Homework problems 26-31
This is the last homework set for ES 242r / ENGM 940
Spring 2007
ES 241 Advanced Elasticity Final Examination
Update on 23 May 2009: I'm adding links to the slides as they are uploaded.
The final exam will take the form of a pedagogical workshop. We have 8 students taking the class for credit. I have divided the lecture notes into 8 parts as follows.
Lecture 18--Aspects of dynamic fracture
A very breif introduction to aspects of dynamic fracture mechanics.
Instabilities
- Free energy and generalized coordinate. Equilibrium and stability
- Control parameter
- Configurational transitions of two types
- Critical point of configurational transition of the second type. Bifurcation analysis
- Behavior near a critical point. Post-bifurcation analysis
- Load-displacement relation near a critical point
- Koiter's theory of imperfection sensitivity
- A family of systems of many degrees of freedom
- Mode of bifurcation
- Vibration in the neighborhood of an equilibrium configuration
lecture 17. Introduction to Computational Ductile Fracture
An overview of several approaches to computational fracture mechanics for ductile structural metals.
Lecture 16 Corner singularity and applications
In this lecture I'll describe a recent PhD Thesis by Zhen Zhang.
Complex variable methods
- What types of PDEs can be solved using complex variable methods
- Anti-plane shear
- Elements of a function of a complex variable (contour integral, analytic continuation, conformal mapping)
- Line force
- Screw dislocation
- Crack
- Circular hole
- Elliptic hole
- Plemelj formulas
- Riemann-Hilbert problem
- Crack interacting with a point singularity
- In-plane deformation
- Dundurs parameters
- Interfacial cracks
- Anisotropic materials. Stroh formalism
Lecture 15 Ratcheting induced slow crack (RISC)
- Slides are attached.
- Reading material: Section 4 of Z. Suo, " Reliability of interconnect structures." pp. 265-324 in Volume 8: Interfacial and Nanoscale Failure (W.
Homework problems 20-25, Fracture Mechanics
This set is related to buckle-driven delamination, crack bridging, and interfacial cracks.
Lectures 14 & 16; Matrix cracking, cracks intersecting an interface, and crack kinking
Matrix cracking in composites and the competition between penetration and deflection when a crack approaches an interface, and the competition between advance in the interface and kinking out of the interface for an interface crack.