A nonlocal treatment technique based on the background cell concept for micro-mechanical damage modeling

Abstract

In the present paper, a new nonlocal treatment for micro-mechanical damage modeling is introduced based on the background cell concept. The nonlocal damage variable in the modified GTN damage model is defined as the weighted porosity in analogy to the element-free Galerkin method. The evolution of the damage variable is related to the support domain surrounds the integration point. The efficient computational algorithm is taken from the regular background cell and implemented into the commercial finite element code ABAQUS via the user interface UMAT for both two-dimensional and three-dimensional problems. To verify the nonlocal damage model, extensive computational simulations of 2D and 3D cracked as well as holed specimens are presented and confirmed that the nonlocal damage overcomes mesh sensitivity and is computationally more efficient than other nonlocal treatment methods. The computational simulation of a compact-tension shear specimen reveals that the nonlocal damage model is able to predict mixed-mode crack growth independently of the element orientation.

Viscoelastic free vibration behavior of nano-scaled beams via finite element nonlocal integral elasticity approach

“…As far as the implementation of the integration-algorithm of the nonlocality into a commercial FE code (e.g., ABAQUS) is concerned, the authors have come across two past studies in which the damage behavior of the corresponding structures are investigated (Duddu and Waisman, 2012; Li et al., 2014). In the latter studies, the relevant user material (UMAT) codes are developed to deal with the problem under investigation.…”

“…In the latter studies, the relevant user material (UMAT) codes are developed to deal with the problem under investigation. It is clearly stated in Li et al. (2014) that “A common difficulty in this approach is in implementation into a commercial FE code, moreover, searching adjoining points is a time-consuming task and a challenge for the storage capacity, especially for three-dimensional 3D modeling.” This statement can be elaborated by considering the fact that in the integral formulations, the corresponding functions in the UMAT should be integrated among all the points in the element vicinity, whilst the relevant distance from a given reference point must be taken into account.…”