Relations between stress growth and stress relaxation functions

The stress relaxation function after steady shear flow and the stress growth function at inception of steady flow are derived for several constitutive equations of the integral and differential types. Relationships between these functions are deduced and discussed.     

Growth and remodeling in highly stressed solid tumors

Meccanica - Growing biological media develop residual stresses to make compatible elastic and inelastic growth-induced deformations, which in turn remodel the tissue properties modifying the actual...     

极坐标中应力与应力函数之间的关系

在极坐标下,通过极坐标的应力平衡方程推导出极坐标应力（）与应力函数之间的关系．     

On the interplay between material flaws and dynamic necking

In this paper we investigate the interplay between material defects and flow localization in elastoplastic bars subjected to dynamic tension. For that task, we have developed a 1D finite difference scheme within a large deformation framework in which the material is modelled using rate-dependent J₂ plasticity. A perturbation of the initial yield stress is introduced in each node of the finite difference mesh to model localized material flaws. Numerical computations are carried out within a wide spectrum of strain rates ranging from 500 s⁻¹ to 2500 s⁻¹. On the one hand, our calculations reveal the effect of the material defects in the necking process. On the other hand, our results show that the necking inception, instead of being a random type process, is the deterministic result of the interplay between the mechanical behaviour of the material and the boundary conditions. This conclusion agrees with the experimental evidence reported by Rittel et al. [1] and Rotbaum et al. [2].     

The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition

An assessment of the stress tensors used currently for the modeling of partially saturated porous media is made which includes concepts like total stress, solid phase stress, and solid pressure. Thermodynamically constrained averaging theory is used to derive the solid phase stress tensor. It is shown that in the upscaling procedure the Hill conditions are satisfied, which is not trivial. The stress tensor is then compared to traditional stress measures. The physical meaning of two forms of solid pressure and of the Biot coefficient is clarified. Finally, a Bishop-Skempton like form of the stress tensor is obtained and a form of the total stress tensor that does not make use of the effective stress concept.     

On the measurement of stress in solid propellant

The problems related to the direct measurement of stresses in solid propellant are identified and reviewed. The piezoresistance phenomenon is discussed and it is shown how this phenomenon can be utilized to measure stresses in elastomers and solid propellant. One version of a piezoresistive stress transducer is used to measure radial stresses in an uncontained thick-walled elastic cylinder which is internally pressurized. A smaller similar version of the piezoresistive stress transducer is employed in a rosette configuration to measure the stress state at five critical locations in a quarter-scale Surveyor solid-propellant motor three times during a four-year storage period. The instrumentation and calibration of these piezoresistive stress transducers are briefly described.     

The interaction between shock waves and solid spheres arrays in a shock tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in the wave propagation process. The wave interactions with vortices behind each sphere‘s wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.     

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

The present paper presents a general treatment of the transient thermoelastic stresses in a rotating nonhomogeneous anisotropic solid under compressive initial stress. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for the temperature, displacement components and stress components. The results indicate that the effects of inhomogeneity and initial stress are very pronounced.     

The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions

We study shear banding flows in models of wormlike micelles or polymer solutions, and explore the effects of different boundary conditions for the viscoelastic stress. These are needed because the equations of motion are inherently non-local and include “diffusive” or square-gradient terms. Using the diffusive Johnson–Segalman model and a variant of the Rolie-Poly model for entangled micelles or polymer solutions, we study the interplay between different boundary conditions and the intrinsic stress gradient imposed by the flow geometry. We consider prescribed gradient (Neumann) or value (Dirichlet) of the viscoelastic stress tensor at the boundary, as well as mixed boundary conditions in which an anchoring strength competes with the gradient contribution to the stress dynamics. We find that hysteresis during shear rate sweeps is suppressed if the boundary conditions favor the state that is induced by the sweep. For example, if the boundaries favor the high shear rate phase then hysteresis is suppressed at the low shear rate edges of the stress plateau. If the boundaries favor the low shear rate state, then the high shear rate band can lie in the center of the flow cell, leading to a three-band configuration. Sufficiently strong stress gradients due to curved flow geometries, such as that of cylindrical Couette flow, can convert this to a two-band state by forcing the high shear rate phase against the wall of higher stress, and can suppress the hysteresis loop observed during a shear rate sweep.     

MASS TRANSPORT IN SOLID TUMORS(Ⅱ)──DRUG DELIVERY

Based on the flow field solution of the three-porous-medium model for tumor microcirculation, the diffusion-convection equations are solved with various initial and boundary conditions using finite element method. The concentration profile of two therapeutic agents: immunoglobulin G (IgG) and its antigen-binding fragment (Fab) in blood, lymph and interstitial fluid are obtained for normal-tissue-surrounded tumor. The effect of tumor microvasculature, lymph function, drug injection mode, the molecular weight and binding kinetics of the drug on the distribution in tumors are also considered.     

MASS TRANSPORT IN SOLID TUMORS (Ⅰ)──FLUID DYNAMICS

A three-porous-medium model for transvascular exchange and extravascular transport of fluid and macromolecules in a spherical solid tumor is developed. The microvasculature, lymphatics, and tissue space are each treated as a porous medium with the flow of blood. lymph, and interstitial fluid obeying Darcy’s law and Starling’s assumption. In this part, the role of interstitial pressure and fluid convection are studited. The analytical soiutions are obtained for foe isolated tumor and the normal-tissue-surrounded tumor respectively. The calculated interstitial pressure profue are consistent with the experimental observation that the elevated interstitial pressure is a major barrier in the penetration of macromolecular drug into tumors. The factors which may reduce the interstitial pressure are analyzed in details.     

