Plate tectonicsPlate tectonics (from the tectonicus, from the τεκτονικός) is the scientific theory that Earth's lithosphere comprises a number of large tectonic plates which have been slowly moving since about 3.4 billion years ago. The model builds on the concept of continental drift, an idea developed during the first decades of the 20th century. Plate tectonics came to be accepted by geoscientists after seafloor spreading was validated in the mid-to-late 1960s.
Nazca PlateThe Nazca Plate or Nasca Plate, named after the Nazca region of southern Peru, is an oceanic tectonic plate in the eastern Pacific Ocean basin off the west coast of South America. The ongoing subduction, along the Peru–Chile Trench, of the Nazca Plate under the South American Plate is largely responsible for the Andean orogeny. The Nazca Plate is bounded on the west by the Pacific Plate and to the south by the Antarctic Plate through the East Pacific Rise and the Chile Rise respectively.
Stress–strain curveIn engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves.
Ring strainIn organic chemistry, ring strain is a type of instability that exists when bonds in a molecule form angles that are abnormal. Strain is most commonly discussed for small rings such as cyclopropanes and cyclobutanes, whose internal angles are substantially smaller than the idealized value of approximately 109°. Because of their high strain, the heat of combustion for these small rings is elevated. Ring strain results from a combination of angle strain, conformational strain or Pitzer strain (torsional eclipsing interactions), and transannular strain, also known as van der Waals strain or Prelog strain.
Finite strain theoryIn continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue.
Strain (chemistry)In chemistry, a molecule experiences strain when its chemical structure undergoes some stress which raises its internal energy in comparison to a strain-free reference compound. The internal energy of a molecule consists of all the energy stored within it. A strained molecule has an additional amount of internal energy which an unstrained molecule does not. This extra internal energy, or strain energy, can be likened to a compressed spring.
Stress (mechanics)In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).
Stress–energy tensorThe stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.
TensorIn mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product.
Maxwell stress tensorThe Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the Lorentz force law. When the situation becomes more complicated, this ordinary procedure can become impractically difficult, with equations spanning multiple lines.
Electromagnetic stress–energy tensorIn relativistic physics, the electromagnetic stress–energy tensor is the contribution to the stress–energy tensor due to the electromagnetic field. The stress–energy tensor describes the flow of energy and momentum in spacetime. The electromagnetic stress–energy tensor contains the negative of the classical Maxwell stress tensor that governs the electromagnetic interactions. In free space and flat space–time, the electromagnetic stress–energy tensor in SI units is where is the electromagnetic tensor and where is the Minkowski metric tensor of metric signature (− + + +).
Indian PlateThe Indian Plate (or India Plate) is a minor tectonic plate straddling the equator in the Eastern Hemisphere. Originally a part of the ancient continent of Gondwana, the Indian Plate broke away from the other fragments of Gondwana , began moving north and carried Insular India with it. It was once fused with the adjacent Australian Plate to form a single Indo-Australian Plate, and recent studies suggest that India and Australia have been separate plates for at least 3 million years and likely longer.
Antarctic PlateThe Antarctic Plate is a tectonic plate containing the continent of Antarctica, the Kerguelen Plateau, and some remote islands in the Southern Ocean and other surrounding oceans. After breakup from Gondwana (the southern part of the supercontinent Pangea), the Antarctic plate began moving the continent of Antarctica south to its present isolated location, causing the continent to develop a much colder climate. The Antarctic Plate is bounded almost entirely by extensional mid-ocean ridge systems.
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.
Cauchy stress tensorIn continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e: or, The SI units of both stress tensor and traction vector are N/m2, corresponding to the stress scalar.
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.
Plane stressIn continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 (representable as a 2×2 matrix rather than 3×3). A related notion, plane strain, is often applicable to very thick members.
Strain energy density functionA strain energy density function or stored energy density function is a scalar-valued function that relates the strain energy density of a material to the deformation gradient. Equivalently, where is the (two-point) deformation gradient tensor, is the right Cauchy–Green deformation tensor, is the left Cauchy–Green deformation tensor, and is the rotation tensor from the polar decomposition of . For an anisotropic material, the strain energy density function depends implicitly on reference vectors or tensors (such as the initial orientation of fibers in a composite) that characterize internal material texture.
Prelog strainIn organic chemistry, transannular strain (also called Prelog strain after chemist Vladimir Prelog) is the unfavorable interactions of ring substituents on non-adjacent carbons. These interactions, called transannular interactions, arise from a lack of space in the interior of the ring, which forces substituents into conflict with one another. In medium-sized cycloalkanes, which have between 8 and 11 carbons constituting the ring, transannular strain can be a major source of the overall strain, especially in some conformations, to which there is also contribution from large-angle strain and Pitzer strain.
Electric displacement fieldIn physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in topics such as the capacitance of a material, as well the response of dielectrics to electric field, and how shapes can change due to electric fields in piezoelectricity or flexoelectricity as well as the creation of voltages and charge transfer due to elastic strains.
