Comparison of current methods for polymer analysis by boundary element

Abstract

In this paper, quasi-static analyses of polymers, based on the boundary element method, are reviewed and implemented. Linear viscoelasticity, for which the correspondence principle applies, is assumed. Thus, one of the adopted BEM approaches solves the problem in the Laplace transform domain and relies on numerical inversion for the determination of the time-dependent response.
The second solves directly in the time domain using fundamental solutions specific to the solid geometry and the viscoelastic model used. A third, recently proposed method also produces directly the time-dependent response but relies on the different algorithms are developed and applied to benchmark problems in order to assess their relative accuracy and efficiency. Particular attention is given to the effectiveness of the methods to predict fracture parameters in cracked plate problems. The versatility, computational efficiency and accuracy of the different schemes are compared. In general, good agreement is achieved between various BEM predictions and other published numerical results. Schemes for possible extension of the method to account for more complex viscoelastic models are briefly discussed.

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