A simple Kelvin and Boltzmann viscoelastic analysis of three-dimensional solids by the boundary element method

Mesquita, A.D.; Coda, Humberto Breves

doi:10.1016/s0955-7997(03)00060-2

Cited by 30 publications

(19 citation statements)

References 22 publications

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“…In deriving (1), the assumption that h k ¼ h l ¼ c is adopted [2,4,7,8], where h k and h l are the hydrostatic and deviatoric viscosity coefficients, respectively, with the dimension of time. This results in a constant Poisson's ratio but allows one to obtain only boundary values in the governing integral equations for the problem.…”

Section: Boltzmann Modelmentioning

confidence: 99%

“…The method combines the elastic boundary integral approach for multiple holes and inclusions developed by Crouch and Mogilevskaya [1] and the time-marching approach for viscoelastic analysis described by Mesquita and Coda [2][3][4][5][6][7][8]. An approach based on a Kelvin model is not able to simulate instantaneous behavior of materials, and this is very important in most applications.…”

Section: Introductionmentioning

confidence: 99%

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Direct boundary integral procedure for a Boltzmann viscoelastic plane with circular holes and elastic inclusions

2005

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A direct boundary integral method in the time domain is presented to solve the problem of an infinite, isotropic Boltzmann viscoelastic plane containing a large number of randomly distributed, non-overlapping circular holes and perfectly bonded elastic inclusions. The holes and inclusions are of arbitrary size and the elastic properties of all of the inclusions can, in general, be different. The method is based on a direct boundary integral approach for the problem of an infinite elastic plane containing multiple circular holes and elastic inclusions described by Crouch and Mogilevskaya [1], and a time marching strategy for viscoelastic analysis described by Mesquita and Coda [2-8]. Benchmark problems and numerical examples are included to demonstrate the accuracy and efficiency of the method.

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Section: Boltzmann Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct boundary integral procedure for a Boltzmann viscoelastic plane with circular holes and elastic inclusions

2005

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“…Using constitutive differential equations for viscoelastic models Coda and his co-workers presented a quasi-stationary formulation based on cell discretization for the Kelvin [43] and for the Boltzmann [42] viscoelastic models. This formulation leads to a matrix differential equation, the solution of which does not require the storage of a new system matrix at every time step.…”

Section: Introductionmentioning

confidence: 99%

“…The twodimensional case was treated in [41] and the 3-D case was discussed in the paper of 2003 [42]. Through the use of differential viscoelastic relations they did avoid the use of relaxation functions and the convolutional solution procedure.…”

Section: Introductionmentioning

confidence: 99%

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

Mesquita

Antes

Thomazo

et al. 2012

Lat. Am. j. solids struct.

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This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The influence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. (continued on next The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.

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“…By the elasticviscoelastic correspondence principle [5], the viscoelastic governing equations can be transformed into a set of corresponding elastic governing equations using the Laplace transform, and then the solutions are transformed back to the time domain by numerical methods. From the basic assumptions of viscoelastic constitutive relations and weighted residual techniques, Mesquita et al [6][7][8][9] presented a boundary element alternative procedure for Boltzmann and Kelvin viscoelasticity. They produced the differential systems of equations with respect to time variable, which are solved by an appropriate time marching process.…”

Section: Introductionmentioning

confidence: 99%

A fast multipole boundary element method for 2D viscoelastic problems

Zhu

Chen

Huang

et al. 2011

Engineering Analysis with Boundary Elements

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A simple Kelvin and Boltzmann viscoelastic analysis of three-dimensional solids by the boundary element method

Cited by 30 publications

References 22 publications

Direct boundary integral procedure for a Boltzmann viscoelastic plane with circular holes and elastic inclusions

Direct boundary integral procedure for a Boltzmann viscoelastic plane with circular holes and elastic inclusions

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

A fast multipole boundary element method for 2D viscoelastic problems

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