A BEM formulation applied in the mechanical material modelling of viscoelastic cracked structures

Abstract

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.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

“…Different numerical formulations have been developed to analyze the viscoelastic behavior of solid materials, as demonstrated in the works of Chen [1], Aköz and Kadioǧlu [2], Beijer and Spoormaker [3], Zheng et al [4], Mesquita and Coda [5], Galucio et al [6], Bottoni et al [7], Payette and Reddy [8], Panagiotopoulos et al [9], Latorre and Montáns [10], dos Santos Becho et al [11], Carniel et al [12], Oliveira and Leonel [13], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. is interest is due to the need for modeling behavior of unconventional materials and the more complex and realistic analyzes of structures and structural components.…”

Probabilistic mechanical modelling of concrete creep based on the boundary element method

“…Under hypothesis of locality, homogeneity, isotropy and small displacements and rotations for operator A [ · ] , the Boltzmann model is chosen on its differential form. In addition to its simple expression, it has demonstrated to be efficient enough to approximate accurately the solution of several viscoelastic systems (Oliveira and Leonel, 2017). Furthermore, this model can be used to represent the macroscopic behaviour of concrete without temperature and humidity effects.…”

“…When a strain history is applied to this material, the response is obtained from equation (5). Note that the response does not depend only on this strain, but on its entire history (Oliveira and Leonel, 2017)…”

“…The domain integral in equation (9) can be simplified making the proportionality assumption, θ lmik = γ C lmik (Mesquita and Coda, 2001). Applying equation (12) to all nodes defined at the boundary will produce a set of linear equation that can be arranged in a matrix form as follows (Oliveira and Leonel, 2017)…”

“…It has major importance in the serviceability state of concrete structures, especially in cases of prestressing. Creep can be formulated by means of viscoelastic models (Oliveira and Leonel, 2017). The gross estimates of creep deformations lead to the undesirable consequences for designers, builders, owners, users, insurers and so on.…”