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Topic: Stress tensor

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Stress (physics)

	Stress Tensor (Site not responding. Last check: 2007-10-21)
		It is known that the motion of atoms is decided by the stress tensor on them.
		Stress is a symmetric tensor which has 6 independent components.
		Because the two dataset-position and stress tensor are correlated, we integrate the visualization to one single program so that user can see the relation between them clearly.
	www.prism.gatech.edu /~gt6211a/project/Stress.html (862 words)

	Tensor Information - tensor lamps
		In the field of diffusion tensor imaging, for instance, a tensor quantity that expresses the differential permeability of organs to water in varying directions is used to produce scans of the brain.
		Perhaps the most important engineering examples are the stress tensor and strain tensor, which are both 2nd rank tensors, and are related in a general linear material by a fourth rank elasticity tensor.
		Examples of physical tensors are the tensor analysis tensor fasciae latae energy-momentum tensor, the inertia tensor and the polarization tensor.
	www.inanot.com /Ina-Electronics_Topics_T-/Tensor.html (1961 words)

	Analysis of Stress
		Mathematically, the stress tensor is a second-order Cartesian tensor with nine stress components.
		You assume the sign of a stress component is positive when its direction and the normal vector of the surface, on which the component of the stress tensor is acting, are of the same sign.
		This is a vector representation of the symmetric stress tensor.
	documents.wolfram.com /applications/structural/AnalysisofStress.html (2251 words)

	Mechanics of Materials: Stress
		The stress field is the distribution of internal "tractions" that balance a given set of external tractions and body forces.
		For example, the stress state at point P can be represented by an infinitesimal cube with three stress components on each of its six sides (one direct and two shear components).
		This grouping of the nine stress components is known as the stress tensor (or stress matrix).
	www.efunda.com /formulae/solid_mechanics/mat_mechanics/stress.cfm (598 words)

	Stress-energy tensor - Wikipedia, the free encyclopedia
		Warning: In solid state physics and fluid mechanics, the stress tensor is defined to be the spatial components of the stress-energy tensor in the comoving frame of reference.
		is the Ricci tensor, R is the Ricci scalar (the tensor contraction of the Ricci tensor), and G is the universal gravitational constant.
		In GR, this tensor agrees with the Hilbert stress-energy tensor.
	en.wikipedia.org /wiki/Stress-energy_tensor (901 words)

	The Stress Tensor
		In order to completely describe the stresses acting at a point in an elastic medium, consider the stresses acting on the infinitesimally small cube of material in Figure 1B.
		Intuitively, a tensor can be thought of as a quantity composed of a collection of vectors, and in three dimensions a tensor is a combination of three vectors.
		By this definition, a scalar is a tensor of rank zero and is invariant under orthogonal transformation.
	www.geofys.uu.se /bl/Avh/node5.html (439 words)

	Properties of the stress tensor
		The principal stress magnitudes (the eigenvalues) are denoted
		Due to the presence of the free surface, the stress field close to the Earth's surface is expected to have one principal stress vertical and hence two horizontal principal stresses.
		This separates the stress tensor into one component that determines the uniform compression or dilatation, and one component that determines the distortion or shearing, the deviatoric component.
	www.geofys.uu.se /bl/Avh/node6.html (605 words)

	StressMohr Program (Site not responding. Last check: 2007-10-21)
		In the second display, you explore the stress on a plane as you vary the orientation of the plane and the state of stress in the system.
		In two dimensions, the stress tensor is a two by two array and three numbers define the stress tensor and allow us to calculate the stress vector for any plane.
		For lithostatic stress the magnitude of the stress is independent of the orientation of the plane, the stress is always perpendicular to the plane, and the shear component is always zero.
	www.geo.lsa.umich.edu /~vdpluijm/stressmohr/stressmohr.html (4386 words)

	Envisioning n-th Order Tensors ©
		Unlike the quadric surface the largest principal stress corresponds to the largest dimension and unlike the Haber glyph the exaggerated curvature of the peanut shape emphasizes the anisotropy of the normal component of the principal stress.
		By mapping stress type as color, the green shear stress is observed to coincide with the conical surface of the quadric glyph, where shear is expected, but shear is observed on the Reynolds glyph surface where it was not expected.
		Many problems in continuum mechanics emphasize continuous changes in tensor properties: such as the comoving derivative of a property associated with a fluid particle moving through a fluid in Eulerian space or continuous lines of principal stress in a solid where the deformation field is defined in Lagrangian space.
	www.sv.vt.edu /classes/ESM4714/methods/EEG.html (8852 words)

	Stress (physics) - Wikipedia, the free encyclopedia
		The stress axis on a stress-strain graph is often engineering stress, even though the sample may undergo a substantial change in cross-sectional area during testing.
		They are the eigenvalues of the stress tensor and are orthogonal because the stress tensor is symmetric (as per the spectral theorem).
		Being a tensor, the stress has two directional components: one for force and one for plane orientation; in three dimensions these can be two forces within the plane of the area A, the shear components, and one force perpendicular to A, the normal component.
	en.wikipedia.org /wiki/Stress_(physics) (3316 words)

	energy-momentum/stress-energy tensor - Advanced Physics Forums (Site not responding. Last check: 2007-10-21)
		The stress-energy tensor isn\'t (directly) a property of the metric of spacetime.
		Roughly, the stress-energy tensor can be thought of as being the flow of energy-momentum in some space-time direction.
		Are the \"stress-energy\" and the \"energy-momentum\" seperate tensors?
	www.advancedphysics.org /forum/showthread.php?t=474 (861 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		stress-energy tensor is a generalization of the three dimensional stress tensor developed late in the last century and used by all materials science engineers to compute stresses in solid materials.
		These numbers are the components of the tensor and they are analogous to the n components of a vector or covector.
		This tensor measures the field energy and flow of that energy of the EM field.
	math.ucr.edu /home/baez/PUB/tensor (848 words)

	All I wanna know about Viscous Stress
		In a nutshell, viscous stress try to stop relative motion between different small part of the fluid … I can even say whenever there is a strain rate (i.e., deformation that changes with time and is caused by the velocity gradient) within the fluid, a viscous stress act to reduce that rate-of-strain.
		For example, it can be sometimes seen in some (bad) books that the stress tensor is defined positive in compression but the rate-of-strain is defined negative in compression or that the stress tensor is positive in compression and in the next chapter positive in extension, all this is horribly confusing, complicate and pure non-sense.
		This means, for a given normal applied stress and a given volumetric grain concentration, it is impossible to have shear stress within a frictional granular flow higher than its yield shear stress (i.e., the flow is at yield and flow plastically).
	www.granular-volcano-group.org /viscous_stress.html (4861 words)

	Direct inversion of earthquake first motions for both the stress tensor and focal mechanisms and application to ...
		To address these issues, we present a new method for constraining stress tensors, in which first-motion observations are directly inverted for stress without assuming that focal mechanisms are known.
		The technique produces estimates of four stress parameters, a suite of focal mechanisms consistent with both the stress tensor and the first motions, and estimates of the uncertainty in stress.
		It also provides a natural test of the stress homogeneity hypothesis and a means to identify those earthquakes whose first motions are not consistent with a homogeneous stress tensor.
	www.agu.org /pubs/crossref/2001/2001JB000437.shtml (476 words)

	A Review of Plastic-Frictional Theory (Part. 1)
		is the first invariant or the "trace" of the stress tensor (i.e., the sum of the diagonal element).
		If the shear stress is increased for a given normal stress such that the stress state of the material is exactly on the yield line, then plastic strain or yielding will results.
		The octahedral shear stress is proportional to the root mean square of the three maximum possible shear stress as shown by Eq.17.
	www.granular-volcano-group.org /frictional_theory.html (2795 words)

	[No title]
		The stress drop, tD, averaged over the ruptured fault surface, can be described in terms of a stress tensor, S in the coordinate system shown in Figure 1a.
		The slip vector for a given earthquake, assuming the direction is the direction of maximum shear stress, is primarily a function of several parameters, which include (1) the orientation of the remote stress field, (2) the orientation of the fault plane, and (3) the relative magnitudes of the principal stresses.
		The inferred magnitudes of the principal stresses estimated from the 1952 earthquake stress drop and the measured stress directions indicates that f ~0.9.
	www.aapg.org /datashare/data_002/data_002.doc (1318 words)

	5.8. Maxwell Stress Tensor (Site not responding. Last check: 2007-10-21)
		Notation summarizes the vector and tensor algebraic notations.
		Maxwell Tensor From Maxwell's Equations derives the Maxwell stress tensor from Maxwell's equations using Equation 5.246.
		This section summarizes the notations of vector and tensor algebraic notations used to derive the Maxwell stress tensor.
	www.oulu.fi /tietohallinto/ohjeet/unix/ansys-6.1/content/thy_emg8.html (418 words)

	Finite Element Analysis engineering - What is a stress tensor?
		Stress tensors come from the mathematical theory of elasticity where the stress state is defined in indicial notation.
		That is, the notation for the stress field can be described in the form of a scalar (zero rank), vector (first rank) or a matrix (second rank).
		The "stress tensor" then is (in 3-space) the 3 x 3 symmetric matrix which describes the state of stress.
	www.eng-tips.com /viewthread.cfm?qid=54705 (440 words)

