-brittle damage evolution of concrete structures under high-temperature conditions.The validity and effectiveness of the proposed model are verified through two-dimensional numerical examples,in which the influence of temperature on the damage behavior of concrete structures is investigated.Furthermore,the thermal effects on the fracture path of concrete structures are analyzed by numerical results.

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.

A CONTINUUM DAMAGE MODEL OF AGING CONCRETE

There is up to now no constitutive model in the current theoriesof CDM that could give a description for the degradation of agingconcrete. The two internal state variable β and ω are intro- ducedin this paper β is called cohesion variable as an additionalkinematic parameter, reflecting the cohesion state among materialparticles. ω is called damage factor for micro-defects such s voids.Then a damage model and a series of constitutive equations aredeveloped on Continuum Mechanics. The model proposed could give avalid description for the whole-course-degradation of aging concretedue to chemical and mechanical actions. Finally, the validity of themodel is evaluated by an example and experimental results.

Ductile Fracture Characterization for Medium Carbon Steel Using Continuum Damage Mechanics

This paper presents the ductility characterization for a medium carbon steel, for two microstructural conditions, that has been evaluated using the continuum damage mechanics theory, as proposed by Kachanov and developed by Lemaitre. Tensile tests were carried out using loading-unloading cycles in order to capture the gradual deterioration of the elastic modulus, which may be linked to the ductile damage increase with increasing plastic strain. The mechanical parameters for the isotropic damage evolution equation were obtained and then used as inputs for a plasticity-damage coupled nu- merical algorithm, validated through numerical simulations of the experimental tensile tests. A comparison between the SAE 1050 steels studied and two carbon steel alloys (obtained from the literature), provided some basic understanding of the influence of the carbon level on the evolution of the damage parameters. An empiric relationship for this set of parameters, which can provide useful data for preliminary studies envisaging prediction of ductile failure in carbon steels, is also presented.

A New Class of Simple,General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems

In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.

Curved Space-Time at the Planck Scale

This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.

Derivation of Cylindrical Internal-Surface Acoustic Waves and Their Small Gravity Effect

The properties of Cylindrical Internal-Surface Acoustic Waves (CISAW) propagating on the inside surface of a high purity fused quartz tubular fiber are derived from basic principles using a variational method. The CISAW consist of Energy Momentum Packets (EMP) moving in a looping motion. The EMP have mass and are affected by gravity similar to a pendulum bob. The effect of gravity on CISAW is much larger than the effect of gravity in a light wave. Therefore, one can build much smaller CISAW Interferometer Gravity wave Observatories (CIGO) than the present km size Light Interferometer Gravity wave Observatories (LIGO). An array of CIGO can be used to detect gravity wave images. Since the wavelength of gravity waves is much larger than the expected spacing between CIGO array elements this would result in sub-wavelength images. It would be interesting to determine what new discoveries could be made using such an array.

Damage evolution model of strain hardening cementitious composites under the uniaxial stress state

The deformation and damage behaviors of strain hardening cementitious composites （SHCC） under the uniaxial stress state were investigated in this paper. Two ductile failure-based constitutive models were introduced to describe the uniaxial tension and compression properties of SHCC only using a few parameters. The computation method of model parameters was developed to ease the simulation procedures. Damage evolution of the SHCC was simulated by the formulation of continuum damage mechanics subsequently. The results show that the proposed models fit the stress-strain curves reasonably well, and the damage variables show different growth rules under uniaxial tension and compression. It is concluded that the proposed method can not only simply simulate the constitutive behavior of SHCC with the reasonable accuracy but also capture the characteristic of material degradation.

VARIATIONAL PRINCIPLFS OF NONLINEAR PIEZOTHERMOELASTIC MEDIA

Through the phenomenological approach,the nonlinear constitutive equations coupling the electro/magnetic therrnoelastic media are derived.Several nonlinear variational principles for piezothermoelastic continua are presented and employed to formulate the incremental variational princi- ples which are of important significance in practical applications such as the nonlinear finite element analysis,the buckling,postbuckling and dynamic stability analyses of piezoelectric smart structures.

Investigation of FE Model Size Definition for Surface Coating Application

An efficient prediction mechanical performance of coating structures has been a constant concern since the dawn of surface engineering. However, predictive models presented by initial research are normally based on traditional solid mechanics, and thus cannot predict coating performance accurately. Also, the high computational costs that originate from the exclusive structure of surface coating systems （a big difference in the order of coating and substrate） are not well addressed by these models. To fill the needs for accurate prediction and low computational costs, a multi-axial continuum damage mechanics （CDM）-based constitutive model is introduced for the investigation of the load bearing capacity and fracture properties of coatings. Material parameters within the proposed constitutive model are determined for a typical coating （TIN） and substrate （Cu） system. An efficient numerical subroutine is developed to implement the determined constitutive model into the commercial FE solver, ABAQUS, through the user-defined subroutine, VUMAT. By changing the geometrical sizes of FE models, a series of computations are carried out to investigate （1） loading features, （2） stress distributions, and （3） failure features of the coating system. The results show that there is a critical displacement corresponding to each FE model size, and only if the applied normal loading displacement is smaller than the critical displacement, a reasonable prediction can be achieved. Finally, a 3D map of the critical displacement is generated to provide guidance for users to determine an FE model with suitable geometrical size for surface coating simulations. This paper presents an effective modelling approach for the prediction of mechanical performance of surface coatings.

