Finite layer analysis of layered viscoelastic materials under three-dimensional loading conditions

A method is presented which enables the calculation of the settlement behaviour of circular or general loadings on horizontally layered soils which undergo secondary or ‘creep’ consolidation. The method of analysis involves the use of Hankel or double Fourier transforms to simplify the equations governing the consolidation process. This leads to great savings in the preparation of data and the amount of computer storage needed to solve problems involving three-dimensional loadings since such problems are essentially reduced to that of one spatial dimension: Solutions are then obtained by a ‘forward marching’ process where solutions at a particular time are found from those at a previous time. A method is presented which eliminates the need to store the solutions at all previous time steps, and is therefore very efficient. The theory is illustrated by examples of the behaviour of rectangular and circular loadings on layered soil profiles.     

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

Transient elastodynamic crack analysis in two-dimensional (2D), layered, anisotropic and linear elastic solids is presented in this paper. A time-domain boundary element method (BEM) in conjunction with a multi-domain technique is developed for this purpose. Time-domain elastodynamic fundamental solutions for homogenous, anisotropic and linear elastic solids are applied in the present time-domain BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method, while a collocation method is adopted for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the unknown boundary data and the crack-opening-displacements (CODs). To show the effects of the crack configuration, the material anisotropy, the layer combination and the dynamic loading on the dynamic stress intensity factors and the scattered elastic wave fields, several numerical examples are presented and discussed.     

Experimental investigation of fracture surface energy of a solid propellant under different loading rates

Fracture tests on solid propellants have been performed under three ranges of loading rate leading to fracture toughness results in terms of J_IC and (Andrews' parameter). Using two different specimen shapes, finite size effects have been pointed out (considering SENT sample) when dealing with Andrews' theory and a modified equation, taking into account the specimen compliance, is proposed. Significant influence of loading rate on J_IC is observed leading to few conclusions concerning fracture process of solid propellants.     

Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loading

 As a direct extension of the asymptotic spatial homogenization method we develop a temporal homogenization scheme for a class of homogeneous solids with an intrinsic time scale significantly longer than a period of prescribed loading. Two rate-dependent material models, the Maxwell viscoelastic model and the power-law viscoplastic model, are studied as an illustrative examples. Double scale asymptotic analysis in time domain is utilized to obtain a sequence of initial-boundary value problems with various orders of temporal scaling parameter. It is shown that various order initial-boundary value problems can be further decomposed into: (i) the global initial-boundary value problem with smooth loading for the entire loading history, and (ii) the local initial-boundary value problem with the remaining (oscillatory) portion of loading for a single load period. Large time increments can be used for integrating the global problem due to smooth loading, whereas the integration of the local initial-boundary value problem requires a significantly smaller time step, but only locally in a single load period. The present temporal homogenization approach has been found to be in good agreement with a closed-form analytical solution for one-dimensional case and with a numerical solution in multidimensional case obtained by using a sufficiently small time step required to resolve the load oscillations. Received: 22 November 2001 / Accepted: 21 May 2002     

Time-dependent behaviour of clay-concrete interfaces with different contact surface roughnesses under shear loading

Mechanics of Time-Dependent Materials - Mechanical properties of the interface between a pile and soil greatly affect the bearing capacity of a pile. The creep of soil causes a long-term strength...     

Elastoplastic behavior of two-dimensional solids with rectilinear cracks under mixed-mode loading

This paper investigates the elastoplastic behavior of a two-dimensional solid with rectilinear cracks. Plastic strip model is used to reduce plasticity problem to the equivalent linear eleasticity formulation. The effective mechanical response predictions are obtained for mode I and mixed-mode cracks. For mixed-mode cracks, the modification of Dugdale (1960) model proposed by Becker and Gross (1988) is applied. Results are compared with known elastic solutions.     

Deformation and energy absorption of wood cell walls with different nanostructure under tensile loading

The nanostructure of the S2 cell wall layer in tracheids of Picea abies (Norwegian spruce), in particular the cellulose microfibril angle, has been shown to control not only the stiffness but also the extensibility of wood within a wide range. In order to further elucidate this effect, the deformation of wood under tensile load parallel to the longitudinal cell axis was studied in a contact-free way using a video extensometer. The combination of these measurements with small-angle X-ray scattering on the same microtome sections allowed us to establish a direct relationship between the microfibril angle and deformation behaviour. The microfibril angle was shown to influence not only the extensibility in longitudinal direction but also the deformation perpendicular to the applied load. Moreover, the results showed that the energy absorption capacity is higher for specimens with larger microfibril angle. SEM pictures of the fractured samples indicated clearly the differences in the fracture process as the fracture zones of samples with low microfibril angle were smooth and the fracture zones of samples with high microfibril angle were heavily torn and deformed indicating a more ductile behaviour.     

Measurement of the specific free surface energy of solids

A set of equations is proposed that makes it possible to obtain calculation equations for experimental determination of the specific free surface energy of solids. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 68–69, October, 2007.     

