ME 7201: Computational Mechanics of Materials

Offered as Required


Credit Hours: 2-3-3
Prerequisites: ME 6201 or equivalent, or with the consent of the instructor
Catalog Description: Computational treatments of material and geometric nonlinearity, with emphasis on rate-dependent elastoplasticity and fracture.
Textbooks: None
Instructors: David McDowell (ME), Jiamin Qu (ME), Min Zhou (ME)
References:
  • 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.
Goals: 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.
Topics:

  1. Nonlinearity in finite element solutions
    1. A review: important aspects of finite elements
      Governing equations and variational principles
      Implementation issues
      Problem: code development for 1D or 2D linear DE's
    2. Nonlinearity
      Interactive solutions to nonlinear equations
      Material nonlinearity
      Geometric nonlinearity
    3. Plasticity
      Rate-independent plasticity
      Cyclic loading
      Rate-dependent viscoplasticity
      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
    4. Special considerations
      Singularities (e.g. cracks)
      VCE, contour and area domain integrals
      Node separation
      Contact
      Problem solution: crack-tip field, calculation of J-integral, stress intensity factor (K), COD, and 2D crack analysis
    5. 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
    6. Representation of Material Heterogeneities
      Microstructural discretization
      Calculation of effective properties
      Periodic and non-periodic cell analyses
      Interface and interphases
      Damage and failure
      Problem solution: Effective properties of metal matrix composites
  2. Boundary Element Method
    1. Introduction
    2. Weighted residual methods
    3. Potential Problems
    4. Boundary-integral equation formulation and solution
      Governing equations of elasticity
      Fundamental solutions
      Boundary-integral equations
      Boundary conditions
    5. The boundary element method
      Numerical foundation
      Linear approximation
    6. Two-dimensional Elastostatics
      Derivation of the boundary Integral equation
      Boundary element solution
    7. Elastoplastic fracture mechanics analysis
    8. Elastoplastic BIE formulation
    9. Numerical implementation
    10. 2D numerical problem solution
Grading Scheme:

Midterm

1/3

Computer Assignments

1/3

Final

1/3