Error Controlled Adaptive Multiscale Method for Fracture in Polycrystalline Materials

A lack of separation of scales is the major hurdle hampering predictive and computationally tractable simulations of fracture over multiple scales. In this thesis an adaptive multiscale method is presented in an attempt to address this challenge. This method is set in the context of FE2 Feyel and Chaboche [2000] for which computational homogenisation breaks down upon loss of material stability (softening). The lack of scale separation due to the coalescence of microscopic cracks in a certain zone is tackled by a full discretisation of the microstructure in this zone. Polycrystalline materials are considered with cohesive cracks along the grain boundaries as a model problem. Adaptive mesh refinement of the coarse region and adaptive initiation and growth of fully resolved regions are performed based on discretisation error and homogenisation error criteria, respectively. In order to follow sharp snap-backs in load-displacement paths, a local arc-length technique is developed for the adaptive multiscale method. The results are validated against direct numerical simulation

Scale selection in nonlinear fracture mechanics of heterogeneous materials

A new adaptive multiscale method for the non-linear fracture simulation of heterogeneous materials is proposed. The two major sources of errors in the finite element simulation are discretization and modelling errors. In the failure problems, the discretization error increases due to the strain localization which is also a source for the error in the homogenization of the underlying microstructure. In this paper, the discretization error is controlled by an adaptive mesh refinement procedure following the Zienkiewicz–Zhu technique, and the modelling error, which is the resultant of homogenization of microstructure, is controlled by replacing the macroscopic model with the underlying heterogeneous microstructure. The scale adaptation criterion which is based on an error indicator for homogenization is employed for our non-linear fracture problem. The control of both discretization and homogenization errors is the main feature of the proposed multiscale method

Error controlled adaptive multiscale method for fracture in polycrystalline materials

A lack of separation of scales is the major hurdle hampering predictive and computationally tractable simulations of fracture over multiple scales. In this thesis an adaptive multiscale method is presented in an attempt to address this challenge. This method is set in the context of FE2 Feyel and Chaboche [2000] for which computational homogenisation breaks down upon loss of material stability (softening). The lack of scale separation due to the coalescence of microscopic cracks in a certain zone is tackled by a full discretisation of the microstructure in this zone. Polycrystalline materials are considered with cohesive cracks along the grain boundaries as a model problem. Adaptive mesh re nement of the coarse region and adaptive initiation and growth of fully resolved regions are performed based on discretisation error and homogenisation error criteria, respectively. In order to follow sharp snap-backs in load-displacement paths, a local arc-length technique is developed for the adaptive multiscale method. The results are validated against direct numerical simulatio

A robust local arc-length method for multiscale problems

In this paper, a new local arc-length method has been introduced to follow the snap-back at the microscale as well as in the macroscale for a multiscale problem. First order multiscale computational homogenization (FE2) approach has been employed to study the behaviour of a one dimensional (1D) bar with cohesive cracks in the both scale. The macroscale material properties and constitutive equations are unknown. The local macroscopic constitutive response is determined by solving the related microscale Representative Volume Element (RVE). Each RVE has cohesive cracks whose damage parameters are a function of the displacement jump. The non-damaged part of RVEs are assumed to be linear elastic. In FE2 multiscale methods, the arc-length method is used in the macroscale and the displacement control method is used in the microscale, however, the displacement control cannot follow the snap back. The comparison of the new local arc-length method and conventional local arc-length is presented

Room temperature screening of thermal conductivity by means of thermal transient measurements

A proof of concept of the possibility to estimate thermal conductivity of bulk disc samples at room temperature by means of thermal decays is demonstrated. An experimental set-up was designed and fabricated, which is able to perform thermal transient measurements by using a specially designed multifunctional probe that has the ability to measure temperature at its tip. Initially, the probe is heated by a heater coil located in its interior until the tip temperature reaches a steady state. Then, the probe is contacted with a disc sample which produces a temperature decay until a new state is reached. The difference between the initial and final states temperatures shows a correlation with the thermal conductivity of the sample. Employing a calibration equation, obtained using reference materials, the thermal conductivity can be calculated. Reasonably good random and systematic errors (<13% and ~9% respectively) are obtained. Theoretical simulations performed using COMSOL show a good qualitative agreement with experimental results. This new method involves an inexpensive and simple set-up which can be especially useful for thermal conductivity screening and high-throughput measurements