Stress tensor Definition and 119 Threads

Homework Statement If \sigma_{ij} = \begin{pmatrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{pmatrix} represents a stress tensor, on what plane(s) will the normal stress be a minimum? On what plane(s) will the shear stress be a maximum? Homework EquationsThe Attempt at a Solution The first...

Hi Guys I am trying to figure out what stresses in different planes mean physically for composite laminates. Say S stands for stress then SXX SYY SZZ would be longitudinal/axial stresses in respective Axes. (If we take the laminates to be in XY plane, failure stress SZZ would be equal to...

Hello, In CFD computation of the Navier-Stokes Equation, is stress tensor assumed to be symmetric? We know that in NS equation only linear momentum is considered, and the general form of NS equation does not assume that stress tensor is symmetric. Physically, if the tensor is asymmetric then...

The stress-energy tensor is an actual tensor, i.e., under a spacetime parity transformation it stays the same, which is what a tensor with two indices is supposed to do according to the tensor transformation law. This also makes sense because in the Einstein field equations, the stress-energy...

(this is not a hw) Assume you have a magnet of dimensions x_m, h_m, remanent flux density Br, and coercive field density Hc. The magnet is placed in a magnetic "C" structure (perfect iron) such that it is connected on one side but there is an airgap on the other side. xxxxxxxx xx... xx...

I've been working on Ex 5.4 in MTW. The maths is fairly straight forward, but I don't really understand what is going on! In part (b) what are the 'forces' pushing the volume through a distance? If they are forces, they must produce an acceleration but we have a constant velocity. Are these...

hey pf! in reading a book on viscous stresses i found the following: \tau_{ij}=2\mu\Big(s_{ij}-\frac{1}{3}s_{kk}\delta_{ij}\Big) where einstein summation is used. now we have s_{ij}=\frac{1}{2}\Big(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\Big) and then the claim is...

Homework Statement Hi, I am not sure if this is the right place for my question but here goes! The stress tensor in the Si coordinate system is given below: σ’ij = {{-500, 0, 30}, {0, -400, 0}, {30, 0, 200}} MPa Calculate the stress tensor in the L coordinate system if: cos-1a33=45°, and...

Should it be added to the Cauchy stress to calculate a "total stress", or it doesn't have such a physical interpretation as a surface force(EM field force is usually considered more of a "body force")? Certainly when the MST was first derived before aether theories were made superfluous by...

Hello, I am not sure what the first indice in the cauchy stress tensor indicates For example, σ_xy means that the stress in the y direction, but does x mean the cross sectional area is normal to the x direction?

Hi guys, I would like to know if the answer given to this thread is correct https://www.physicsforums.com/showthread.php?t=457405 I got the same doubt, is the expression for the tensor given in cartesian coordinates or is it general to any orthogonal coordinate system? Thanks in advance

http://im32.gulfup.com/u6n3f.jpg

Hi. I have a huge problem and without solving it I can't move forward. I will appreciate any help. Having the stress tensor S: 163.666557052527 -63.0272557558942 0.000000000000000E+000 -63.0272557558942 70.3802282767392 0.000000000000000E+000...

I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia, 1. Start with Lorentz force: \mathbf{F} = q(\mathbf{E} + \mathbf{v}\times\mathbf{B}) 2. Get force density \mathbf{f} =...

Homework Statement Given a cylinder in the Ox1x2x3 coordinate system, such that x1 is in the Length direction and x2 and x3 are in the radial directions. The stress components are given by the tensor $$ [T_{ij}] = \begin{bmatrix}Ax_2 + Bx_3 & Cx_3 & -Cx_2 \\ Cx_3 & 0 & 0 \\ -C_2 & 0 &...

Hi all, I have been reading up about continuum mechanics recently, and have a question regarding the reduction in stiffness coefficients in the stiffness matrix. I am aware of how the stiffness matrix is reduced to 21 coefficients. However, in order to reduce it from 21 to 13, one has to...

Homework Statement Calculate the deformation of a sphere of radius R and density \rho under the influence of its own gravity. Assume Hooke's law holds for the material. Homework Equations Not applicable; my question is simply one of understanding. The Attempt at a Solution I want...

