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A. F. Bower is the author of Applied Mechanics of Solids by A. F. Bower, an online text whose title page gives his name as Allan F. Bower. The text connects elasticity, plasticity in continuum mechanics and fracture mechanics to explicit models of how solids deform. Its treatment of single-crystal plastic deformation follows slip systems and the rotation of the tensile axis, showing why a single crystal's response depends on its orientation.^[ref]

David Roylance developed an engineering treatment of fracture mechanics connecting cracks, loading and a material's resistance to failure. His notes derive an energy-balance description and introduce the stress intensity factor as a measure of crack-tip loading.^[ref]

In a simple linear-elastic mode-I geometry, $K_I=Y\sigma \sqrt{\pi a}$, with crack scale $a$ and dimensionless geometry coefficient $Y$. Comparing $K_I$ with the relevant fracture toughness shows why a nominally moderate bulk stress can be critical when a sufficiently large flaw is present. The geometry and elastic regime are essential assumptions.

Fracture mechanics studies the initiation and growth of cracks under loading. It connects a defect's geometry with the local driving force for crack extension and the material's resistance. A component's average stress alone cannot describe the concentration of deformation near a crack tip.^[ref]

In linear elastic fracture mechanics, a mode-I stress intensity factor often has the form $K_I=Y\sigma \sqrt{\pi a}$, where $a$ is a specified crack dimension and $Y$ accounts for geometry. Doubling $a$ increases $K_I$ by $\sqrt{2}$ at fixed nominal stress. Comparing the appropriate intensity with measured fracture toughness is meaningful only when the loading, geometry and small-scale yielding assumptions of the model apply.