ENERGY PRINCIPLES IN THEORY OF ELASTIC MATERIALS WITH VOIDS

According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author, various energy principles in theory of elastic materials with voids can be established systematically, In this paper, an important integral relation is given, which can be considered essentially as the generalized pr- inciple of virtual work. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem of work in theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field and two-field generalized variational principles, and the principle of minimum potential and complementary energies. Furthermore, with this appro ach, the intrinsic relationship among various principles can be explained clearly.

Cavitation for Incompressible Anisotropic Hyper-Elastic Materials

The cavitation problem in a solid sphere composed of an incompressible anisotropic hyper elastic material under a uniform radial tensile dead load was examined. A new analytical solution was obtained. The stress contributions were given and the jumping and concentration of stresses were discussed. The stability of solutions and the effect of the degree of anisotropy of the material were analyzed.

ON SOME BASIC PRINCIPLES IN DYNAMIC THEORY OF ELASTIC MATERIALS WITH VOIDS

According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids,but also to derive systematically the complementary functionals for the eight-field,six-field, four-field and two-field simplified Gurtin-type variational principles.Furthermore,with this approach,the in- trinsic relationship among various principles can be explained clearly.

EVOLUTION OF ROUGHNESS ON THE SURFACE OF A STRAINED ELASTIC MATERIAL DUE TO STRESS-DRIVEN SURFACE DIFFUSION

The free energy of a stressed crystal is assumed to consist of elastic strain energy and surface energy, and the chemical potential for surface diffusion at constant temperature is obtained under this assumption. A gradient in chemical potential results in diffusive mass transport along the surface. The result is applied in considering the phenomena of instability of a flat surface in a stressed material under fluctuations in surface shape, and the transient evolution of surface roughness due to an initial perturbation in the nearly flat free surface of the material, both under plane strain conditions.

Derivation of the Orthotropic Nonlinear Elastic Material Law Driven by Low-Cost Data(DDONE)

Orthotropic nonlinear elastic materials are common in nature and widely used by various industries.However,there are only limited constitutive models available in today's commercial software(e.g.,ABAQUS,ANSYS,etc.)that adequately describe their mechanical behavior.Moreover,the material parameters in these constitutive models are also difficult to calibrate through low-cost,widely available experimental setups.Therefore,it is paramount to develop new ways to model orthotropic nonlinear elastic materials.In this work,a data-driven orthotropic nonlinear elastic(DDONE)approach is proposed,which builds the constitutive response from stress–strain data sets obtained from three designed uniaxial tensile experiments.The DDONE approach is then embedded into a finite element(FE)analysis framework to solve boundary-value problems(BVPs).Illustrative examples(e.g.,structures with an orthotropic nonlinear elastic material)are presented,which agree well with the simulation results based on the reference material model.The DDONE approach generally makes accurate predictions,but it may lose accuracy when certain stress–strain states that appear in the engineering structure depart significantly from those covered in the data sets.Our DDONE approach is thus further strengthened by a mapping function,which is verified by additional numerical examples that demonstrate the effectiveness of our modified approach.Moreover,artificial neural networks(ANNs)are employed to further improve the computational efficiency and stability of the proposed DDONE approach.

Research on sound velocity measurement in a laboratory for large elastic materials

A measurement scheme carried out in a tank is designed to obtain the compressionaland shear-wave velocities of a large elastic material.A hydrophone is used to receive the high frequency acoustic signals which penetrate the tested material,in order to determine the transmission time from the source to the hydrophone,the transmission time is also calculated according to the ray acoustic theory in layered media.A cost function is built based on the measured and the calculated transmission time,then the compressional- and shear-wave velocities can be obtained using the optimization algorithm.Compared with the traditional measurement scheme,this approach can not only get the 2 kinds of sound velocities in the tested material at the same time,but also keep the integrality of the tested material.With the proposed measurement system,the uncertainty of measurement results is less than 3.5%.

Characterization of Elastic Modulus of Granular Materials in a New Designed Uniaxial Oedometric System

A simple uniaxial oedometric system is developed to test the elastic modulus of granular materials. The stress- strain relationship is first measured under conditions of uniaxial compression with additional lateral stress and strain, then the elastic modulus of the material is determined by the linear fitting method. It is found that the modulus is positively correlated to the grain size and negatively correlated to the container size. Arching and dragging are revealed to be the mechanism of such correlations by using the digital image correlation method and the pressure film technology based on the statistical method.

AN INVESTIGATION ON ASYMPTOTIC NEAR-TIP FIELDS OF DYNAMIC CRACK IN AN ELASTIC-PERFECTLY PLASTIC COMPRESSIBLE MATERIAL

The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of infinitesimal displacement gradient theory, the material is characterized by the Von Mises yield criterion and the associated J(2) flow theory of plasticity. Through rigorous mathematical analysis, this paper eliminates the possibilities of elastic unloading and continuous asymptotic fields with singular deformation, and then constructs a fully continuous and bounded asymptotic stress and strain field. It is found that in this solution there exists a parameter phi(0) which cannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly the variations of continuous stresses, velocities and strains around the crack tip are given numerically for different values of phi(0).

A MATHEMATICAL THEORY OF MATERIALS WITH ELASTIC RANGE AND THE DEFINITION OF BACK STRESS TENSOR

In this paper, the theory of materi als with elastic range by Lucchesi and Podio_Guidugli(1988) has been generalized . It has also shown that there are some difficulties on the definition of back s tress as the “center” of the yield surface in the Cauchy space. The back stres s tensor is Lagrangian,and must be defined in the Lagrangian stress space.

