||ME 6201 or equivalent, or with the consent of the instructor
||Computational treatments of material and geometric nonlinearity, with emphasis on rate-dependent elastoplasticity and fracture.
||David McDowell (ME), Jiamin Qu (ME), Min Zhou (ME)
- Thomas J. R. Hughes, The finite element method : linear static and dynamic finite element analysis, Prentice-Hall, 1987.
- O.C. Zienkiewicz and R.L. Taylor , The finite element method, 4th ed., McGraw-Hill, 1989.
- K. J. Bathe, Finite element procedures, Prentice Hall, 1996.
- R. H. Gallagher, Finite element analysis: fundamentals, Prentice-Hall, 1974.
- A. Curnier, Computational methods in Solid Mechanics, Kluwer Academic Publishers, 1993.
- W. S. Hall, The boundary element method, Kluwer Academic Publishers, 1994.
- T. A. Cruse, Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, 1988.
||This course is intended for second year graduate students interested in learning computational tools that are useful in modeling nonlinear behavior of materials. Computer assignments will involve implementation of 2D elastoplasticity, deformation, fracture, and stress wave propagation using in-house codes and/or a commercial code such as ABAQUS.
- Nonlinearity in finite element solutions
- A review: important aspects of finite elements
Governing equations and variational principles
Problem: code development for 1D or 2D linear DE's
Interactive solutions to nonlinear equations
Internal state variable models
Solution procedures for quasi-static problems: generalized implicit and semi-implicit mid-point schemes
Implementation exercise: elastoplastic flow of notched body
- Special considerations
Singularities (e.g. cracks)
VCE, contour and area domain integrals
Problem solution: crack-tip field, calculation of J-integral, stress intensity factor (K), COD, and 2D crack analysis
- Transient problems
Solution procedures for time-dependent problems
Implicit Euler's method
Explicit Euler's method
Semi-implicit Euler's methods
Problem solution: 2D-elastoplastic wave propagation
- Representation of Material Heterogeneities
Calculation of effective properties
Periodic and non-periodic cell analyses
Interface and interphases
Damage and failure
Problem solution: Effective properties of metal matrix composites
- Boundary Element Method
- Weighted residual methods
- Potential Problems
- Boundary-integral equation formulation and solution
Governing equations of elasticity
- The boundary element method
- Two-dimensional Elastostatics
Derivation of the boundary Integral equation
Boundary element solution
- Elastoplastic fracture mechanics analysis
- Elastoplastic BIE formulation
- Numerical implementation
- 2D numerical problem solution