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ME458 - BME487 NONLINEAR FINITE ELEMENT ANALYSIS |
OBJECTIVES
The theory and
application of
nonlinear finite element analysis in solid and biosolid mechanics. Topics: review and generalization of FE
concepts, review of solid mechanics, nonlinear incremental analysis,
displacement based FE formulation for large displacements and large
strains,
nonlinear constitutive relations, incompressibility and contact
conditions,
rubberlike materials, biomechanical materials, solution methods,
element
libraries.
OUTLINE
1. REVIEW
OF LINEAR FINITE ELEMENT CONCEPTS
Discrete
systems. Displacement-based finite element method. Potential energy and
variational
formulation. Weighted residual-Galerkin method. Lagrange multipliers
and
penalty functions. Isoparametric elements.
2. BASIC
CONTINUUM MECHANICS
Tensors. Stress and strain. Transformations and rotations. Green's and Almansi's strains. Cauchy stress. The polar-decomposition theorem. Second Piola-Kirchhoff stress.
3. FINITE
ELEMENTS FOR NONLINEAR SOLID AND STRUCTURAL MECHANICS
Incremental
solution to the nonlinear problem. Newton-Raphson iterations. Total and
updated
Lagrangian formulation. Incremental equations of motion. Isoparametric
finite
element discretization (truss, 2D, 3D elements).
4.
CONSTITUTIVE
RELATIONS
Elastic materials. Hyperelastic and
hypoelastic
materials. Incompressible and anisotropic materials. Biomechanical
characterization.
5. SPECIAL
TOPICS IN BIOSOLID MECHANICS
Mixed
element formulation. Modeling residual stresses, muscle activation, and
growth.
Multiscale modeling for complex structures.
6. IMPLEMENTATION
Data
structures. Incompressible elements: 2 and 3-D, tetrahedral elements.
Active/passive
element formulation. Solution procedures. Postprocessing.
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content
updated 23 January 2007
By Renato Perucchio