## Abstract

This important work covers the fundamentals of finite deformation in solids and constitutive relations for different types of stresses in large deformation of solids. In addition, the book covers the fracture phenomena in brittle or

quasi-brittle materials in which large deformation does not occur. This is provided in part two of the book, whereby chapters 6 to 10 present a thorough step-by-step understanding of fracture mechanics can be achieved.

Since mathematical proof with full derivation is demonstrated throughout the book, readers will gain the skills to understand and drive the basic concepts on their own, enabling them to put forward new ideas and solutions.

Finite deformations in material can occur with change of geometry such that the deformed shape may not resemble the initial shape. Analyzing these types of deformations needs a particular mathematical tool that is always associated with tensor notations. In general the geometry may be non-orthogonal, and the use of covariant and contra-variant tensor concepts to express the finite deformations and the associated mechanical strains are needed. In addition, it is obvious that in large deformations, there are several definitions for stress, each depending on the frame of the stress definitions. The constitutive equations in material, also depends on the type of stress that is introduced. In simulation of

the material deformation, components of the deformation tensor will be transformed from one frame to another either in orthogonal or in non-orthogonal coordinate of geometry. This informative book covers all this in detail.

quasi-brittle materials in which large deformation does not occur. This is provided in part two of the book, whereby chapters 6 to 10 present a thorough step-by-step understanding of fracture mechanics can be achieved.

Since mathematical proof with full derivation is demonstrated throughout the book, readers will gain the skills to understand and drive the basic concepts on their own, enabling them to put forward new ideas and solutions.

Finite deformations in material can occur with change of geometry such that the deformed shape may not resemble the initial shape. Analyzing these types of deformations needs a particular mathematical tool that is always associated with tensor notations. In general the geometry may be non-orthogonal, and the use of covariant and contra-variant tensor concepts to express the finite deformations and the associated mechanical strains are needed. In addition, it is obvious that in large deformations, there are several definitions for stress, each depending on the frame of the stress definitions. The constitutive equations in material, also depends on the type of stress that is introduced. In simulation of

the material deformation, components of the deformation tensor will be transformed from one frame to another either in orthogonal or in non-orthogonal coordinate of geometry. This informative book covers all this in detail.

Original language | English |
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Publisher | Apple Academic Press |

Number of pages | 290 |

ISBN (Electronic) | 978-1-4987-1702-1 |

ISBN (Print) | 978-1-771880-98-5 |

Publication status | Published - Oct 2015 |

## Keywords

- Mechanics of Finite Deformations
- Mechanics of Fracture