Implementation of Brittle Damage Model by Isogeometric Analysis Approach for 2D Problems
Year: Sept. 2014- Jun. 2017.
In this research, Isogeometric analysis is used as a suitable tool for modeling damage in semi-brittle materials. Isogeometric analysis presents a new developed technology in computational mechanics. The main idea of this method is based on using a geometrical model as the computational model for analyzing problems and as the time spent from designing to analysis is highly reduced, the efficiency is increased. This approach solves problems using NURBS functions with acceptable accuracy and, moreover, the problems are solved faster. Also, these functions present a higher order of continuity compared to functions used in Finite Element Method. In this research, the isotropic damage model for brittle materials with exponential growth relationship and using Isogeometric analysis is implemented in GeoPDEs based on MATLAB programing language. Due to nonlinearity, direct iteration method is used and the convergence history for a step of damage model solution is studied using the direct iteration algorithm. In order to evaluate the damage, the Mazars and the Modified Von-Mises definitions of equivalent strain are used. After numerical implementation and creation of the program using isotropic damage model, uniaxial tension and compression specimens are simulated for validating the model and the resulting force-displacement diagrams of the two tests are compared with the available references. Afterwards, the three-point bending beam specimen is studied. At first, the geometry creation is explained step by step and the convergence of the mesh is checked. At the end, the variable damage growth in the beam is studied.
Keywords: Isogeometric Analysis, Finite Element Method, Brittle Damage, NURBS