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.
Stress–strain analysisStress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.
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.
Linear elasticityLinear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.
Hooke's lawIn physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F_s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram.
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.
Elasticity (physics)In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.
Elasticity tensorThe elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness tensor. Common symbols include and . The defining equation can be written as where and are the components of the Cauchy stress tensor and infinitesimal strain tensor, and are the components of the elasticity tensor. Summation over repeated indices is implied. This relationship can be interpreted as a generalization of Hooke's law to a 3D continuum.
Rubber elasticityRubber elasticity refers to a property of crosslinked rubber: it can be stretched by up to a factor of 10 from its original length and, when released, returns very nearly to its original length. This can be repeated many times with no apparent degradation to the rubber. Rubber is a member of a larger class of materials called elastomers and it is difficult to overestimate their economic and technological importance. Elastomers have played a key role in the development of new technologies in the 20th century and make a substantial contribution to the global economy.
Deformation (physics)In physics and continuum mechanics, deformation is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of relative displacement of particles in the body that excludes rigid-body motions.
Share (finance)In financial markets, a share (sometimes referred to as stock) is a unit of equity ownership in the capital stock of a corporation, and can refer to units of mutual funds, limited partnerships, and real estate investment trusts. Share capital refers to all of the shares of an enterprise. The owner of shares in a company is a shareholder (or stockholder) of the corporation. A share is an indivisible unit of capital, expressing the ownership relationship between the company and the shareholder.
Share capitalA corporation's share capital, commonly referred to as capital stock in the United States, is the portion of a corporation's equity that has been derived by the issue of shares in the corporation to a shareholder, usually for cash. "Share capital" may also denote the number and types of shares that compose a corporation's share structure. In accounting, the share capital of a corporation is the nominal value of issued shares (that is, the sum of their par values, sometimes indicated on share certificates).
Chat roomThe term chat room, or chatroom (and sometimes group chat; abbreviated as GC), is primarily used to describe any form of synchronous conferencing, occasionally even asynchronous conferencing. The term can thus mean any technology, ranging from real-time online chat and online interaction with strangers (e.g., online forums) to fully immersive graphical social environments. The primary use of a chat room is to share information via text with a group of other users.
Online chatOnline chat may refer to any kind of communication over the Internet that offers a real-time transmission of text messages from sender to receiver. Chat messages are generally short in order to enable other participants to respond quickly. Thereby, a feeling similar to a spoken conversation is created, which distinguishes chatting from other text-based online communication forms such as Internet forums and email.
Price elasticity of demandA good's price elasticity of demand (, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded.
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.
Price elasticity of supplyThe price elasticity of supply (PES or Es) is a measure used in economics to show the responsiveness, or elasticity, of the quantity supplied of a good or service to a change in its price. Price elasticity of supply, in application, is the percentage change of the quantity supplied resulting from a 1% change in price. Alternatively, PES is the percentage change in the quantity supplied divided by the percentage change in price. When PES is less than one, the supply of the good can be described as inelastic.
Constitutive equationIn physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations.
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.
Information security auditAn information security audit is an audit of the level of information security in an organization. It is an independent review and examination of system records, activities, and related documents. These audits are intended to improve the level of information security, avoid improper information security designs, and optimize the efficiency of the security safeguards and security processes. Within the broad scope of auditing information security there are multiple types of audits, multiple objectives for different audits, etc.
