Stress tensor Definition and 104 Threads

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 &...

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...

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...

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...

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...

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...

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...

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 =...

Homework Statement Stress tensor at a point Q in a body has components: pij: | 1 -1 0 | |-1 2 1 | | 0 1 3 | (i) Calculate components of the stress force f across a small area of surface at Q normal to n = (2,1,-1). (ii) The component of f in the direction of n...

This hasn't been asked before, and I am more or less new to this subject. Therefore, I haven't done an attempt on the solution. Say we have a 2 dimensional square of sides "a". 2 forces "F" of equal magnitude and opposite direction act on the opposite ends of the square such that the square...

Hello, I perform FEA (finite element analysis) and write massive amounts of VBA code in Access in order to streamline heat exchanger designs and I have a Boss with no experience with Tensors and the ASME (American Society of Mechanical Engineers) Section VIII, Div. 2 requires one to calculate...

Well lately i have in mess for this. The problem is about the stress energy tensor. Well we know that T_mn = r0 U^m U^n where r0 is mass density and U is proper velocity. Ok now consider the local observer. For him except for U^0 other U^m will be jero. So for local observer. T_00 = r0 c^2...

Would someone please be able to run me through the different components of the Maxwell Stress Tensor equation. T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} E^2 \right) I don't understand some of it and...

Hi all, I'm doing a MEMS project, I have a cantilever beam with a mass at its end, I need to calculate the stress tensor at the beam contact point, there is a piezoelectric matirial there, and I want to calculate the voltage it generates. somebody can please help me and explain how to calculate...

Hi all, I'm doing a MEMS project, I have a cantilever beam with a mass at its end, I need to calculate the stress tensor at the beam contact point, there is a piezoelectric matirial there, and I want to calculate the voltage it generates. somebody can please help me and explain how to calculate...

Maxwell stress tensor: T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} E^2 \right) We can interpret T as the force per unit area acting on the surface. But what surprises me is, T_{ij} = T_{ji}, i.e. the...

I am working through a set of notes on conformal field theory by Schellekens and want to show the conformal invariance of N=4 SYM theory in four dimensions. I start with the action S=\frac{1}{4g}\int d^Dx \sqrt{g}Tr\left(F_{\mu\nu}F^{\mu \nu}) There's only the metric in the action to worry...

Hello ! I'm having trouble with the symmetry of the stress tensor. What it means physically? In the demostration of the symmetry my book applies the angular momentum equation to a third material volume (a cube, length L). In the final step we have: 0 = \mathop {\lim }\limits_{L \to 0}...

Can we curl a stress tensor? What physically meaning will it be?

URGENT! Hi, I have a couple of urgent problems which are listed below. I am not sure what to do in either of them! If someone could help me as soon as possible that would be great! Cheers Problems: 1. Consider a linearly polarised plane wave incident normally on a slab of material...

what is a tensor. what is a stress tensor? what is a inertia tensor?