Reynolds, O., 1903, *The Sub-Mechanics of the Universe*, Cambridge University Press, Cambridge, UK.

Gurtin, M. E., Fried, E., and Anand, L., 2010, *The Mechanics and Thermodynamics of Continua*, Cambridge University Press, Cambridge, UK.

Lee, J. M., 2002, *Introduction to Smooth Manifolds*, Springer, New York, NY.

Betounes, D. E., 1986, “Kinematics of Submanifolds and the Mean Curvature Normal,” Arch. Rational Mech. Anal., 96(1), pp. 1–27.

[CrossRef]Gurtin, M. E., Struthers, A., and Williams, W. O., 1989, “A Transport Theorem for Moving Interfaces,” Quart. Appl. Math., 47(4), pp. 773–777.

Gurtin, M. E., 2000, *Configurational Forces as Basic Concepts of Continuum Physics*, Springer, New York, NY.

Catalan, G., Seidel, J., Ramesh, R., and Scott, J. F., 2012, “Domain Wall NanoElectronics,” Rev. Mod. Phys., 84(1), pp. 119–156.

[CrossRef]Stanley, H. E., 1992, “Fractal Landscapes in Physics and Biology,” Physica A, 186(1–2), pp. 1–32.

[CrossRef]Bucur, D., and Buttazzo, G., 2005, *Variational Methods in Shape Optimization Problems* (Progress in Nonlinear Differential Equations and Their Applications 65), Birkhäuser, Boston, MA.

Seguin, B., and Fried, E., 2014, “Roughening It—Evolving Irregular Domains and Transport Theorems,” Math. Models Methods Appl. Sci., 24(2014), 1729–1779.

[CrossRef]Harrison, J., 2014, “Operator Calculus of Differential Chains and Differential Forms,” J. Geom. Anal. (accepted ms published online).

[CrossRef]Marzocchi, A., 2005, *Singular Stresses and Nonsmooth Boundaries in Continuum Mechanics*, Lecture notes from a summer school in Ravello, Italy.

Rodnay, G., and Segev, R., 2003, “Cauchy's Flux Theorem in Light of Geometric Integration Theory,” J. Elasticity, 71(1–3), pp. 183–203.

[CrossRef]Whitney, H., 1957, *Geometric Integration Theory*, Princeton University Press, Princeton, NJ.

Harrison, J., 1999, “Flux Across Nonsmooth Boundaries and Fractal Gauss/Green/Stokes theorems,” J. Phys. A: Math. General, 32(28), pp. 5317–5327.

[CrossRef]Federer, H., 1969, *Geometric Measure Theory*, Springer, New York, NY.

Flanders, H., 1973, “Differentiating Under the Integral Sign,” Am. Math. Monthly, 80(6), pp. 615–627.

[CrossRef]Thomas, T. Y., 1957, “Extended Compatibility Conditions for the Study of Surfaces of Discontinuity in Continuum Mechanics,” J. Math. Mech., 6(3), pp. 311–322.

Cermelli, P., Fried, E., and Gurtin, M. E., 2005, “Transport Relations for Surface Integrals Arising in the Formulation of Balance Laws for Evolving Fluid Interfaces,” J. Fluid Mech., 544, pp. 339–351.

[CrossRef]Fosdick, R., and Tang, H., 2009, “Surface Transport in Continuum Mechanics,” Math. Mech. Solids, 14(6), pp. 587–598.

[CrossRef]Lidström, P., 2011, “Moving Regions in Euclidean Space and Reynolds' Transport Theorem,” Math. Mech. Solids, 16(4), pp. 366–380.

[CrossRef]Estrada, R., and Kanwal, R. P., 1991, “Non-Classical Derivation of the Transport Theorems for Wave Fronts,” J. Math. Anal. Appl., 159(1), pp. 290–297.

[CrossRef]Angenent, S., and Gurtin, M. E., 1989, “Multiphase Thermomechanics With Interfacial Structure 2. Evolution of an Isothermal Interface,” Arch. Rational Mech. Anal., 108(3), pp. 323–391.

[CrossRef]Mandelbrot, B. B., 2002, *Gaussian Self-Affinity and Fractals*, Springer-Verlag, New York, NY.

Lamb, H., 1895, *Hydrodynamics*, Cambridge University Press, Cambridge, UK.

Oseen, C. W., 1911, “Über Wirbelbewegung in einer reibenden Flüssigkeit,” Arkiv för Matematik, astronomi och Fysik, 7(14), pp. 1–11.

Ogden, R. W., 1984, *Nonlinear Elastic Deformations*, Halsted Press/John Wiley & Sons, New York, NY.

Griffith, A. A., 1921, “The Phenomenon of Rupture and Flow in Solids,” Philos. Trans. Roy. Soc., 221, pp. 163–198.

[CrossRef]Francfort, G., and Marigo, J. J., 1998, “Revisiting Brittle Fracture as an Energy Minimization Problem,” J. Mech. Phys. Solids, 46, pp. 1319–1342.

[CrossRef]Anand, L., 1996, “A Constitutive Model for Compressible Elastomeric Solids,” Comput. Mech., 18, pp. 339–355.

[CrossRef]Gdoutos, E. E., Daniel, I. M., and Schubel, P., 2003, “Fracture Mechanics of Rubber,” Mech., Autom. Control Robot., 13, pp. 497–510.

Gurtin, M. E., Williams, W. O., and Ziemer, W. P., 1986, “Geometric Measure Theory and the Axioms of Continuum Thermodynamics,” Arch. Rational Mech. Anal., 92(1), pp. 1–22.

[CrossRef]Noll, W., and Virga, E. G., 1988, “Fit Regions and Functions of Bounded Variation,” Arch. Rational Mech. Anal., 102(1), pp. 1–21.

[CrossRef]Šilhavý, M., 2006, “Fluxes Across Parts of Fractal Boundaries,” Milan J. Math., 74(1), pp. 1–45.

[CrossRef]Schuricht, F., 2007, “A New Mathematical Foundation for Contact Interactions in Continuum Physics,” Arch. Rational Mech. Anal., 184(3), pp. 495–551.

[CrossRef]Harrison, J., 2014, “Soap Film Solutions to Plateau's Problem,” J. Geom. Anal., 24(1), pp. 271–297.

[CrossRef]