Nonlinear compressive deformation of viscoelastic porous materials

Two nonlinear viscoelastic solutions are presented for a porous, foam type material. The first is for the hydrostatic compression of the foam, while the second is for the one-dimensional compression of an infinite slab of the material. Relative to the particular viscoelastic constitutive equation employed, the first solution is exact, whereas the second, obtained through the use of a physical hypothesis, is approximate. Both solutions predict the macroscopic, average stress in the foam, required by the corresponding deformation processes. The theoretical results are compared with experimental measurements on a foam material at a porosity of 48.5%. The effect of material hysteresis is revealed and discussed.     

Crack-growth criterion for dynamic brittle fracture

An approach to the solution of problems of the mechanics of brittle dynamic fracture, which is based on the energy principle and the principle of time separation, is proposed. A so-called wave criterion of fracture, which can be used to estimate dynamic crack growth in an elastic body, is formulated on the basis of these principles. A general procedure is described for this estimation, and a comparison is made between experimental and theoretical values of crack-growth rate in a rectangular bar in a plane stress state (PSS); this confirms the applicability of the developed approach for engineering calculations.Translated from Problemy Prochnosti, No. 2, pp. 12–18, February, 1994.     

Integral representations for the viscoelastic deformation of ice

Various single integral representations which describe non-linear viscoelastic response are examined with regard to the types of test required to determine the respective kernels. A strain formulation determined by constant uni-axial stress response typical of ice, and its predictions for constant strain-rate response, are reviewed, showing that the latter are sensitive to kernel detail. An alternative stress formulation which is determined by constant strain-rate response is constructed, and it is shown that the predicted strain and strain-rate responses at constant stress are compatible with the typical responses exhibited by ice.     

Linear viscoelastic behavior of porous media with non-uniform saturation

Heterogeneous moisture distribution is usually observed in partially saturated porous media in the form of saturation patches. Such local heterogeneity can significantly influence the macroscopic hydro-mechanical and acoustic behavior of porous media. In this paper, a linear viscoporoelastic model is presented that can be used to address the effects of local fluid flow in the heterogeneously saturated porous media subjected to a small perturbation. The effects of local flow are characterized using the notion of capillary relaxation. The complex, frequency-dependent material properties characterizing the viscoporoelastic behavior are derived. A rigorous procedure is presented to evaluate the material parameters. The proposed model describes well the effects of patchy saturation on the dispersion and attenuation of the compressional wave in partially saturated rocks. It is found that at high saturation the effects of local gas-pressure redistribution are not negligible. A procedure is proposed to determine the capillary relaxation times using acoustic data. The proposed model provides an alternative methodology to characterize the effects of patchy saturation on the acoustic behavior of partially saturated porous media.     

A study of craze deformation in the fatigue fracture of polymethylmethacrylate

Continuous measurements of the craze contour have been undertaken for fatigue crack propagation in polymethylmethacrylate. The craze contour was determined by an interference fringe method, using equipment specially constructed for continuous load cycling, mounted on the stage of an optical microscope. It was found that there was a very great variation in the size of the craze for a fixed loading programme, although the crack growth rate showed a good correlation with the applied stress intensity range. A general result is that the craze length in fatigue was found to be greater than that for continuous crack propagation under simple fracture. This result suggested that it would be instructive to examine an extension of the Dugdale line-zone model, where the craze stress is not assumed to be constant along the length of the craze. It is shown that this modified line-zone model can provide some understanding of the observed results for craze deformation in fatigue.     

Anisotropic viscoelastic models in large deformation for architectured membranes

Due to the industrial elaboration process, membranes can have an in-plane anisotropic mechanical behaviour. In this paper, anisotropic membranes elaborated with two different materials were developed either by calendering or by inducing a force in one direction during the process. Experimental tests are developed to measure the differences of mechanical behaviour for both materials in different in-plane properties: stiffness, viscoelasticity and stress-softening. A uniaxial formulation is developed, and a homogenisation by means of a sphere unit approach is used to propose a three-dimensional formulation to represent the materials behaviour. An evolution of the mechanical parameters, depending on the direction, is imposed to reproduce the anisotropic behaviour of the materials. Comparison with experimental data highlights very promising results.     

Memory functions for mechanical relaxation in viscoelastic materials

The roles of memory functions for compliance retardation and modulus relaxation in viscoelastic materials are examined. It is shown that essential features of the mechanical responses are the components which occur instantaneously on the application of either a stress or a strain. Taking these features into consideration it is shown that at non-zero time the cooperative memory function of compliance retardation is the time differential of the modulus relaxation function and the cooperative memory function of modulus relaxation is the time differential of the compliance relaxation function for step up functions of stress and strain, respectively. Zero time singularities in the memory functions have been eliminated in the derivation of the reduced dynamical equations, whose memory functions are limited to non-singular contributions which are always present.     

