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The present study aims at performing a mechanical analysis of 2D viscoelastic cracked structural materials using the Boundary Element Method (BEM). The mesh dimensionality reduction provided by the BEM and its accuracy in representing high gradient fields make this numerical method robust to solve fracture mechanics problems. Viscoelastic models address phenomena that provide changes on the mechanical material properties along time. Well-established viscoelastic models such as Maxwell, Kelvin-Voigt and Boltzmann are used in this study. The numerical viscoelastic scheme, which is based on algebraic BEM equations, utilizes the Euler method for time derivative evaluation. Therefore, the unknown variables at the structural boundary and its variations along time are determined through an ordinary linear system of equations. Moreover, time-dependent boundary conditions may be considered, which represent loading phases. The dual BEM formulation is adopted for modelling the mechanical structural behaviour of cracks bodies. Three examples are considered to illustrate the robustness of the adopted formulation. The results achieved by the BEM are in good agreement with reported data and numerical stability is observed.

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The prediction of the future structural behaviour is an essential activity during the design phase. In this study, a novel numerical framework is proposed for investigating the future structural behaviour of two-dimensional structures. The model utilizes the boundary element method for obtaining the mechanical responses. The constitutive material is admitted to manifest viscoelastic response, which enables it to creep. The input parameters such as material, loads parameters and geometry dimensions are considered to possess random characteristics. A probabilistic criterion is proposed using metamodelling by the response surface method. All these features make the proposed numerical model more realistic. As an application, a specific structure is utilized, which is inspired from the real world. The results demonstrate that small geometric deviations do not necessarily impact the global reliability of the structure. At the same time, load estimations have major influence on the global structural reliability. The numerical framework proposed can be utilized for preliminary investigations on the design phase in order to aid the engineers into the decision-making process. Moreover, these observations demonstrate that the boundary element method can be efficiently coupled to other numerical strategies in order to elaborate new robust numerical frameworks able to represent realistically engineering problems.