Tentative Course Outline:
1) Introduction (3 hrs)
1.1 Overview of nonlinear problems in solid mechanics
1.2 Review of needed topics in tensor and linear algebra
1.3 Computer programming and the finite element environment
2) Finite elasticity (12hrs)
2.1 Lagrangian formulation
2.2 Deformation gradients
2.3 Strain and stress measures
2.4 Frame invariance and objectivity in constitutive formulations
3) Average theories in micromechanics (9 hrs)
3.1 Linear micromechanical models (review)
3.2 Simplified 3D micromechanical models
3.3 Composite cylindrical assemblage (CCA) – nonlinear case
3.3 Mori-Tanaka – nonlinear case
3.3 Method of cells (MC)
3.4 Generalized method of cells (GMC)
3.5 High fidelity GMC
4) Computational Nonlinear Constitutive Models (small strain) (9 hrs)
4.1 Nonlinear elastic homogeneous anisotropic models for unidirectional layers
4.2 Rate independent multi--axial plasticity
4.3 Stress update algorithms
4.4 Consistent tangents
4.5 Hyperelastic formulation
4.6 Nonlinear viscoelastic Schapery Single Integral Model
5) Damage and failure of composite materials (6 hrs)
5.1 Discrete fracture versus continuum damage
5.2 Failure modes and criteria
5.3 Micro-buckling in unidirectional composites
5.4 Progressive damage and degradation techniques
5.5 Thermodynamics with internal variables in damage constitutive models
6) Nonlinear computational unit-cell models (3 hrs)
6.1 Formulation, periodicity and boundary conditions
6.2 Fiber reinforced polymeric composites
6.3 Metal matrix composites
7) Composite beams and plates (6 hrs if time permits)
7.1 Timoshenko beam theory
7.2 Love-Kirchhoff plate theory
7.3 Mindlin-Reissner plate theory
7.4 Shallow--arch formulation
7.5 multi-scale finite-elements
7.6 Buckling and post-buckling of composite plates