Time-dependent behavior of layered arches with viscoelastic interlayers

This work studies the time-dependent behavior of a layered arch adhesively bonded by viscoelastic interlayers. The deformation of the viscoelastic interlayer is represented by the Maxwell–Wiechert model. The constitutive relation in an interlayer is simplified through the quasi-elastic approximation approach. The mechanical property of an arch layer is described by the exact two-dimensional (2-D) elasticity theory in polar coordinates. The stress and displacement components in an arch layer, which strictly satisfy the simply supported boundary conditions, have been analytically derived out. The stresses and displacements are efficiently obtained by means of the recursive matrix method for the arch with any number of layers. The comparison study shows that the 2-D finite element solution has good agreement with the present one, while the solution based on the one-dimensional (1-D) Euler–Bernoulli theory has considerable error, especially for thick arches. The influences of geometrical and material parameters on the time-dependent behavior of the layered arch are analyzed in detail.     

A study of free surface effects on through cracks under impact loading

This paper deals with the implementation of a three-dimensional time-domain boundary integral formulation for a center-crack, finite solid under symmetrically applied step loading. The BEM displacement time domain formulations have, hitherto, been limited to analyzing two-dimensional crack problems, though hypersingular formulations have been used to analyze finite cracks in infinite domains. In this paper, variation of dynamic stress intensity factor (DSIF) along the crack front for a stationary, through-thickness straight crack is studied for a finite solid under step loading. The state of stress is evaluated at the crack vertex, where crack front meets the free surface. The effect of free surface on DSIF is investigated. The effect of waves traveling in thickness direction is explained. It is possible to estimate accurately the critical intersection angle of the crack front with the free surface at which square-root singularity is restored at the crack vertex under step loading. A new partitioning scheme is proposed for spatial integration of elastodynamic kernels.     

BIEM solution of piezoelectric cracked finite solids under time-harmonic loading

The time-harmonic behavior of cracked finite piezoelectric 2D solids of arbitrary shape is studied by the nonhypersingular traction boundary integral equation method (BIEM). Plane strain and generalized traction free boundary conditions along the crack are assumed. The system may be loaded at the external boundary by arbitrary mechanical or electrical loads. As numerical example a center cracked rectangular piezoelectric plate under time-harmonic tension and electrical displacement is investigated in detail. The accuracy of the proposed numerical algorithm is checked by comparison with available results obtained by other methods for special cases. Parametric studies revealing the sensitivity of the stress intensity factors (SIFs) on the frequency of the applied mechanical and electrical load, on its coupled and uncoupled character and on the piezoelectric properties of the material are presented.     

Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model

This paper presents a model for predicting damage evolution in heterogeneous viscoelastic solids under dynamic/impact loading. Some theoretical developments associated with the model have been previously reported. These are reviewed briefly, with the main focus of this paper on new developments and applications. A two-way coupled multiscale approach is employed and damage is considered in the form of multiple cracks evolving in the local (micro) scale. The objective of such a model is to develop the ability to consider energy dissipation due to both bulk dissipation and the development of multiple cracks occurring on multiple length and time scales. While predictions of these events may seem extraordinarily costly and complex, there are multiple structural applications where effective models would save considerable expense. In some applications, such as protective devices, viscoelastic materials may be preferred because of the considerable amount of energy dissipated in the bulk as well as in the fracture process. In such applications, experimentally based design methodologies are extremely costly, therefore suggesting the need for improved models. In this paper, the authors focus on the application of the newly developed multiscale model to the solution of some example problems involving dynamic and impact loading of viscoelastic heterogeneous materials with growing cracks at the local scale.     

Nature of mass transfer in solids under conditions of impact loading

The article presents an explanation of the anomalously high mobility of atoms under the conditions of impact loading when shock waves act on a crystal.     

Some features of stress and strain distribution in solids with inhomogeneities under dynamic loading

Results are presented for experimental studies of the effect of material inhomogeneity and curvature of the wave front connected with it on the development of strain and stress localization, and the effect of accumulation in an elastoplastic body with dynamic loading. It is established that propagation of elastoplastic and shock waves in a material with macro- and microinhomogeneity is accompanied by redistribution of stresses and strains, and their amplitude and the distance between them depend not only on the distribution of inhomogeneities, but also on load intensity and on distance from these inhomogeneities.Translated from Problemy Prochnosti, No. 7, pp. 64–67, July, 1991.     

Three-dimensional elasticity solution of layered plates with viscoelastic interlayers

An analytical solution for simply supported layered plates with viscoelastic interlayers under a transverse load is proposed. The deformation of each plate layer is described by the exact three-dimensional elasticity equations. The viscoelastic property of interlayer is simulated by the generalized Maxwell model. The constitutive relation of the interlayer is simplified by the quasi-elastic approximation, which significantly simplifies the analytical process. The solution of stress and displacement fields with undetermined coefficients is derived by solving a group of ordinary differential equations. The undetermined coefficients can be efficiently deduced by using the recursive matrix technique for the plate with any number of layers. The practical convergence is observed during numerical tests. The comparison analysis indicates that the present solution has a close agreement with the finite element solution. However, the solution based on the Mindlin–Reissner hypothesis is significantly different from the present solution for thick plates. Finally, the effect of interlayer thickness on stress and displacement distributions of a five-layer plate is discussed in detail.