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Longer titles found: Cauchy stress tensor (view), Maxwell stress tensor (view), Viscous stress tensor (view), Piola–Kirchhoff stress tensors (view)

searching for Stress tensor 102 found (307 total)

alternate case: stress tensor

Radiation stress (3,159 words) [view diff] exact match in snippet view article find links to article

The radiation stresses behave as a second-order tensor. The radiation stress tensor describes the additional forcing due to the presence of the waves, which

the scale current is then the trace of the stress tensor. In the absence of any mass scales the stress tensor trace vanishes ( ℏ = 0 {\displaystyle \hbar

pressure and τ {\displaystyle {\boldsymbol {\tau }}} is the viscous stress tensor. Note that v v {\displaystyle \mathbf {v} \mathbf {v} } is a tensor

of movements on abundant faults, a particular solution T (the reduce stress tensor) is attained. It gives more comprehensive and accurate results in reconstructing

importance for the dynamics of the interaction is the wave radiation stress tensor. Wave–current interaction is also one of the possible mechanisms for

expressed in terms of the Beltrami stress tensor. Stress functions are derived as special cases of this Beltrami stress tensor which, although less general

Examples include the deformation gradient and the first Piola–Kirchhoff stress tensor. As with many applications of tensors, Einstein summation notation is

\mathbf {u} =0.\end{array}}} In a wide variety of applications, the stress tensor τ {\displaystyle \tau } is given as a linear function of the gradient

A second-order fluid is a fluid where the stress tensor is the sum of all tensors that can be formed from the velocity field with up to two derivatives

}}=2\eta _{0}\mathbf {D} } where: T {\displaystyle \mathbf {T} } is the stress tensor; λ {\displaystyle \lambda } is the relaxation time; T ∇ {\displaystyle

Cauchy stress tensor, and J 2 , J 3 {\displaystyle J_{2},J_{3}} are the second and third invariants of the deviatoric part of the Cauchy stress tensor. There

with bars), σ i j {\displaystyle \scriptstyle \sigma _{ij}} is the stress tensor (note that on the left is a tensor-vector product), γ {\displaystyle

where: T {\displaystyle \mathbf {T} } is the deviatoric part of the stress tensor; λ 1 {\displaystyle \lambda _{1}} is the relaxation time; λ 2 {\displaystyle

the e1 direction. In this test, the only non-zero component of the stress tensor is T11. Mansour, J. M. (2003). Biomechanics of cartilage. Kinesiology:

of the Ladyzenskaya-type model with a non-linear velocity dependent stress tensor was performed unfortunately no analytical solutions could be derived

crazing normally requires the presence of a dilative component of the stress tensor and can be inhibited by applying hydrostatic pressure. From a solid

a tensor, and the σ 11 {\displaystyle \sigma _{11}} element of the stress tensor is tensile force per area, or compression force per area, denoted as

}_{I}}+{{\sigma }_{II}}+{{\sigma }_{III}}}  denotes first invariant of Cauchy stress tensor, σ I , σ I I , σ I I I {\displaystyle {{\sigma }_{I}},{{\sigma }_{II}}

with the residual stress tensor τ i j {\displaystyle \tau _{ij}} grouping all unclosed terms. Leonard decomposed this stress tensor as τ i j = L i j +

hypothesis is avoided and the individual components of the Reynolds stress tensor are directly computed. These models use the exact Reynolds stress transport

the Jeans equations contain 9 unknowns (3 average velocities and 6 stress tensor terms), but only 3 equations. This means that Jeans equations are not

local curvature. At a more refined level, the beam is a 2D body whose stress-tensor is a function of local strain-tensor, and strain-tensor is a function

\;\operatorname {tr} ({\boldsymbol {\varepsilon }})I,} where σ is the stress tensor, ε the strain tensor, I the identity matrix and tr the trace function

