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Topics in finite elasticity

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Finite elasticity is a theory of elastic materials that are capable of undergoing large deformations. This theory is inherently nonlinear and is mathematically quite complex. This monograph presents a derivation of the basic equations of the theory, a discussion of the general boundary-value problems, and a treatment of several interesting and important special topics such as simple shear, uniqueness, the tensile deformations of a cube, and antiplane shear. The monograph is intended for engineers, physicists, and mathematicians.

Author(s): Morton E. Gurtin
Series: CBMS-NSF regional conference series in applied mathematics 35
Edition: First Edition
Publisher: Society for Industrial and Applied Mathematics
Year: 1987

Language: English
Pages: 67
City: Philadelphia, Pa
Tags: Механика;Механика деформируемого твердого тела;Теория упругости;

Topics in Finite Elasticity......Page 1
Contents......Page 5
Preface......Page 7
CHAPTER 1 Introduction......Page 9
CHAPTER 2 Kinematics......Page 11
CHAPTER 3 Stress......Page 13
CHAPTER 4 Elastic Materials. Change of Observer......Page 15
CHAPTER 5 Material Symmetry......Page 19
CHAPTER 6 Simple Shear7......Page 23
CHAPTER 7 The Piola-Kirchhoff Stress......Page 27
CHAPTER 8 Hyperelasticity......Page 31
CHAPTER 9 The Elasticity Tensor......Page 35
CHAPTER 10 The Boundary-Value Problem......Page 37
CHAPTER 11 Variational Formulation......Page 41
CHAPTER 12 Stability and Uniqueness26......Page 45
CHAPTER 13 Incompressible Materials......Page 53
CHAPTER 14 Deformations of a Cube35......Page 55
CHAPTER 15 Anti-Plane Shear38......Page 59
References......Page 65