Fiber bundle construction theoremIn mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of transition functions. The theorem also gives conditions under which two such bundles are isomorphic. The theorem is important in the associated bundle construction where one starts with a given bundle and surgically replaces the fiber with a new space while keeping all other data the same. Let X and F be topological spaces and let G be a topological group with a continuous left action on F.
Tensile testingTensile testing, also known as tension testing, is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimate tensile strength, breaking strength, maximum elongation and reduction in area. From these measurements the following properties can also be determined: Young's modulus, Poisson's ratio, yield strength, and strain-hardening characteristics.
Fiber cropFiber crops are field crops grown for their fibers, which are traditionally used to make paper, cloth, or rope. Fiber crops are characterized by having a large concentration of cellulose, which is what gives them their strength. The fibers may be chemically modified, like in viscose (used to make rayon and cellophane). In recent years, materials scientists have begun exploring further use of these fibers in composite materials. Due to cellulose being the main factor of a plant fiber's strength, this is what scientists are looking to manipulate to create different types of fibers.
Universal testing machineA universal testing machine (UTM), also known as a universal tester, materials testing machine or materials test frame, is used to test the tensile strength and compressive strength of materials. An earlier name for a tensile testing machine is a tensometer. The "universal" part of the name reflects that it can perform many standard tensile and compression tests on materials, components, and structures (in other words, that it is versatile). Several variations are in use.
Deformation (engineering)In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve.
Glass fiberGlass fiber (or glass fibre) is a material consisting of numerous extremely fine fibers of glass. Glassmakers throughout history have experimented with glass fibers, but mass manufacture of glass fiber was only made possible with the invention of finer machine tooling. In 1893, Edward Drummond Libbey exhibited a dress at the World's Columbian Exposition incorporating glass fibers with the diameter and texture of silk fibers. Glass fibers can also occur naturally, as Pele's hair.
Pullback bundleIn mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and a continuous map f : B′ → B one can define a "pullback" of E by f as a bundle fE over B′. The fiber of fE over a point b′ in B′ is just the fiber of E over f(b′). Thus f*E is the disjoint union of all these fibers equipped with a suitable topology. Let π : E → B be a fiber bundle with abstract fiber F and let f : B′ → B be a continuous map.
Infinitesimal strain theoryIn continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.
PlywoodPlywood is a composite material manufactured from thin layers, or "plies", of wood veneer that are glued together with adjacent layers, having their wood grain rotated up to 90° to one another. It is an engineered wood from the family of manufactured boards, which include medium-density fibreboard (MDF), oriented strand board (OSB), and particle board (or chipboard). All plywoods bind resin and wood fibre sheets (cellulose cells are long, strong and thin) to form a composite material.
FiberFiber or fibre (British English; from fibra) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorporate fibers, for example carbon fiber and ultra-high-molecular-weight polyethylene. Synthetic fibers can often be produced very cheaply and in large amounts compared to natural fibers, but for clothing natural fibers can give some benefits, such as comfort, over their synthetic counterparts.
