Static And Dynamic Crack Propagation In Brittle Materials With Xfem

The aim of this thesis is the simulation of progressive damage in brittle materials due to cracking. With this aim, the mathematical crack model will be solved using the eXtended Finite Element Method for the spatial discretization and time integration schemes for the numerical integration in the time domain. The time integration schemes considered are the Generalized-? method, the continuous GALERKIN method and the discontinuous GALERKIN method.

The planning meeting for a conference on Dynamic Crack Propagation was held at M.LT. in February 1971 and attended by research workers from several industrial, governmental and academic organizations. It was felt that a more specialized meeting would provide a better opportunity for both U.S. and foreign researchers to exchange their ideas and views on dynamic fracture, a subject which is seldom emphasized in national or international fracture conferences. Dynamic crack propagation has been a concern to specialists in many fields: continuum mechanics, metallurgy, geology, polymer chemistry, orthopedics, applied mathematics, as well as structural design and testing. It impinges on a wide variety of problems such as rock breaking and earthquakes, pressure vessels and line pipes, comminution and the per formance of armament and ordnance, etc. Advances have been numerous, covering theories and experiments from both the microscopic and macro scopic points of view. Hence, the need for comparing the theoretical and experimental results and bridging the gaps between the atomistic and continuum approaches must be constantly emphasized. It also appeared that the overall problem of dynamic fracture could benefit from a con solidation of crack models proposed for the various types of materials: metals, ceramics, composites, rocks, glasses, polymers and biomaterials.

Covering a wide variety of topics in dynamic fracture mechanics, this volume presents state-of-the-art experimental techniques and theoretical analysis on dynamic fracture in standard and exotic materials. Written by world renowned researchers, this valuable compendium contains eleven chapters on crack initiation, crack propagation, crack arrest, crack-stress wave interactions, and experimental, analytical and numerical methods in dynamic fracture mechanics. Contents: Modeling Dynamic Fracture Using Large-Scale Atomistic Simulations (H-J Gao & M J Buehler); Dynamic Crack Initiation Toughness (D Rittel); The Dynamics of Rapidly Moving Tensile Cracks in Brittle Amorphous Material (J Fineberg); Optical Methods for Dynamic Fracture Mechanics (H V Tippur); On the Use of Strain Gages in Dynamic Fracture (V Parameswaran & A Shukla); Dynamic and Crack Arrest Fracture Toughness (R E Link & R Chona); Dynamic Fracture in Graded Materials (A Shukla & N Jain); Dynamic Fracture Initiation Toughness at Elevated Temperatures with Application to the New Generation of Titanium Aluminides Alloys (M Shazly et al.); Dynamic Fracture of Nanocomposite Materials (A Shukla et al.). Readership: Researchers, practitioners, and graduate students in fracture mechanics and materials science.

This book provides an up-to-date knowledge on theory and experimental results of rate-dependent fracture processes in metallic materials. The objective is to expose the current status of a growing branch of fracture mechanics called generally "Dynamic Fracture". Crack dynamics takes into account not only the effects of inertia but also rate sensitivity of a material under consideration. This volume has been prepared by four leading authorities in fracture dynamics: D.R. Curran, J.F. Kalthoff, J.R. Klepaczko and F. Nilsson. A broad range of problem is covered: dynamic fracture theory, application of dynamic fracture mechanics, dynamic crack inition and microstatistical fracture mechanics in dynamic fracture. The book in its present format may serve as a text supplement in lecturing on fracture mechanics. On the other hand, it may serve as an instructional aid in engineering of fracture prevention.

Dynamic fracture in solids has attracted much attention for over a century from engineers as well as physicists due both to its technological interest and to inherent scientific curiosity. Rapidly applied loads are encountered in a number of technical applications. In some cases such loads might be applied deliberately, as for example in problems of blasting, mining, and comminution or fragmentation; in other cases, such dynamic loads might arise from accidental conditions. Regardless of the origin of the rapid loading, it is necessary to understand the mechanisms and mechanics of fracture under dynamic loading conditions in order to design suitable procedures for assessing the susceptibility to fracture. Quite apart from its repercussions in the area of structural integrity, fundamental scientific curiosity has continued to play a large role in engendering interest in dynamic fracture problems In-depth coverage of the mechanics, experimental methods, practical applications Summary of material response of different materials Discussion of unresolved issues in dynamic fracture

The present thesis investigates the usage of higher order accurate time integrators together with appropriate error estimators for small and finite dynamic (visco)plasticity. Therefore, a general (visco)plastic problem is defined which serves as a basis to create closed-form solution strategies. A classical access towards small and finite (visco)plasticity is integrated into this concept. This approach is based on the idea, that the balance of linear momentum is formulated in a weak sense and the material laws are included indirectly. Thus, separate time discretizations are implemented and an appropriate coupling between them is necessary. Limitations for the usage of time integrators are the consequence. In contrast, an alternative multifield formulation is derived, adapting the principle of Jourdain. The idea is to assume that the balance of energy - taking into account a pseudopotential representing dissipative effects – resembles a rate-type functional, whose stationarity condition leads to the equations describing small or finite dynamic (visco)plasticity. Accordingly, the material laws and the balance of linear momentum can be solved on the same level and only one single time discretization has to be performed. A greater freedom in the choice of time integrators is obtained and the application of higher order accurate schemes - such as Newmark’s method, fully implicit as well as diagonally implicit Runge-Kutta schemes, and continuous as well as discontinuous Galerkin methods - is facilitated. An analysis and a comparison of the classical and the multifield formulation is accomplished by means of distinct examples. In this context, a dynamic benchmark problem is developed, which allows to focus on the effect of different time integrators. For this investigation, a variety of time discretization error estimators are formulated, evaluated, and compared.

Translation of hugely successful book aimed at advanced undergraduates, graduate students and researchers.

The current paper establishes an axisymmetric model for an inductive heating process. Therein, the fully coupled MAXWELL equations, assuming a temperature dependent permeability, are combined with the non-linear heat conduction equation to yield a monolithic solution strategy. The latter is based on a consistent linearization together with a higher order finite element discretization using GALERKIN'S method in space. For the temporal discretization, the generalized Newmark-? methods, higher order RUNGE-KUTTA methods, and discontinuous and continuous GALERKIN methods are used. Furthermore, the residual error is introduced to open an alternative way to obtain a numerically efficient estimation of the time integration accuracy. Simulation results of the electric, magnetic and thermal fields are provided, together with parameter studies concerning spatial discretization, frequency dependence and penetration depth of the heating zone. Another topic analyzed is the residual error and its estimation quality regarding polynomial degree and time step size. A further aspect of this work is the investigation of the thermal fluid-structure interaction with respect to functionally graded materials. Different coupling strategies for the acceleration of the fixed-point iteration in each time step is in the foreground. Relaxation methods as well as extrapolation methods make it possible to significantly reduce the number of fixed point iterations. At the same time, an adaptive strategy with higher order RUNGE-KUTTA methods can provide a further advantage in combination with acceleration methods.