Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance.
The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics.
- Offers a thorough, concise and organized presentation of continuum mechanics formulation
- Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems
- Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study
- Features extensive use of exercises, providing more material for student engagement and instructor presentation
1. Introduction 2. Mathematical Preliminaries 3. Kinematics of Motion and Deformation Measures 4. Force and Stress 5. General Conservation or Balance Laws 6. Constitutive Relations and Formulation of Classical Linear Theories of Solids and Fluids 7. Constitutive Relations and Formulation of Theories Involving Multiple Constitutive Fields 8. General Constitutive Relations and Formulation of Nonlinear Theories of Solids and Fluids 9. Constitutive Relations and Formulation of Theories Incorporating Material Microstructure
Martin H. Sadd is Emeritus Professor of Mechanical Engineering and Applied Mechanics at the University of Rhode Island. He received his Ph.D. in mechanics from the Illinois Institute of Technology and began his academic career at Mississippi State University. In 1979 he joined the faculty at Rhode Island and served as department chair from 1991 to 2000. Professor Sadd's teaching background is in the area of solid mechanics with emphasis in elasticity, continuum mechanics, wave propagation, and computational methods. He has taught elasticity at two academic institutions, in several industries, and at a government laboratory. Professor Sadd's research has been in the area of computational modeling of materials under static and dynamic loading conditions using finite, boundary, and discrete element methods. Much of his work has involved micromechanical modeling of geomaterials including granular soil, rock, and concretes. He has authored more than 70 publications and has given numerous presentations at national and international meetings.