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An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.
Purdue University has played a leading role in providing the engineers who designed, built, tested, and flew the many aircraft and spacecraft that so changed human progress during the 20th century. It is estimated that Purdue has awarded 6% of all BS degrees in aerospace engineering, and 7% of all PhDs in the United States during the past 65 years. The University's alumni have led significant advances in research and development of aerospace technology, have headed major aerospace corporations and government agencies, and have established an amazing record for exploration of space. More than one third of all US manned space flights have had at least one crew member who was a Purdue engineering graduate (including the first and last men to step foot on the moon). The School of Aeronautics & Astronautics was founded as a separate school within the College of Engineering at Purdue University in 1945. The first edition of this book was published in 1995, at the time of the school's 50th anniversary. This corrected and expanded second edition brings the school's illustrious history up to date, and looks to Purdue's future in the sky and in space.
This volume reports the latest technological advances in polymeric composites and blends, reinforced polymeric and composite materials, and ceramics of engineering importance. It covers topics ranging from physical and mechanical properties testing and characterization to specialty composites.
This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design. After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks. In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive cracks propagating in brittle solids may help readers to understand the formation of a fractal-like cracking patterns in brittle solids, while the stability theory of crack paths helps to identify the straight versus sharply curved or sometimes wavy crack paths observed in brittle solids. In part four, the numerical simulation method of a system of multiple cracks is introduced by means of the finite element method, which may be used for the better implementation of fracture control in engineering structures. This book is part of a series on “Mathematics for Industry” and will appeal to structural engineers seeking to understand the basic backgrounds of analyses, but also to mathematicians with an interest in how such mathematical solutions are evaluated in industrial applications.