Nonlinear Continuum Mechanics and Physics

Nonlinear Continuum Mechanics and Physics provides a differential geometry approach to nonlinear continuum mechanics that will appeal to both engineers and material scientists. It includes heuristic and rigorous expositions of crucial concepts like finite deformation compatibility conditions, the Lie-derivative, frame-indifference and material symmetry principles. With exercises at the end of each chapter to emphasize concepts, readers will be able to further understand the latest techniques and research. This book is designed to support postgraduates and researchers in the areas of mechanical engineering, nano-mechanics, biomechanics and computational mechanics.

• Systematically uses a differential geometric approach
• Provides new developments in convex analysis and variational calculus in finite deformation
• Investigates applications in biomechanics and soft matter mechanics
• Explains the atomistic interpretation of stress

1. Vectors and Tensors 2. Tensor analysis on Manifold 3. Concepts of Continuum Physics 4. Finite Deformation Kinematics 5. Strain Measures 6. Stress Measures 7. Principle of Frame-indifference 8. Balance Laws and Continuum Thermodynamics 9. Constitutive Relations 10. Variational Principles 11. Configurational Force 12. Nanomechanics 13. Geometrically-exact structural theory

graduate students, researchers, and engineers interested in nonlinear finite element methods, which will include civil engineers, materials scientists, aerospace engineers, mechanical engineers, and more.