MATERIAL MULTIPOLE MECHANICS OF ELASTIC DIELECTRIC COMPOSITES

The overall mechanical and electrical behaviors of elastic dielectric composites are investigated with the aid of the concept of material multipoles. In particular, by introducing a statistical continuum material multipole theory, the effects of the electric-elastic interaction and the microstructure (size, shape, orientation,...) of inhomogeneous particles on the overall behaviors of the composites can be obtained. A basic solution for an ellipsoidal elastic inhomogeneity with electric polarization in an infinite elastic dielectric medium is first given, which shows that classical Eshelby 's elastic solution is modified by the presence of electric-elastic interaction. The overall macroscopic constitutive relations and their overall macroscopic material parameters accounting for electroelastic interaction effect are then derived for the elastic dielectric composites. Some quantitative calculations on the problems with statistical anisotropy, the shape effect and the electric-elastic interaction are finally given for dilute composites.

Effect of partial elastic foundation on free vibration of fluid-filled functionally graded cylindrical shells

The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elas- tic foundations are investigated by an analytical method. The elastic foundation of partial axial and angular dimen- sions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear defor- mation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material prop- erties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh-Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.

NEAR-TIP FIELDS FOR A CRACK GROWING ALONG AN ELASTIC PERFECTLY PLASTIC INTERFACE

The stress and deformation fields near the tip of an anti-plane crack growing quasi-statically along an interface of elastic perfectly plastic materials are given in this paper. A family of solutions for the growing crack fields is found covering all admissible crack line shear stress ratios.

Nonlinear dynamic characteristics of piles embedded in rock

The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail.

Test and Analysis of the Sound Insulation Performance of Four Types of Timber Structure Floors under Jumping Excitation

To improve the impact sound insulation performance of building floors and meet the objective requirements for living comfort of residents,in this article,three kinds of elastic cushion materials,Portuguese cork board,BGL insulation sound insulation foam board,and EPP polypropylene plastic foam board,are applied to the sound insulation of a light frame wood floor structure of the same bedroom and compared to the ordinary floor.This study uses the transfer function method and transient excitation method to measure the sound insulation,damping ratio,and elastic modulus of materials,as well as the sound insulation of the floor under the jumping excitation method of daily behavior.Through comparative analysis,the results and factors of improving the sound insulation performance of the floor are obtained,according to which three types of elastic cushion materials and the floor covering composed of them have higher vibration and noise reduction performance.Among them,the overall sound insulation performance of BGL board floor is the highest,followed by EPP board and cork board floor,and ordinary OSB floor is the lowest.Under the jumping excitation method,three floating floors can improve the impact sound insulation performance of the middle and low-frequency bands.

Elastic Mechanical Stress Analysis in a 2D-FGM Thick Finite Length Hollow Cylinder with Newly Developed Material Model

In this paper a new 2D-FGM material model based on Mori-Tanaka scheme and third-order transition function has been developed for a thick hollow cylinder of finite length.Elastic mechanical stress analysis is performed by utilizing the finite element method.The corresponding material,displacement and stress distributions are evaluated for different values of nr and nz.Moreover,the effects of different material property distributions on the effective stress with respect to the metallic phase volume fraction are investigated.It is demonstrated that the increase in nr and V_m leads to a significant reduction in the effective stress.Finally,it is shown that the ceramic phase rich cylinder wall has lower maximum effective stresses of which the lowest value of effective stress has been evaluated for nr=20 and nz=5.This minimum value is about half the maximum effective stress which has been evaluated for the non-FGM cylinder case（nr=nz=0.1）.

Nanoindentation Characteristics of Cement Paste and Interfacial Transition Zone in Mortar with Rice Husk Ash

The nanostructure of cementitious materials has important effects on concrete properties. The effects of rice husk ash（RHA） on cement hydration product phases and interfacial transition zone（ITZ） in mortar were investigated from the nano-scale structure perspective. The experimental results indicate that, with the increase of RHA dosages of samples, the volume fraction of high-density calcium-silicate-hydrate（HD C-S-H） in porosity and hydration product phases increases. The volume fractions of HD C-S-H in C-S-H of samples show an increasing trend with the increase of RHA dosages. RHA decreases the thickness of ITZ and increases the matrix elastic moduli of samples, however, the RHA dosoges hardly affect the thickness and elastic moduli.

Gradient estimates for parabolic systems from composite material

In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.

Composite Waves for a Cell Population System Modeling Tumor Growth and Invasion

In the recent biomechanical theory of cancer growth,solid tumors are considered as liquid-like materials comprising elastic components.In this fluid mechanical view,the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate,with the latter depending on the local cell density(contact inhibition) or/and on the mechanical stress in the tumor.For the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modeling,the authors prove that there are always traveling waves above a minimal speed,and analyse their shapes.They appear to be complex with composite shapes and discontinuities.Several small parameters allow for analytical solutions,and in particular,the incompressible cells limit is very singular and related to the Hele-Shaw equation.These singular traveling waves are recovered numerically.

Optimal Control of a Frictional Contact Problem

We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca＇s friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.

BLUNT CRACK-TIP ELASTOPLASTIC ZONE OF MIXED MODE FRACTURE

This article discusses the characterization of fracture process zone at the tip of a blunt crack in elastoplastic materials under mixed mode loading. The analysis includes the description of elastoplastic zone geometry around the blunt crack tip for predicting crack growth direction. The deformed zone appearing at the crack front is described by presenting a criterion based on the subloading surface concept falling within the framework of unconventional plasticity. The mixed mode crack propagates along the minimum value of the elastoplastic region. The present solutions are reduced to those previously reported in literature, when the elastic perfectly plastic material is considered.