Amir Hosein Hadadgar
Implementation of Ductile Damage Model with Crack Closure Effect by Finite Element and Finite Cell Methods.
Year: Sept. 2011- Feb. 2014.
Damage mechanic is concerned with the representation or modeling of damage of materials that is suitable for making engineering predictions about the initiation, propagation and fracture of materials without resorting to a microscopic description that would be too complex for practical engineering analysis. Damage of materials means the progressive or sudden deterioration of their mechanical strength because of loadings or thermal or chemical effects. From a physical point of view, damage can originate from multiple causes: debonding of atoms, nucleation, or growth and coalescence of microcracks and microcavities. Despite the discontinuous nature of such processes at the microscale, continuous damage means a homogeneous modeling in which microcracks and microvoids are represented by a continuous variable in the sense of the mechanics of continuous media. This researsh discusses some aspects of the Finite Element and Finite Cell prediction of damage growth and fracture initiation by considering crack closure effect in ductile materials under small strains and nonlinear isotropic hardening conditions. The Finite Cell Method (FCM) is the result of combining the p-version finite element (p-FEM) and fictitious domain methods, and has been shown to be effective in solving problems with complicated geometries for which the meshing procedure can be quite expensive. It, therefore, combines fast and simple mesh generation with a high convergence rate inherited from p-FEM. The simple geometry of the embedding domain can be readily discretized. Therefore, the FCM is appropriate especially for problems of complex geometries while the problem of discretization is replaced by the problem of integration. In the first step, a fully coupled elastic-plastic-damage model based on modified Lemaitre ductile damage model in axisymmetric, plane strain and three-dimensional problems was developed and implemented into FEM and FCM implicit codes and an optimization algorithm was presented. In this context, we focus on the crucial issues of constitutive modelling, finite element implementation (Abaqus-umat) and finite cell performance. Constitutive modelling is treated within the framework of continuum damage mechanics. The effect of micro-crack closure, which may dramatically decrease the rate of damage growth under compression, is incorporated and its computational implementation is discussed. The performance of the method is verified by means of numerical examples such as extrusion and upsetting, and then the results were compared with exprimental observations. Comparison of the results showed that modified Lemaitre damage model can be used as a quick and accurate tool to predict ductile damage, fracture, and forming limits in forming processes.
Ductile damage, Finite element method, Finite cell method, Crack closure effect