Summary of concepts
Important concepts are listed here by chapter.
Chapter 2
Body forces and stress forces.
Definition of traction.
Calculation of traction across arbitrary plane.
Mathematics of Cartesian tensors and vectors.
Matrix and addition and multiplication.
Changing coordinate systems.
Eigenvalues, eigenvectors, and principal axes.
Dot, cross, and dyadic products of vectors.
Definition of stress tensor and its relationship to traction.
Symmetry of stress tensor.
Traction and stress on boundaries.
Chapter 3
Newton's second law in continuous media.
Mass budget.
Momentum budget.
Open systems.
Accelerated reference frames and inertial forces.
Non-Cartesian coordinates.
Lagrangian coordinates in continuum mechanics.
Chapter 4
Displacements of continuous media.
Decomposition of displacements into translation, rotation, and strain.
Rotation tensor and its dual vector.
Strain tensor and unit extensions.
Strain tensor and angle changes.
Strain tensor and fractional volume change.
Principal axis frame of strain tensor.
Compatibility conditions on strain tensor and derivation of displacement field.
Continuous motion and strain and rotation rates.