On the dynamics of non-linear viscoelastic solids with material moduli that depend upon pressure

We investigate the dynamic response, of a generalization of an incompressible Kelvin-Voigt viscoelastic solid, whose viscosity depends on the pressure. Bodies with pressure-dependent material moduli have relevance to numerous technologically significant problems in geomechanics, the mechanics of granular media and powder compaction. We obtain analytical results for creep and recovery phenomena as well as solutions to the propagation of waves in such bodies. We are able to obtain explicit exact solutions that clearly illustrate the marked difference in the response of bodies with pressure-dependent material moduli as opposed to their counterparts whose moduli do not depend on the pressure. We also show that the governing equations for such materials can change type, and that their solutions exhibit singularities and localization.     

Efficient and accurate approach for powder compaction problems

 In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations. Received: 20 March 2002 / Accepted: 15 October 2002 The partial financial support of the Ministerio de Ciencia y Tecnología (grant number DPI 2001-2204) is gratefully acknowledged.     

Thermomechanical stress fields in high-temperature fibrous composites. I: Unidirectional laminates

This two-part paper presents a closed-form procedure for evaluation of estimates of local thermomechanical stress fields in two-phase fibrous composites and laminates. The first part is concerned with a unidirectional elastic laminate subjected to uniform mechanical loads and to uniform changes in temperature. Both phases are assumed to be elastic, with temperature-dependent moduli and expansion coefficients; the solution reflects the influence of thermomechanical interactions. Exact solutions are not possible for any real system, because the local geometry is not known in detail. Instead, estimates of the fields are found from a modified Mori-Tanaka approximation. Examples are presented for two SiC/Ti---Al---Nb composites. Local stresses of interest are found after cooling from fabrication to room temperature. The presence of local yielding, and the influence of coupling terms on the local stress magnitudes are examined. Extension of the results to laminated plates is presented in Part II (Dvorak, G.J., Chen, T. & Teply, J., Composites Science and Technology, 43 (1992) 359–368, this issue).     

Viscoelastic Windows of Pressure-Sensitive Adhesives

A viscoelastic window (VW) concept has been proposed to identify different types of pressure-sensitive adhesives (PSA's). Such viscoelastic windows are constructed from the values of dynamic storage modulus: G' and dynamic loss modulus G' at frequencies of 10^-2 and 10² rad/sec. These frequencies are chosen because the range covers most of the time scales corresponding to the uses of PSA's at different application rates in performance tests. A four quadrant concept has also been recommended to categorize different types of PSA's based on the location of their VW's on the log-log cross plot of G' and G'. It was found that for most PSA's, the range of G' and G' at room temperature within these selected frequencies falls between 10³ and 10⁶ Pascals. The proposed four-quadrants (top-left hand quadrant of high G' and low G', top-right hand quadrant of high G' and high G', lower left hand quadrant of low G' and low G', and lower right-hand quadrant of low G' and high G') correspond respectively to (1) non-PSA or release coatings (2) high shear PSA's, (3) removable PSA's and medical PSA's and (4) quick and cold stick PSA's. It was also observed that the VW's of general purpose permanent PSA's occupy the central region which straddles part of the four quadrants.     

Development of damage in a 2D woven C/SiC composite under mechanical loading: I. Mechanical characterization

An investigation has been undertaken to determine the damage mechanisms and the associated mechanical response of a 2D reinforced composite of carbon fibers in an SiC CVI-processed matrix subjected to uniaxial tensile and compressive loadings at room temperature. Under tension loading, an extended non-linear stress/strain response was evidenced and related to a multi-stage development of damage involving transverse matrix microcracking, bundle/matrix and inter-bundle debonding as well as thermal residual stress release. This tensile behavior proved to be damageable-elastic with respect to a fictitious thermalstress-free origin of the stress/strain axis lying in the compression domain. In compression, after an initial stage involving closure of the thermal microcracks present from processing, the composite displayed a linear-elastic behavior until failure. The extent of damage over the material was characterized quantitatively at the microscale by the decrease of the average transverse microcrack spacing and at the macroscale by the decrease of both the longitudinal Young's modulus and the in-plane Poisson's ratio.     

铝/空心微珠复合材料弹性性能的预测研究

根据复合材料的基本原理建立了复合材料弹性模量的本构方程，在这基础上利用有限元的方法预测了空心微珠增强铝基复合材料的弹性模量，并在模拟中考察了空心微珠体积百分比（Vf）、空心微珠壁厚与空心微珠半径的比值（t／R）两个参数对弹性模量的影响。通过将有限元模拟结果与理论计算结果相比较，发现结果具有较好的一致性。由于有限元模型和公式是理想模型，其结果比实验值要高，为此，通过考虑空心微珠增强铝基复合材料的主要缺陷，从而使模拟值更接近于实验值。     

Effect of temperature and age on the relationship between dynamic and static elastic modulus of concrete

This study investigates the effects of cement type, curing temperature, and age on the relationships between dynamic and static elastic moduli or compressive strength. Based on the investigation, new relationship equations are proposed. The impact-echo method is used to measure the resonant frequency of specimens from which the dynamic elastic modulus is calculated. Types I and V cement concrete specimens with water-cement ratios of 0.40 and 0.50 are cured isothermally at 10, 23, and 50 °C and tested at 1, 3, 7, and 28 days.Cement type and age do not have a significant influence on the relationship between dynamic and static elastic moduli, but the ratio of static to dynamic elastic modulus approaches 1 as temperature increases. The initial chord elastic modulus, which is measured at low strain level, is similar to the dynamic elastic modulus. The relationship between dynamic elastic modulus and compressive strength has the same tendency as the relationship between dynamic and static elastic moduli for various cement types, temperatures, and ages.     

Young's modulus of cement paste at elevated temperatures

Calcium silicate hydrate is a porous hydrate that is sensitive to temperature and readily loses strength at elevated temperatures. Mechanical and chemical changes in the microstructure, due to escaping water, can significantly affect the mechanical properties, but these changes occur over different temperature ranges. By measuring Young's modulus as a function of temperature using the dynamic mechanical analyzer, the temperature range in which the greatest change in stiffness occurs can be identified. Additional mineralogy, pore size distribution, and composition analysis from high temperature X-ray diffraction, nitrogen sorption, and thermogravimetric analysis will demonstrate the changes in the microstructure. The results demonstrate that over 90% of the loss in stiffness occurs below 120 °C. Therefore, the damage is due to microcracking caused by pore water expansion and evaporation and not the change in mineralogy or composition. More damage, as indicated by greater loss in stiffness, occurs in stiffer and less permeable samples where higher stresses can develop.     

A multiscale model for effective moduli of concrete incorporating ITZ water-cement ratio gradients, aggregate size distributions, and entrapped voids

This paper develops a model for the effective elastic properties of concrete, which is a function of the volume fractions, size distributions, and elastic properties of fine aggregate (FA) and coarse aggregate (FA) and entrapped voids. Furthermore, the model is a function of the overall water-cement ratio and specific gravity of cement. Explicitly modeled are the water-cement ratio gradients through the interfacial transition zone (ITZ), which, in turn, affect the variation of the cement paste elastic properties through the ITZ, while maintaining the total fractions of cement and water consistent with the overall water-cement ratio. The ITZ volume is also conserved.     

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0,45 and 90,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.