MEC E 788-A2
Mechanics of Microstructured Materials: Fiber composites, Biomembranes
Course objectivesThe primary objectives of this course are to expand graduate students’ knowledge and practical expertise in the field of modeling and analysis of microstructured materials
Course outline I. Preliminaries
1. Linear spaces
2. Vectors and tensors in Euclidean spaces: Gateaux derivative
II. Kinematics of deformations
1. Bodies, configurations and motions
2. Deformation gradient: Polar decomposition, stress and strain measure 3. Gradient of deformation: Strain-gradient
III. Fiber-reinforced composite materials
1. Strain-gradient theory: High-order tensors and their multilinear transformations 2. Gradient of deformation gradient tensor
3. Applications in fiber-reinforced composite: extensible unidirectional and bidirectional fiber composites
IV. Superposed incremental deformations
1. Leading order approximations of kinematics and kinetic variables 2. Linearization of governing equations and boundary conditions 3. Solutions of linearized systems of equations
V. Biological membranes
1. Curvilinear coordinate: covariant and contravariant vectors 2. Line segments, Curvatures and Coordinates on a surface
3. Applications in lipid bilayer membranes: Membrane-substrate interactions, intramembrane viscous flows
4. Admissible linearization of membrane shape equations and associated boundary conditions
Course outcomes
Introduce students to the notion of exploiting differential geometry to gain insight in the mechanics of microstructured materials. Familiarize students with classifications and applications of continuum theories arising in the modeling and analysis of engineering materials. Discuss the developments of compatible two-dimensional theory from the general three-dimensional counterparts. Enable students to establish Euler equilibrium equations of microstructured materials such as fiber-reinforced composites and lipid membranes.
Developing linearized formulas under the assumption of superposed incremental deformations.
Application of linearized theory to the two-dimensional materials (including simplification of
three-dimensional materials). Upon completion of the course, students shall be able to: apply continuum principles to the deformation analyses of engineering materials; Establish constitutive equations of microstructured materials; simulate the deformations of two- dimensional materials whose equilibrium equations and boundary conditions are obtained from the variational principles; Linearize the resulting equilibrium equations; obtains analytical expressions for linearized system of equations
Assignment: 10%
Project: 20%
Midterm: 30%
Final: 40%
