Poisson's Ratio
Poisson's Ratio defines the ratio between the negative lateral strain and the longitudinal strain, so lateral strain can be calculated using: [1]
- .
In continuum mechanics, lateral strain, also known as transverse strain, is defined as the ratio of the change in diameter of a circular bar of a material to its diameter due to deformation in the longitudinal direction. It occurs when under the action of a longitudinal stress, a body will extend in the direction of the stress and contract in the transverse or lateral direction (in the case of tensile stress). When put under compression, the body will contract in the direction of the stress and extend in the transverse or lateral direction. It is a dimensionless quantity, as it is a ratio between two quantities of the same dimension.
Poisson's Ratio defines the ratio between the negative lateral strain and the longitudinal strain, so lateral strain can be calculated using: [1]
Some materials, known as auxetics, possess a negative Poisson's ratio because of their unique molecular structure. Because of this property, they experience a positive lateral strain alongside a positive longitudinal strain, and vice versa.
In 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 than any relevant dimension of the body; so that its geometry and the constitutive properties of the material at each point of space can be assumed to be unchanged by the deformation.
Young's modulus, or the Young modulus, is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress and strain in a material in the linear elasticity regime of a uniaxial deformation.
Hooke's law is a law of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance—that is, , where k is a constant factor characteristic of the spring, 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. He published the solution of his anagram in 1678 as: ut tensio, sic vis. Hooke states in the 1678 work that he was aware of the law already in 1660.
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. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis.
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. These curves reveal many of the properties of a material such as the Young's modulus, the yield strength and the ultimate tensile strength.
Poisson's ratio is a measure of the Poisson effect, that describes the expansion of a material in directions perpendicular to the direction of compression. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, is the amount of transversal expansion divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. Incompressible materials such as rubber, have a ratio near 0.5. In mathematical formula, the ratio is usually denoted by the Greek letter (nu). The ratio is named after the French mathematician and physicist Siméon Poisson.
Strength of materials, also called mechanics of materials, deals with the behavior of solid objects subject to stresses and strains. The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.
An elastic modulus is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form:
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.
In material science and solid mechanics, orthotropic materials have material properties that differ along three mutually-orthogonal twofold axes of rotational symmetry at a particular point. They are a subset of anisotropic materials, because their properties change when measured from different directions.
Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into other forms of energy, such as kinetic energy and sound energy, when the object is allowed to return to its original shape (reformation) by its elasticity.
The J-integral represents a way to calculate the strain energy release rate, or work (energy) per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov and independently in 1968 by James R. Rice, who showed that an energetic contour path integral was independent of the path around a crack.
Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance R, to the mechanical strain ε. The gauge factor is defined as :
Viscoplasticity is a theory in continuum mechanics that describes the rate-dependent inelastic behavior of solids. Rate-dependence in this context means that the deformation of the material depends on the rate at which loads are applied. The inelastic behavior that is the subject of viscoplasticity is plastic deformation which means that the material undergoes unrecoverable deformations when a load level is reached. Rate-dependent plasticity is important for transient plasticity calculations. The main difference between rate-independent plastic and viscoplastic material models is that the latter exhibit not only permanent deformations after the application of loads but continue to undergo a creep flow as a function of time under the influence of the applied load.
Material failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure (fracture) or ductile failure (yield). Depending on the conditions most materials can fail in a brittle or ductile manner or both. However, for most practical situations, a material may be classified as either brittle or ductile. Though failure theory has been in development for over 200 years, its level of acceptability is yet to reach that of continuum mechanics.
Deformation in continuum mechanics 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.
The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed to the strain rate, the rate at which it is deforming around that point.
Plasticity theory for rocks is concerned with the response of rocks to loads beyond the elastic limit. Historically, conventional wisdom has it that rock is brittle and fails by fracture while plasticity is identified with ductile materials. In field scale rock masses, structural discontinuities exist in the rock indicating that failure has taken place. Since the rock has not fallen apart, contrary to expectation of brittle behavior, clearly elasticity theory is not the last work.
Drucker stability refers to a set of mathematical criteria that restrict the possible nonlinear stress-strain relations that can be satisfied by a solid material. The postulates are named after Daniel C. Drucker. A material that does not satisfy these criteria is often found to be unstable in the sense that application of a load to a material point can lead to arbitrary deformations at that material point unless an additional length or time scale is specified in the constitutive relations.
Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material.
 | This classical mechanics–related article is a stub. You can help Wikipedia by expanding it. |