Homework Statement http://img842.imageshack.us/img842/9577/stresstensor.png Homework Equations 'traction vectors' are just the rows of the stress tensor. that is, the first row of the stress tensor(the i-component of the tensor) is the first traction vector, second row is the second,etc...

I'm sure there's a trivial explanation for this, but it's escaping me. The space-space components of the stress-energy tensor are interpreted as the 3x3 stress tensor. But WP claims that the symmetry of the stress tensor need only hold in the case of equilibrium: "However, in the presence...

Homework Statement Using method of virtual displacement get the stress tensor for this problem. http://img32.imageshack.us/img32/7272/problemba.png The attempt at a solution The given system is 4-times tatically indeterminate. Since it is symetrical we can split it in half vertically...

Hi all, It seems to me that the derivation of Maxwell stress tensor is independent of the permeability of the media or the nonliterary of its B-H relation. By this I mean that we use μ0 in the equations rather than μ. Would you please confirm that?

Hi all, I have a fundamental question about ( mechanical) stress tensor. Stress tensor a 3x3 tensor whose 9 entries looks "scalars" but in figures, the stress is illustrated by nine "vectors". Does it mean the stress tensors is in fact a 3x3x3 tensor of scalars whose nonzero entries are ignored?

For fluid with viscosity \mu our stress strain relationship takes the form \sigma_{ij} = -p \delta_{ij} + 2 \mu u_{ij}. I was wondering how to express this in cylindrical coordinates. The strain tensor I can calculate in cylindrical coordinates (what I get matches eq 1.8 in [1]). But how...

First of all, thanks for all the helpful comments to my previous posts. I'm trying to get a grasp of stress tensors and have been doing some studying. In the literature I've been looking at, it says something about the eigenvalues of stress tensors and the principle stresses. This is...

Hello everyone, I have a confusion about the application of Maxwell stress tensor: I have read some materials about Maxwell stress tensor and its application in calculating electromagnetic force on a body. To this end, a closed surface is assumed around the body and a surface integral on...

In fluid dynamics, always when some textbook talks about stress tensor, there is a figure like this: http://www.fea-optimization.com/ETBX/hooke_help_files/stress.gif it shows how stress tensor is defined based on a small cubic volume. I kind of understand why the shear stress τxz should be...

Homework Statement Show that in vacuum the pressure tensor of a (complex) plane electromagnetic wave only has a contribution for both directions in this bivector being along the direction of motion, and that contribution is equal in magnitude to the energy density. HINT: Choose 3 orthogonal...

Hello, so I was asked a question in two parts (Peskin & Schroeder problem 2.1). The first part asked me to derive the source-free Maxwell's equations from the action: S=\int{d^4 x \frac{-1}{4}F_{\mu\nu}F^{\mu\nu}} Given that the vector potential itself is the dynamical variable. I derived...

in a perfect fluid the stress energy tensor is: T_{AB} = (P + \rho) u_A u_B + P g_{AB} queation1 : always u_A =1, \vec{0}? question2: if the space time have a line element h_{AB}dx^A dx^B...for the calculus of T_{AB}, ¿ g_{AB} = h_{AB}? ¿can i to use g_{AB}=\eta_{AB} if h_{AB}...

My question is regarding exercise 5.1 on page 141 of MTW. How come the tension and the pressure have the same value ? The field lines here are they the field lines of the electromagnetic force ? Thanks,

Homework Statement find all elements of maxwell stress tensor for a monochromatic plane wave traveling in z direction and linearly polarized in x. Homework Equations Tij=\epsilono(EiEj-(1/2)\deltaij E2+1/\muo(BiBj-(1/2)\deltaB2 The Attempt at a Solution So i found what E and B is well not...

Hi, I have a problem in classical field theory. I have a Lagrangian density \mathcal{L}=\frac{1}{2}\partial_\lambda \phi \partial^\lambda \phi + \frac{1}{3}\sigma\phi^3 . Upon solving the Euler-Lagrange equation for this density, I get an equation of motion for my scalar field \phi (x), where...

Can anyone tell me why this is true? I can't find an explanation anywhere, and it doesn't make sense to me geometrically either, especially for i=j. Isn't viscous force, by definition, a shear force? How can it produce a normal stress? Also why would Txy=Tyx? Why can't they be different...