On the interplay between inertial and viscoelastic effects for the flow in weakly modulated channels

The flow inside a spatially modulated channel is examined for viscoelastic fluids of the Oldroyd‐B type. The lower wall is flat and the upper wall is sinusoidally modulated. The modulation amplitude is assumed to be small. Thus, a regular perturbation expansion of the flow field coupled to a variable‐step finite‐difference scheme is used to solve the problem. Convergence and accuracy assessment against earlier experimental results indicate that there is a significant range of validity of the perturbation approach. The influences of wall geometry, inertia and viscoelasticity on the flow kinematics and stresses are investigated systematically. In particular, the interplay between the flow and fluid parameters effects on the conditions for the onset of backflow, number of vortices, their size and location is revealed. The distance between the flow separation and reattachment locations identifies the vortex size. Non‐monotonic dependence of the vortex size on elasticity is reported. The critical conditions for the onset of negative elasticity effects on vortex size are identified. The critical Reynolds number for the onset of backflow initially decreases then levels off or even increases as elasticity increases. For highly elastic fluid and large enough Reynolds number, more than one vortex appear near the lower wall. Copyright © 2005 John Wiley & Sons, Ltd.     

Contact laws between solid particles

This paper presents a comprehensive study for the contact laws between solid particles taking into account the effects of plasticity, strain hardening and very large deformation. The study takes advantage of the development of a so-called material point method (MPM) which requires neither remeshing for large deformation problems, nor iterative schemes to satisfy the contact boundary conditions. The numerical results show that the contact law is sensitive to impact velocity and material properties. The contact laws currently used in the discrete element simulations often ignore these factors and are therefore over-simplistic. For spherical particles made of elastic perfectly plastic material, the study shows that the contact law can be fully determined by knowing the relative impact velocity and the ratio between the effective elastic modulus and yield stress. For particles with strain hardening, the study shows that it is difficult to develop an analytical contact law. The same difficulty exists when dealing with particles of irregular shapes or made of heterogeneous materials. The problem can be overcome by using numerical contact laws which can be easily obtained using the material point method.     

The effect of rotation and initial stress on the propagation of waves in a transversely isotropic elastic solid

In this paper the equations governing small amplitude motions in a rotating transversely isotropic initially stressed elastic solid are derived, both for compressible and incompressible linearly elastic materials. The equations are first applied to study the effects of initial stress and rotation on the speed of homogeneous plane waves propagating in a configuration with uniform initial stress. The general forms of the constitutive law, stresses and the elasticity tensor are derived within the finite deformation context and then summarized for the considered transversely isotropic material with initial stress in terms of invariants, following which they are specialized for linear elastic response and, for an incompressible material, to the case of plane strain, which involves considerable simplification. The equations for two-dimensional motions in the considered plane are then applied to the study of Rayleigh waves in a rotating half-space with the initial stress parallel to its boundary and the preferred direction of transverse isotropy either parallel to or normal to the boundary within the sagittal plane. The secular equation governing the wave speed is then derived for a general strain–energy function in the plane strain specialization, which involves only two material parameters. The results are illustrated graphically, first by showing how the wave speed depends on the material parameters and the rotation without specifying the constitutive law and, second, for a simple material model to highlight the effects of the rotation and initial stress on the surface wave speed.     

Prediction of stress in a linear viscoelastic solid strained while cooling

A simplethermoelastic method is proposed, and justified, for predicting stresses arising during cooling of a linearviscoelastic solid. It is equivalent to representing the material by an array of spring-switch thermoelastic elements. The final stress resulting from an increment of strain is calculated using isochronal modulus data applying to the temperature at which the strain was applied, modified to accommodate temperature dependence of the limiting moduli. The method is exact for a material whose relaxation times and limiting moduli scale uniformly with change in temperature, with time-temperature shift factora _T obeying the Arrhenius equation, cooled such that reciprocal absolute temperature is linear in time. For other cooling sequences it is useful as an approximation. In particular, it assists the computational prediction of stresses arising during cooling in polymer processes.     

横观各向同性体应力波传播问题的特征分析

本文根据广义特征理论,对横观各向同性体轴对称弹性波传播问题进行了理论分析。提出了一个简化特征分析的方法,这种方法将成为应用特征线法求解各类各向异性应力波问题的一个突破口。     

Characteristics of adhesion between soil and solid surfaces

The capillary attraction and viscous resistance caused by a water film between two solid surfaces were evaluated theoretically. The surface morphology of soil at the soil-solid adhesion interface was examined by scanning electron microscopy. The contact models of the soil adhesion interface are given and mechanism of the normal adhesion is discussed. The wettability and normal soil adhesion of polytetrafluoroethylene (PTFE) sheet, polyethersulforne (PES)-PTFE coating, enamel coating, iron base alloy-epoxy composite coating and the conventional material were determined. The draft force of ploughs with mouldboards coated with PES-PTFE, enamel and iron base alloy-epoxy and the conventional mouldboard plough were measured. The soil surface at the soil-solid interface displays rough structure at various sizes. The adhesion force between soil and solid is mainly composed of Laplace pressure, meniscus tension and viscous resistance caused by water film and loops. Polymers can reduce both normal adhesion and sliding resistance, whereas, enamel coating or iron base alloy-epoxy composite coating can reduce the sliding resistance to some extent.