Continuum mechanics

right|thumb|300px|The second-order Cauchy stress tensor \mathbf{T} describes the stress experienced by a material at a given point. For any unit vector \mathbf{v}, the product \mathbf{T} \cdot \mathbf{v} is a vector, denoted \mathbf{T}(\mathbf{v}), that quantifies the force per area along the plane perpendicular to \mathbf{v}. This image shows, for cube faces perpendicular to \mathbf{e}_1, \mathbf{e}_2, \mathbf{e}_3, the corresponding stress vectors \mathbf{T}(\mathbf{e}_1), \mathbf{T}(\mathbf{e}_2), \mathbf{T}(\mathbf{e}_3) along those faces. Because the stress tensor takes one vector as inpu

transformation of a body from a reference configuration to a current configuration

branch of physics which studies the behavior of materials modeled as continuous media

thumb|Tensile test of an Aluminium–magnesium–silicon alloys|Al-Mg-Si alloy. The local necking and the cup and cone fracture surfaces are typical for ductile metals. thumb|This tensile test of a Ductile iron|nodular cast iron demonstrates low ductility.

subdiscipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion

thumb|right|Extension of a coil spring, \delta, caused by an axial force, F.

numerical method for solving physical or engineering problems

component of stress coplanar with a material cross section

branch of science that studies the behavior of solid materials

thumb|Brittle fracture in glass thumb|Brittle fracture in cast iron tensile testpieces A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a sharp snapping sound.

fluid that does not follow Newton's Law of Viscosity, viscosity (the measure of a fluid's ability to resist gradual deformation by shear or tensile stresses) of non-Newtonian fluids is dependent on shear rate or shear rate history

measurable characteristic of the current state of a thermodynamic system, independent of the history of the system

thumb|Toughness as defined by the area under the stress–strain curve for one unit volume of the material. In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. Toughness is the strength with which the material opposes rupture. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. This measure of toughness is different from that used for fracture toughness, which describes the capacity of materials to resist fracture. Toughness requires a balance

thumb|Mānuka honey is an example of a thixotropic material. Thixotropy is a time-dependent shear thinning property. Certain gels or fluids that are thick or viscous under static conditions will flow (become thinner, less viscous) over time when shaken, agitated, shear-stressed, or otherwise stressed (time-dependent viscosity). They then take a fixed time to return to a more viscous state. Some non-Newtonian pseudoplastic fluids show a time-dependent change in viscosity; the longer the fluid undergoes shear stress, the lower its viscosity. A thixotropic fluid is a fluid which takes a finite tim

Viscoelasticity is a material property that combines both viscous and elastic characteristics. Many materials have such viscoelastic properties, especially materials that consist of large molecules. Polymers are viscoelastic because their macromolecules can make temporary entanglements with neighbouring molecules which causes elastic properties. After some time these entanglements will disappear again and the macromolecules will flow into other positions where new entanglements will be made (viscous properties).

In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the generation of lift on wings.

application of inward ("pushing") forces to a material or structure

field lines in a fluid flow

the tissues that connect, support, or surround other structures and organs of the body, not being hard tissue; tendons, ligaments, fascia, skin, fibrous tissues, fat, and synovial membranes (connective tissue), and muscles, nerves and blood vessels

remaining stress in a solid material after removal of the original cause

tensor that describes the state of stress at a point inside a material

relative change of length with respect the original length

moment that results in the bending of a structural element

OpenFOAM (Open Field Operation And Manipulation) is a C++ toolbox for the development of customized numerical solvers, and pre-/post-processing utilities for the solution of continuum mechanics problems, most prominently including computational fluid dynamics (CFD).

term in mechanics

characteristic number of a fluid for the relation between kinetic energy and enthalpy change

thumb|350x350px|Plot of shear rate as a function of the shear stress. Dilatants in green. A dilatant (, ) (also termed shear thickening) material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid. This behaviour is usually not observed in pure materials, but can occur in suspensions.

assertion that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree

solid mechanics theory that is used to describe the plastic behavior of materials

characteristic number of a fluid for the relation between heat produced by viscosity and heat received from outside by conduction

very small amount of fluid, identifiable throughout its dynamic history while moving with the fluid flow

3D generalization of the Leibniz integral rule

concept in physics

The stream function is constant along a streamline

relation between two physical quantities that is specific to a material or substance

equation

characteristic number in continuum mechanics used in the study of compressible flows

non-Newtonian fluid behavior

moment

Model of shear deformation and bending effects

aspect of history

mathematical descriptions of the mechanics of flat plates

Geometric representation of material yield

time derivative of shear strain

structural design tool

theory

type of anisotropic material

In chemistry and chemical physics, a mesophase or mesomorphic phase is a phase of matter intermediate between solid and liquid. Gelatin is a common example of a partially ordered structure in a mesophase. Further, biological structures such as the lipid bilayers of cell membranes are examples of mesophases. Mobile ions in mesophases are either orientationally or rotationally disordered while their centers are located at the ordered sites in the crystal structure. Mesophases with long-range positional order but no orientational order are plastic crystals, whereas those with long-range orientati

material property

In fluid dynamics, the enstrophy \mathcal{E} can be interpreted as another type of potential density; or, more concretely, the quantity directly related to the kinetic energy in the flow model that corresponds to dissipation effects in the fluid. It is particularly useful in the study of turbulent flows, and is often identified in the study of thrusters as well as in combustion theory and meteorology.

Mathematical image techniques

scalar potential used in fluid dynamics

material for which the stress–strain relationship derives from a strain energy density function

Reciprocal work theorem in engineering

equipment and procedure to measure materials' impact resistance

thumb|upright=1.1|Figure 1. Elements used in one-dimensional models of viscoplastic materials.

damage to materials due to cyclic mechanical loads

physical quantity that describes the rate of change of the deformation of a material

Bimoment (aka warping moment) is a term used in the analysis of beams (continuum mechanics) that relates to torsion and warping. Its symbol is Mω.