Boundary element analysis in computational fracture mechanics.

*(English)*Zbl 0648.73039
Mechanics: Computational Mechanics, 1. Dordrecht (Netherlands) etc.: Kluwer Academic Publishers. xiii, 162 p. $ 67.00; £39.00; Dfl. 125.00 (1988).

This book is written by one of the pioneer researchers on boundary elements. It profits from some twenty years of the author’s wide experience on boundary integral equations, with special emphasis on the subject of fracture mechanics applications. The text is a well-written compilation of the various modelling strategies tested by the author during all these years of intensive research activities.

Chapter 1 is dedicated to the history of boundary elements since its early emergence as a powerful numerical technique. Chapter 2 presents a short review of basic fracture mechanics concepts. Chapter 3 introduces the reader to the fundamentals of the boundary integral equations, including isotropic and anisotropic elasticity formulations and Chapter 4 presents the essential mathematical treatment needed to simulate fracture mechanics problems. Chapter 5 presents an elegant and powerful fracture mechanics formulation which gets along with the numerical modelling of the crack surface in two-dimensional-elastic applications. This is extended further in Chapter 6 to deal with elasto-plastic problems. Chapters 7 and 8 discuss alternative approaches (such as displacement discontinuities and weight functions) which are currently being developed to calculate stress intensity factors via boundary elements.

The book is an excellent contribution to the title problem and is recommended to anyone contemplating numerical techniques for fracture problems.

Chapter 1 is dedicated to the history of boundary elements since its early emergence as a powerful numerical technique. Chapter 2 presents a short review of basic fracture mechanics concepts. Chapter 3 introduces the reader to the fundamentals of the boundary integral equations, including isotropic and anisotropic elasticity formulations and Chapter 4 presents the essential mathematical treatment needed to simulate fracture mechanics problems. Chapter 5 presents an elegant and powerful fracture mechanics formulation which gets along with the numerical modelling of the crack surface in two-dimensional-elastic applications. This is extended further in Chapter 6 to deal with elasto-plastic problems. Chapters 7 and 8 discuss alternative approaches (such as displacement discontinuities and weight functions) which are currently being developed to calculate stress intensity factors via boundary elements.

The book is an excellent contribution to the title problem and is recommended to anyone contemplating numerical techniques for fracture problems.

Reviewer: J.C.F.Telles

##### MSC:

74R05 | Brittle damage |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65R20 | Numerical methods for integral equations |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |