دانلود کتاب A course on finite elasticity

فهرست مطالب :

Cover
Preface
Contents
1 Concept of an elastic material
2 Observers and invariance
3 Mechanical power and hyperelasticity
3.1 Elasticity and energy
3.2 Work inequality
4 Material symmetry
4.1 Stress response
4.2 Strain energy
4.3 Isotropy
5 Fiber symmetry
6 Stress response in the presence of local constraints on the deformation
6.1 Local constraints
6.2 Constraint manifolds and the Lagrange multiplier rule
6.3 Material symmetry in the presence of constraints
7 Some boundary-value problems for uniform isotropic incompressible materials
7.1 Problems exhibiting radial symmetry with respect to a fixed axis
7.1.1 Pressurized cylinder
7.1.2 Azimuthal shear
7.1.3 Torsion of a solid circular cylinder
7.1.4 Combined extension and torsion
7.2 Problems exhibiting radial symmetry with respect to a fixed point
7.2.1 Integration of the equation
7.2.2 Pressurized shells, cavitation
8 Some examples involving uniform, compressible isotropic materials
8.1 Spherical symmetry, revisited
8.2 Plane strain
8.3 Radial expansion/compaction
9 Material stability, strong ellipticity and smoothness of equilibria
9.1 Small motions superposed on finitely deformed equilibrium states
9.2 Smoothness of equilibria
9.3 Incompressibility
10 Membrane theory
10.1 General theory
10.2 Pressurized membranes
10.3 Uniqueness of the director
10.4 Isotropic materials
10.5 Axially symmetric deformations of a cylindrical membrane
10.6 Bulging of a cylinder
11 Stability and the energy criterion
11.1 The energy norm
11.2 Instability
11.3 Quasiconvexity
11.4 Ordinary convexity
11.4.1 Objections to ordinary convexity
11.5 Polyconvexity
11.6 Rank-one convexity
11.7 Equilibria with discontinuous deformation gradients
11.8 The Maxwell–Eshelby relation
11.8.1 Example: alternating simple shear
12 Linearized theory, the second variation and bifurcation of equilibria
13 Elements of plasticity theory
13.1 Elastic and plastic deformations
13.2 Constitutive response
13.3 Energy and dissipation
13.4 Invariance
13.5 Yielding, the work inequality and plastic flow
13.6 Isotropy
13.7 Rigid-plastic materials
13.8 Plane strain of rigid-perfectly plastic materials: slip-line theory
13.8.1 State of stress, equilibrium
13.8.2 Velocity field
Supplemental notes
1 The cofactor
2 Gradients of scalar-valued functions of tensors
3 Chain rule
4 Gradients of the principal invariants of a symmetric tensor
5 Relations among gradients
6 Extensions
7 Korn\'s inequality
8 Poincaré\'s inequality
Index