Pulay forces (named for Peter Pulay) is an error that occurs in the stress tensor (or Jacobian matrix) obtained from self-consistent field calculations

non-Newtonian manner.: 145  The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation

note that the stress tensor for pure GR vanishes (this statement is equivalent to the vacuum Einstein equation) and the stress tensor for GR coupled

continuum mechanics, concerning fluids and solids. The Piola–Kirchhoff stress tensor and Piola transformation bear his name. Piazzale Piola and stazione

of a rigid body around its center of mass. In solid mechanics, the stress tensor is symmetric and so can be decomposed into a diagonal tensor with the

generally calculated explicitly at each numerical step. From this, the stress tensor of the system can be calculated and usually is calculated by the numerical

stress–energy tensor between conducting planes (Brown & Maclay 1969). The stress tensor evaluated on a plane yields the Casimir force. Brown was the first to

plasticity, the assumption that the plastic strain increment and deviatoric stress tensor have the same principal directions is encapsulated in a relation called

is usually defined as the average over the diagonals of the negative stress tensor: P a t = − 1 3 T r ( τ ) . {\displaystyle {\mathcal {P}}_{at}=-{\frac

Critical state soil mechanics is the area of soil mechanics that encompasses the conceptual models representing the mechanical behavior of saturated remoulded

pre-existing surface. In a continuum approach one can define a surface stress tensor f i j {\displaystyle f_{ij}} that relates the work associated with the

sense, is a type of transducer. Weirzbicki, Tomasz (12 May 2020). "Stress Tensor". LibreTexts. MIT OpenCourseWare. Retrieved 22 January 2024. COMSOL

the Oldroyd-B model, the relation between the shear stress tensor B and the orientation stress tensor A is given by: S + γ [ D S D t − Δ V ⋅ S − S ⋅ ( Δ

tensor fields across boundaries, see Ciarlet's book. Piola–Kirchhoff stress tensor Raviart–Thomas basis functions Raviart–Thomas Element Rognes, Marie

and T μ ν {\displaystyle T_{\mu \nu }} is a conserved operator (the stress-tensor) of dimension exactly ⁠ d {\displaystyle d} ⁠. For the associated symmetries

The radius of the curvature of the stressed structure is related to stress tensor in the structure, and can be described by modified Stoney formula. The

exemplary pieces referring to such theories are: Inscape, Early life, Stress Tensor, Mineral Life, Caressant l'horizon, InFALL, or ...limite les rêves au-delà

x_{3}\,} directions. For an isotropic, linear elastic material, the stress tensor that results from a state of antiplane shear can be expressed as σ ≡

comprises the generators of the conformal group of the worldsheet, the stress tensor in string theory obeys the commutation relations of (two copies of)

SIESTA routinely provides: Total and partial energies. Atomic forces. Stress tensor. Electric dipole moment. Atomic, orbital, and bond populations (Mulliken)

up, or reversed. The other results then are simple corollaries. The stress tensor of the fluid is σ i j = − p δ i j + μ ( ∂ i u j + ∂ j u i ) {\displaystyle

\nabla \right)\mathbf {u} } Navier–Stokes equations TD = Deviatoric stress tensor f {\displaystyle \mathbf {f} } = volume density of the body forces acting

tangential (shear forces), this can be described mathematically using the stress tensor: σ i j = C i j k l ε k l ⇌ ε i j = S i j k l σ k l {\displaystyle \sigma

p, q and θ {\displaystyle \theta } are invariants dependent on the stress tensor, while F ( p ) {\displaystyle F(p)} is the "meridian" function: F (

More formally, forces in continuum mechanics are fully described by a stress tensor with terms that are roughly defined as σ = F A , {\displaystyle \sigma

theory is necessarily a gravitational one. The source for the conserved stress tensor of the boundary theory is the boundary value of the bulk metric tensor

Academy of Sciences in 1911. "Corotational derivative" expresses the stress tensor in a rotating body. Jaumann was offered a professorship at Prague University

(1975) Memory effects in turbulence (1975) Rotation of the Reynolds' stress tensor in a decaying grid-generated turbulent flow (with P. J. H. Builtjes

representation of the Virasoro group, provides the transformation law of a CFT stress tensor under conformal transformations. From this perspective, the Schwarzian

the electromagnetic contribution. Namely, when the electromagnetic stress tensor F a b {\displaystyle F_{ab}} has only two non-vanishing components:

(U + cg)E is the mean wave energy density flux, S is the radiation stress tensor and ∇U is the mean-velocity shear rate tensor. In this equation in non-conservation

the time – effectively consists of the assumption that the Reynolds stress tensor is aligned with the strain tensor of the mean flow (i.e.: that the shear

to mass as defined by Einstein's equation E=mc2) contributes to the stress tensor and thus to the curvature of space-time, which is the general-relativistic

Moretti, "Direct z-function approach and renormalization of one-loop stress tensor in curved spacetimes, Phys. Rev.D 56, 7797 (1997). Minakshisundaram

that there are some conformal field theories that, in addition to the stress-tensor, have an infinite number of conserved tensors ∂ c j c a 2 . . . a s

David; Simmons-Duffin, David (2024-11-22). "Bootstrapping the 3d Ising stress tensor". Retrieved 2024-11-28. Komargodski, Zohar; Simmons-Duffin, David (14

become static even very far away from the collapse. In addition the stress tensor does not obviously satisfy the Raychaudhuri equation, one needs to make

are effectively three-dimensional quantities, and since the viscous stress tensor is symmetric and traceless, they have respectively three and five linearly

stress and radial stress, circumferential stress is a component of the stress tensor in cylindrical coordinates. It is usually useful to decompose any force

Einstein summation convention. Noting the thermodynamic connection between stress tensor components and strain tensor components, σ i j = ( ∂ f ∂ ε i j ) T

The correction to the free spin-2 equations due to the scalar field stress-tensor was extracted out of the four-dimensional Vasiliev equations and found

r {\displaystyle \sigma _{rr}} are the diagonal terms of the extra-stress tensor. Equation (1) represents mass conservation, and Equation (2) represents

of the NV− centers is as a detector to measure the full mechanical stress tensor in the bulk of the crystal. For this application, the stress-induced

\mathrm {d} N_{i},} where σ i j {\displaystyle \sigma _{ij}} is the stress tensor, and ε i j {\displaystyle \varepsilon _{ij}} is the strain tensor. In

{\tau }}+\rho \mathbf {b} } if the density ρ, pressure p, deviatoric stress tensor τ of the fluid, as well as external body forces b, are all given. The

for h μ ν {\displaystyle h_{\mu \nu }} . Substitute the perfect fluid stress tensor for the matter sources. Step 5: Solve for h 00 {\displaystyle h_{00}}

physicist, known for his treatises on mechanics. The Piola–Kirchhoff stress tensor and Piola transformation are named after him. JPL · 39854 39860 Aiguoxiang

physics) Pincushion distortion Pink noise Pinning force Piola-Kirchhoff stress tensor Pion Pion decay constant Pioneer anomaly Pionium Pipe flow Pipe network

Compatibility (mechanics) Curvilinear coordinates Piola–Kirchhoff stress tensor, the stress tensor for finite deformations. Stress measures Strain partitioning

laser-plasma interaction including dielectric effects in the Maxwellian stress tensor led to the prediction of ultrahigh acceleration of plasma blocks being

density W ( F ) {\displaystyle W({\bf {F}})} , the Piola-Kirchhoff stress tensor S {\displaystyle {\bf {S}}} is given by S = ∂ W ∂ F {\displaystyle {\bf

determine a solution to the Einstein field equations; the electromagnetic stress tensor must be given as well. Both are provided in each section. One way to

{S}}^{i}={\boldsymbol {d}}^{i}\otimes \mathbf {n} ^{i}} where σ is the stress tensor, Si is the Schmid tensor, Pi is its symmetric part, di is the shear

operators in the Sine-Gordon model: $\partial_μϕ\, \partial_νϕ$ and the stress tensor". arXiv:2205.09223 [math-ph]. Chandra, Ajay; Hairer, Martin; Shen, Hao

total energy-momentum of the system is simply given by integrating the stress-tensor on a spacelike slice. P μ = ∫ T μ 0 d 3 x {\displaystyle P^{\mu }=\int

be obtained from the vanishing of the trace of the electromagnetic stress tensor: since this trace equals 3P − u, we get P = u 3 , {\displaystyle P={\frac

