A 1DBEM/BEM COUPLING FORMULATION APPLIED TO REINFORCED VISCOELASTIC DOMAINS

Resumo

This work presents a numerical formulation based on the Boundary Element Method (BEM)
for the mechanical analysis of reinforced viscoelastic materials. The reinforced domain is represented
by a numerical methods coupling technique, in which the material matrix is modelled by the usual
two-dimensional singular BEM formulation and a one-dimensional approach of the BEM, called
1DBEM, is used for the reinforcements. The 1DBEM is based on an axial fundamental solution for
elastic 1D domains, easily found in the literature. No relative displacements between matrix and
reinforcements are considered to formulate the coupling and the contact force is a one-dimensional
load distributed along the reinforcement’s line, which define this 1DBEM/BEM coupling as an
alternative to the usual FEM/BEM coupling. The viscoelastic response is added to the matrix behavior,
using the Kelvin-Voigt rheological model in the two-dimensional BEM formulation. This approach
enables introducing the time-dependent material properties without the need for cells within the
domain or convolution integrals. A time discretization is needed to solve the resulting time-dependent
equation. However, as previously mentioned in the literature, this approach shows a good convergence
behavior regarding the time step size. Finally, the proposed formulation is able to represent reinforced
domains with a viscoelastic matrix, such as reinforced structures or fiber-reinforced materials.
Numerical applications exhibit the convergence of the model and compare the answer obtained with
both 1DBEM/BEM coupling and FEM/BEM coupling techniques with reference results, available in
the literature. The results obtained are stable and accurate, which demonstrates the robustness of the
formulation proposed in this work.