Revised damage evolution equation for high cycle fatigue life prediction of aluminum alloy LC4 under uniaxial loading

The fatigue life prediction for components is a difficult task since many factors can affect the final fatigue life. Based on the damage evolution equation of Lemaitre and Desmorat, a revised two-scale damage evolution equation for high cycle fatigue is presented according to the experimental data, in which factors such as the stress amplitude and mean stress are taken into account. Then, a method is proposed to obtain the material parameters of the revised equation from the present fatigue experimental data. Finally, with the utilization of the ANSYS parametric design language （APDL） on the ANSYS platform, the coupling effect between the fatigue damage of materials and the stress distribution in structures is taken into account, and the fatigue life of specimens is predicted. The outcome shows that the numerical prediction is in accord with the experimental results, indicating that the revised two-scale damage evolution model can be well applied for the high cycle fatigue life prediction under uniaxial loading.

Progressive Damage Analysis(PDA)of Carbon Fiber Plates with Out-of-Plane Fold under Pressure

The out-of-plane fold is a common defect of composite materials during the manufacturing process and will greatly affect the compressive strength as well as the service life.Making it of great importance to investigate the influence of out-of-plane defects to the compressive strength of laminate plates of composite materials,and to understand the patterns of defect evolution.Therefore,the strip method is applied in this article to create out-of-plane defects with different aspect ratios in laminated plates of composite materials,and a compressive performance test is conducted to quantify the influence of out-of-plane defects.The result shows that the compressive strength becomes weaker with a greater aspect ratio.When the highest aspect ratio is set to 0.12 in the experiment,the compressive strength reduces by 36.1%.Then we establish a 3-D progressive damage model based on continuum mechanics,and write it into the UMAT subroutine together with the 3-D Hashin criteria and the non-linear degradation criteria of materials.3-D solid modeling is performed for the samples with an out-of-plane fold based on ABAQUS,and progressive damage analysis is conducted to acquire the inplane evolution process of initial failure strength with different laminates.The experimental results agree well with the simulation results.

GUIDED CIRCUMFERENTIAL WAVES IN DOUBLE-WALLED CARBON NANOTUBES

A model of guided circumferential waves propagating in double-walled carbon nanotubes is built by the theory of wave propagation in continuum mechanics, while the van der Waals force between the inner and outer nanotube has been taken into account in the model. The dispersion curves of the guided circumferential wave propagation are studied, and some dispersion characteristics are illustrated by comparing with those of single-walled carbon nanotubes. It is found that in double-walled carbon nanotubes, the guided circumferential waves will propagate in more dispersive ways. More interactions between neighboring wave modes may take place. In particular, it has been found that a couple of wave modes may disappear at a certain frequency and that, while a couple of wave modes disappear, another new couple of wave modes are excited at the same wave number.

ELECTRIC FIELD EFFECTS ON YOUNG'S MOLULUS OF NANOWIRES

As an important component of nanodevices and nanomachine constructions, the mechanical performance of nanowires （NWs） has been a subject of intense research efforts due to gaining relevance in controlling functionality of nanoelectromechanical systems （NEMS）; meanwhile, one of the characteristics of the NEMS is the dependence of the functionality of the systems upon the applied electric field. The study of the electric effects on the Young＇s modulus of nanostructures is of certain usefulness in the design of NEMS and the precise measurement of mechanical properties of one-dimensional nanostructures. This paper reviews the origin of the size-dependence of the elastic property of NWs and the factors influencing the discrepancies and inconsistencies in the measured values of the Young＇s modulus for the NW, besides the surface effects, nonlinear effects, the electromechanical coupling effects as a possible effect responsible for the differences in quantitative and qualitative performance of the measured Young＇s modulus for the NWs versus the diameter are clarified.

Multi-fracture interactions during two-phase flow of oil and water in deformable tight sandstone oil reservoirs

Tight oil reservoirs are complex geological materials composed of solid matrix,pore structure,and mixed multiple phases of fluids,particularly for oil reservoirs suffering from high content of in situ pressurized water found in China.In this regard,a coupled model considering two-phase flow of oil and water,as well as deformation and damage evolution of porous media,is proposed and validated using associated results,including the oil depletion process,analytical solution of stress shadow effect,and physical experiments on multi-fracture interactions and fracture propagation in unsaturated seepage fields.Then,the proposed model is used to study the behavior of multi-fracture interactions in an unsaturated reservoir in presence of water and oil.The results show that conspicuous interactions exist among multiple induced fractures.Interaction behavior varies from extracted geological profiles of the reservoir due to in situ stress anisotropy.The differential pressures of water and that of oil in different regions of reservoir affect interactions and trajectories of multi-fractures to a considerable degree.The absolute value of reservoir average pressure is a dominant factor affecting fracture interactions and in favor of enhancing fracture network complexity.In addition,difference of reservoir average pressures in different regions of reservoir would promote the fracturing effectiveness.Factors affecting fracture interactions and reservoir treatment effectiveness are quantitatively estimated through stimulated reservoir area.This study confirms the significance of incorporating the two-phase flow process in analyses of multifracture interactions and fracture trajectory predictions during tight sandstone oil reservoir developments.