Thus, minimizing 𝑡 𝐿 requires minimizing 𝑏 0 and maximizing 𝑘 𝑑 . However, this relationship is incomplete. The predefined design constraints dictate 𝑏 0 . From beam theory (Section S2), 𝑏 0 can be defined in terms of the tolerable deflection (𝛿) of the beam, the beam's initial length (𝑙 0 ), the supported load (𝐹), the loading and support configuration (𝐶 1 ), and the Young's modulus (𝐸) of the beam's material (a measure of a material's resistance to elastic deformation) (Equation ).