	The stress tensor (Site not responding. Last check: 2007-10-21)
		When a fluid is at rest, only normal stresses are exerted, the normal stress is independent of the direction of the normal to the surface element across which it acts, and the stress tensor has the form
		It is convenient to regard the stress tensor as the sum of an isotropic part
		is the viscous stress tensor and has the distinctive property of begin entirely due to the existence of the motion of the fluid.
	grus.berkeley.edu /~jrg/ay202/node69.html (423 words)

	The Stress Tensor Calculator
		Visualizing Stress puts the data used to calculate the tractions on each plane in a table next to the stress ellipse shown in Figure 12.
		These two stresses are referred to as the maximum and minimum principal stresses.
		Furthermore, as will be discussed in the next section, if we know the orientation and magnitude of two of the three principal stresses, then we can calculate the normal and shear stresses acting on all possible planes oriented at some given angle to the known maximum principal stress.
	www.geology.sdsu.edu /visualstructure/vss/htm_hlp/st_calc.htm (343 words)

	EN175: Mechanics of Solids - Introduction to Tensors and their properties (Site not responding. Last check: 2007-10-21)
		A tensor is a linear mapping of a vector onto another vector.
		The inverse of a tensor may be computed by calculating the inverse of the matrix of its components. Click Here to see how to do this. The result cannot be expressed in a compact form for a general second order tensor, and is best computed by methods such as Gaussian elimination.
		The eigenvalues of a tensor, and the components of the eigenvectors, may be computed by finding the eigenvalues and eigenvectors of the matrix of components. Click here to recall how to do this.
	www.engin.brown.edu /courses/en175/Notes/tensors/tensors.htm (1277 words)

	9.2.2 Relating strain to stress
		Relating the stress, whose divergence yields the internal forces, to the strain, which arises from the kinematics of parcel deformations, forms a fundamental problem in continuum mechanics.
		In elasticity theory, the relation between stress and strain is typically assumed to follow some form of Hooke's law.
		Under hydrostatic balance, the only form of stress on a fluid parcel is due to the pressure.
	www.gfdl.noaa.gov /~smg/MOM/web/guide_parent/s2node94.html (297 words)

	Surface forces and the general form of the stress tensor (Site not responding. Last check: 2007-10-21)
		Thus, the stress tensor is symmetrical, that is
		are normal stresses in the sense that each of them gives the normal component of surface force acting across a plane surface element parallel to one of the coordinate planes.
		are tangential stresses, sometimes also called shearing stresses, since in both fluids and solids they are set up by a shearing motion or displacement in which parallel layers of matter slide relative to each other.
	grus.berkeley.edu /~jrg/ay202/node4.html (971 words)

	stress-energy tensor of a perfect fluid
		The stress energy tensor of a perfect fluid is composed of two terms of which only one term contains the metric tensor gab.
		What I find bizar however is that the metric tensor enters into the expression of the stress-energy tensor in such an asymmetric way (one part affected, the other not).
		If you're talking about the components of the tensor at a given point then you can choose whatever system of coordinates you like, even locally a locally flat coordinate system in which the metric tensor is diag(1,-1,-1,-1).
	www.physicsforums.com /showthread.php?p=1138724#post1138724 (1534 words)

	The Stress Tensor
		In the previous section we solved for the lithostatic stress, or the stress caused by the weight of an overlying column of rock on its base.
		Point P is located at the base of a granite cube in the upper crust with a vertical stress of 40 MPa and horizontal stress of 20 MPa.
		The forces (F) in their respective directions are resolved from the stress in the same directions divided by the areas of the faces of the right triangular prism on which the force is acting.
	www.geology.sdsu.edu /visualstructure/vss/htm_hlp/stress_tns.htm (735 words)

	Example 3. Tensor (Wind Stress)
		Next, consider a data object consisting of a horizontal wind stress tensor measured over an
		The wind stress tensor has four components, two along each of the dimensions of the grid.
		The data object has data records, so it must have a Level 2 dimension; we will use a generic index counter as the Level 2 dimension.
	code916.gsfc.nasa.gov /Data_services/doc/df/node74.html (149 words)

	Stress-Energy Tensor
		It's possible to show rigorously that there are no solutions to Einstein's equations for 0+1 or 1+1 dimensional stress-energy tensors (within the context of standard distribution theory).
		The reason is that we should have objects important to the theory - in particular the Riemann tensor - be physically interpretable.
		It's hard to even say what specific form a distributional stress-energy tensor should take (it's easy if you assume it is not self-gravitating, but that's not what we're talking about).
	www.physicsforums.com /showthread.php?p=918243 (1167 words)

	stress.energy
		In local coordinates, the stress-energy tensor may be regarded as a 4x4 matrix T
		Also, remember that "energy" is the same as "momentum in the time direction", and that "density" is the same as "flow in the time direction".
		But it's only in general relativity where the stress-energy tensor is sitting proudly on the right side of an equation, telling spacetime how to curve.
	math.ucr.edu /home/baez/gr/stress.energy.html (909 words)

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