Transient dynamic analysis of 3-D gradient elastic solids by BEM

Polyzos, D.; Tsepoura, K. G.; Beskos, D.E.

doi:10.1016/j.compstruc.2004.11.001

Cited by 23 publications

(13 citation statements)

References 18 publications

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“…Boundary element implementations for gradient elasticity have also been developed, in particular by Tsepoura et al (2002), Polyzos et al (2003), Tsepoura et al (2003), Polyzos et al (2005), Karlis et al (2007). However, in this Section we will focus on finite element implementations.…”

Section: Numerical Implementationsmentioning

confidence: 99%

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Askes

Aifantis

2011

International Journal of Solids and Structures

774

503

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a b s t r a c tIn this paper, we discuss various formats of gradient elasticity and their performance in static and dynamic applications. Gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher-order spatial derivatives of strains, stresses and/or accelerations. We focus on the versatile class of gradient elasticity theories whereby the higher-order terms are the Laplacian of the corresponding lower-order terms. One of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum. We start with discussing the general Mindlin theory, that in its most general form has 903 constitutive elastic parameters but which were reduced by Mindlin to three independent material length scales. Further simplifications are often possible. In particular, the Aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures. We also address how this can be extended to dynamics. An overview of length scale identification and quantification procedures is given. Finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions. Details are provided for particular formats of gradient elasticity that can be implemented with simple, linear finite element shape functions. New numerical results show the removal of singularities in statics and dynamics, as well as the size-dependent mechanical response predicted by gradient elasticity.

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Section: Numerical Implementationsmentioning

confidence: 99%

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Askes

Aifantis

2011

International Journal of Solids and Structures

774

503

View full text Add to dashboard Cite

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“…This is due to the inability of the classical theory to predict the experimentally observed scale effects, and also due to the increasing demands for manufacturing devices at very small scales. Recent examples of successful modeling of microstructure and size effects by the couple-stress theory and related gradient theories include work by, among others, Batra [12], Batra et al [13], Fleck et al [14], Vardoulakis and Sulem [15], Huang et al [16,17], Zhang et al [18], Lubarda and Markenscoff [19], Georgiadis and Velgaki [20], Georgiadis [21], Radi and Gei [22], Polyzos et al [23], Lazar and Maugin [24], Grentzelou and Georgiadis [25,26], Georgiadis and Grentzelou [27], Tsamasphyros et al. [28], Giannakopoulos and Stamoulis [29], Gourgiotis and Georgiadis [30], Aravas and Giannakopoulos [31], Gourgiotis et al [32], and dell'Isola et al [33].…”

Section: Introductionmentioning

confidence: 99%

Couple-stress effects for the problem of a crack under concentrated shear loading

Gourgiotis

Georgiadis

Sifnaiou

2011

Mathematics and Mechanics of Solids

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2012) 'Couple-stress eects for the problem of a crack under concentrated shear loading.', Mathematics and mechanics of solids., 17 (5). pp. 433-459. Further information on publisher's website:http://dx.doi.org/10.1177/1081286511423123Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. behavior at infinity in the transformed plane. Nevertheless, an analytic function method is employed which circumvents the aforementioned difficulty. For comparison purposes, the case of a semiinfinite crack subjected to a distributed shear load is also treated in the present study. Numerical results for the dependence of the stress intensity factor and the energy release rate upon the ratio of the characteristic lengths are presented.

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“…As it is shown in [10] the equations of motion (1) and (2) in the frequency domain are transformed into an integral representation, along the boundary of the geometry. The Fast Fourier Transform then is used to solve a transient problem.…”

Section: B Numerical Simulations Using the Boundary Element Methods (mentioning

confidence: 99%

BEM simulations of Rayleigh wave propagation in media with microstructural effects: Application to long bones

Papacharalampopoulos

Vavva

Protopappas

et al. 2010

2010 Annual International Conference of the IEEE Engineering in Medicine and Biology

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Bone is a strongly heterogeneous natural composite with microstructure. Although the classical theory of linear elasticity has been largely used in bone ultrasonic studies, it cannot sufficiently describe the mechanical behavior of materials with microstructure. Furthermore, this theory predicts non-dispersive behavior of Rayleigh waves, which is in conflict with experimental observations. By using the simplest theory of gradient elasticity we recently demonstrated that bone's microstructure significantly affects the dispersion of classical Lamb modes. In this work, we investigate the effect of bone's microstructure on the propagation of Rayleigh waves by using the Boundary Element Method (BEM). We assume an isotropic semi-infinite space with mechanical properties equal to those of bone and microstructure. Microstructural effects are taken into account by introducing in the stress analysis the internal length scale parameters l(1), l(2), h(1), h(2). BEM computations are performed for various combinations of these parameters with values empirically chosen close to the osteon's size. The constants' values are also compared to those derived from closed form relations. The results made clear that bone's microstructure significantly affects Rayleigh wave dispersion.

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Transient dynamic analysis of 3-D gradient elastic solids by BEM

Cited by 23 publications

References 18 publications

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Couple-stress effects for the problem of a crack under concentrated shear loading

BEM simulations of Rayleigh wave propagation in media with microstructural effects: Application to long bones

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