(Bulgaria) seismic sequences of 1986: location, focal mechanism and regional stress tensor". Tectonophysics. 172 (1–2): 121–134. Bibcode:1990Tectp.172..121O. doi:10

ramification, but they may instead exemplify a pattern formed in a stress tensor field. A vein is made up of a vascular bundle. At the core of each bundle

{\displaystyle N=1} super Virasoro algebra. Using a mode expansion where the stress tensor modes are given by L n {\displaystyle L_{n}} and the supercurrent modes

is anisotropic material or orthotropic material. The three-dimension stress tensor is required for stress and strain analysis. The stiffness and compliance

{\displaystyle \mathbf {x} } ) within the volume element, then its stress tensor is given by T = E ∇ u {\displaystyle \mathbf {T} =E\nabla \mathbf {u}

the 1st Piola-Kirchhoff stress tensor P {\displaystyle {\boldsymbol {P}}} (which is the transpose of the nominal stress tensor P T = N {\displaystyle {\boldsymbol

}+U^{5})={\text{constant}}.} Kaluza proposed a five-dimensional matter stress tensor T ~ M a b {\displaystyle {\widetilde {T}}_{M}^{ab}} of the form T ~

{\displaystyle {\bar {\tau }}_{k}} is the k {\displaystyle k} -phase strain stress tensor. g {\displaystyle g} is the acceleration due to gravity. M → I , k {\displaystyle

Donald W. (1984). "An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando

derivation of the same relation for disjoining pressure involves the stress tensor. When the electric potentials or charge densities are not too high,

deviatoric) stress tensor τ d {\displaystyle {\boldsymbol {\tau }}_{d}} . The dissipative stress consists of a compression stress tensor τ c {\displaystyle

the simplest extension of vacuum NEHs, and the nonvanishing energy-stress tensor for electromagnetic fields reads ( 15 ) T a b = 1 4 π ( F a c F b c

{\displaystyle A^{\mu }} also appearing in the electromagnetic energy–stress tensor T μ ν e m {\displaystyle T_{\mu \nu }^{\mathrm {em} }} in second order

exact solutions that are non-vacuum solutions, solutions in which the stress tensor is non-zero. Solving the geodesic equations requires knowledge of the

{vp} }} where s {\displaystyle {\boldsymbol {s}}} is the deviatoric stress tensor, ε ˙ e q {\displaystyle {\dot {\varepsilon }}_{\mathrm {eq} }} is the

condition. The gravitational field is defined by density, velocity and stress tensor of the Lorentz ether, so that the harmonic conditions become continuity

\mathbf {n} } , where σ {\displaystyle {\boldsymbol {\sigma }}} is the stress tensor, and u i {\displaystyle u_{i}} are the components of the displacement

S2CID 829137. Needs, R; Mansfield, M (1989). "Calculations of the surface stress tensor and surface energy of the (111) surfaces of iridium, platinum and gold"

}~Q_{\alpha }~\delta w^{0}\right]~d\Gamma \end{aligned}}} The symmetry of the stress tensor implies that N α β = N β α {\displaystyle N_{\alpha \beta }=N_{\beta

Tomoyuki; Kimura, Hidehiko (2019-12-20). "Intragranular three-dimensional stress tensor fields in plastically deformed polycrystals". Science. 366 (6472): 1492–1496

during Solid-Solid Structural Transformations under a General Applied Stress Tensor: Example of $\mathrm{Si}\text{ }\text{ }\mathrm{I}\ensuremath{\righ

(2020). “Structure functions and invariants of the anisotropic Reynolds stress tensor in turbulent flows on water-worked gravel beds”. Physics of Fluids,

w_{,\alpha }^{0}\right]~d\Gamma \end{aligned}}} The symmetry of the stress tensor implies that N α β = N β α {\displaystyle N_{\alpha \beta }=N_{\beta