Analysis of fatigue data for lifetime predictions for ceramic materials

Accuracy in data analysis is of utmost importance because lifetime predictions are extremely sensitive to experimental uncertainty in the crack growth parameters. The limitations of the conventional data reduction techniques used for analysing static and dynamic fatigue data are reviewed and new, statistical methods of data reduction that offer advantages over the conventional techniques are discussed.     

Generalized viscoelastic model for creep analysis coupled with plastic deformation

A creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step-by-step time integration of the Kelvin-Maxwell rheological model with non-constant parameters. The concept of a rheological model is extended to the multiaxial stresses by the Prandtl-Reuss stress-strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.     

Optimal discrete-time Prony series fitting method for viscoelastic materials

Mechanics of Time-Dependent Materials - Viscoelastic models based on Prony series are usually used due to easy implementation in finite element analysis codes. The experimental data are fitted to a...     

Vibrations of linear viscoelastic materials for any hereditary property

A new analytic method for solutions of vibration problems of linear viscoelastisity with arbitrary relaxation kernels is proposed. The problem is reduced to the solution of a set of ordinary integro-differential equations which are solved using the Laplace integral transform, the method of contour integration and the convolution of functions. The branch points of integrand can not be obtained for arbitrary relaxation kernels. For this reason, successive approximation method for calculating the poles and the inverse Laplace transformation of solution is offered. The first approach coincides with the well-known solution obtained by both the averaging method and the method of complex module. It is shown that the limits of these approximations are unique and it is proved that the obtained solution is the exact solution of the considering problem.     

Asymptotic constitutive approximations for rapid deformations of viscoelastic materials

Summary Asymptotic constitutive approximations for the rapid finite deformation of general viscoelastic materials are developed. The zero-order approximation is an elastic-type constitutive equation, although different from the elastic equation for the slow-deformation approximation. The higher-order terms are multiple integrals of the departure of the deformation history from the step-function history. The approximations are shown to be form-invariant to change of deformation measure. The approximations are specialized to isotropic solids and to fluids. As observed byMetzner, White andDenn [3] andPipkin [4], fluids undergoing rapid deformations exhibit a solid-like behavior.

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Zusammenfassung Es werden asymptotische Materialgleichungen für die rasche endliche Deformation eines allgemeinen viskoelastischen Materials entwickelt. Die nullte Näherung ist eine Materialgleichung vom elastischen Typ, wenn auch verschieden von der elastischen Näherungsgleichung für langsame Deformationen. Die Glieder höherer Ordnung sind Vielfachintegrale der Abweichung der Deformationsgeschichte von der Stufenfunktionsgeschichte. Es wird gezeigt, daß die Näherungen invariant sind gegen eine Änderung des Deformationsmaßes. Sie werden für isotrope Festkörper und für Flüssigkeiten spezialisiert. WieMetzner, White undDenn [3] sowiePipkin [4] beobachtet haben, zeigen Flüssigkeiten, die raschen Deformationen unterworfen werden, ein festkörperähnliches Verhalten.

     

微观非均匀粘弹性材料吸声性能研究

橡胶类粘弹性材料作为吸声覆盖层时,可在内部加入空腔或掺杂其它材料改善其吸声特性.当大量分布的空腔尺度远小于波长时,这种微观非均匀的材料在宏观上看是均匀的,可以用一种均匀材料来等效.本文对含小球形空腔的橡胶材料,数值计算了等效介质参数及吸声系数.研究了腔大小、含量及橡胶材料参数对吸声的影响.     

Dynamic behaviour of two-phase viscoelastic materials

Cylindrical two-phase epoxy resin specimens have been tested under oscillating loading over a wide range of temperatures and frequencies, taking into consideration the role of the interfaces between the main constituent elements of the composites. New bounds for the loss moduli, which were about 10% higher than those predicted by the law of mixtures, have been established for the case of specimens of good interfacial adhesion, a result which supports the assumption of the importance of the role of the interface region.     

Relaxation in elastic and viscoelastic materials

The mechanical compliance and modulus retardation/relaxation functions are examined in terms of a general behaviour which contains more than one process. An analytical approach to the transformation in the anelastic response between the compliance and the modulus is derived and applied to a cooperative model of relaxation behaviour. In particular it is shown that mechanical viscoelasticity is equivalent to the anomalous low frequency dispersion process that has been observed in dielectrics containing quasifree charges. Comparison with published experimental data over a wide range of solid materials shows the validity of the cooperative model to mechanical relaxation.