Hello, I am trying to understand the Maxwell Stress Tensor. Specifically, I would like to know if it is coordinate-system dependent (and if so, what the expressions are for the stress tensor in cylindrical and spherical coordinates). Griffiths gives the definition of the maxwell stress tensor...

Hi, I have a question which was raised after reading the article "Derivation of the string equation of motion in general relativity" by Gürses and Gürsey. The geodesic equation for point particles can apparently be obtained as follows. First one takes the stress tensor of a point particle...

Hi,can u please tell me the difference between the Stress tensor & the Stress matrix...

Homework Statement If I have a 2x2 stress tensor and a normal vector n and want to find the shear stress. Is it the same which shear stress I find? I mean Pn = P dot n Pnn = Pn dot n Shear stress = Pnt = Pn - Pnnn This gives Shear stress with the same unit vectors as n, f.ex i an j But I can...

I've been working my way through GR using mainly D'Inverno's Introducing Einstein's General Relativity, but with MTW as well and a couple of other books. I began to get a sense of what was going to happen and got a big surprise when I reached the Schwartzschild solution. The process goes...

Hi all - first post at PF. As a 'science enthusiast' with no training in the tensor math of GR, was initially bewildered by the common assertion that still hypothetical 'dark energy' would act as a source of 'negative gravity' despite having positive energy density. Finally grasped that pressure...

Was a bit fuzzy as to whether this better fit HW or here, but since there really is no question associated with it, figured this made a bit more sense. I have a couple basic questions about the stress tensor: T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) +...

So I'm working on yet another problem, and have come to a minor stump. 2 wires run parallel with the Z axis in the xz plane, one with current I-1, other with current I-2. I need to determine the components of Maxwell's stress tensor at a field point P, where P is a point on the yz plane (x=0)...

\hat{N}=\{\vec{E},\vec{D}\}+\{\vec{H},\vec{B}\}-\frac{1}{2}(\vec{D}\cdot\vec{E}+\vec{B}\cdot\vec{H})\hat{1} \hat{1} - unit tensor If I look \{\vec{E},\vec{D}\}. I know that \{\vec{E},\vec{D}\}=\{\vec{D},\vec{E}\}^* But when I can say that \{\vec{E},\vec{D}\}=\{\vec{D},\vec{E}\}? and when...

My professor recently tasked me with first understanding maxwell's stress tensor and then applying it to analyze the force produced by a linear pull type solenoid. However after having studied the stress tensor I am not sure that I can apply the stress tensor to a solenoid. I don't believe...

Homework Statement stress tensor in cartesian components. \sigma is the stress tensor. e_i are the basis vectors Homework Equations \sigma \cdot \sigma The Attempt at a Solution I tried to write out the components with a cartesian basis: \sigma=\sigma_{ij} (e_i \otimes e_j) But then I'm...

I have a couple of questions about the stress tensor. I am not an engineering student, so this is the first time I have dealt with internal forces, stress, shears, and such. It is my understanding that the entries in the stress tensor are forces per unit area. I assume this means the total...

So we know that \frac{d}{dt}(P_{mech} + P_{field}) = \oint_S {T_{\alpha \beta } n_\beta da} that is, the time rate of change of the momentum of a system plus the momentum of the electromagnetic fields is equal to the surface integral of the term with the Maxwell Stress Tensor where there is...

First off, I'm not sure if MATLAB questions go here or not, or if they are even dealt with on this forum. If not more or remove I guess. I am no MATLAB wiz so this is mind-boggling to me. I am given a state of stress at a critical point of a component and told to plot a 3D parametric surface...

I'm trying to understand the meaning of the components of the stress(-energy) tensor. Considering just the space-space components, is this right? T^{ij} = \frac{\mathrm{d} F^i}{\mathrm{d} A^j}, where F^i is the x^i[/tex]-component of force, i \neq 0, and \mathrm{d} A^j is an area element...

Homework Statement x and y are nonconducting cylindrical shells. Both cylindrical shells are surrounding long wires that are carrying current. the x shell out of the page and the y shell into the page. x radius has a charge per unit length = to +\lambda y radius has a charge per unit length =...

Homework Statement x and y are nonconducting cylindrical shells. Both cylindrical shells are surrounding long wires that are carrying current. the x shell out of the page and the y shell into the page. x radius has a charge per unit length = to +\lambda y radius has a charge per unit length =...