Stress tensor Definition and 119 Threads

The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

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  1. R

    Stress Tensor - simple problem (I think)

    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...
  2. G

    What are the components of the stress tensor based on the given formulation?

    The following information is given: The Cartesian components of stress tensor are: \sigma_{ij}=m(\hat \lambda _{i}\hat \mu _{j}+\hat \lambda _{j}\hat \mu _{i}) , (i=1,2,3; \ j=1,2,3) . \hat \lambda _{i} and \hat \mu_{j} are the Cartesian components of the unit vectors \hat \lambda...
  3. A

    Analytically finding the stress tensor field

    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...
  4. CFDFEAGURU

    What is a Stress Tensor and How is it Used in FEA Analysis?

    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...
  5. J

    Help with Stress Tensor: Local vs Other Observers

    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...
  6. B

    Maxwell Stress Tensor: Explained for Ben

    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...
  7. L

    Calculating Stress Tensor and Voltage for MEMS Project

    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...
  8. L

    Calculating Stress Tensor for MEMS Project

    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...
  9. T

    Calculating Force on Particle Using Maxwell Stress Tensor

    Consider a particle with charge q in an static, homogeneous electric field. Using the fact that the net force on the particle in the surface integral of the Maxwell Stress Tensor, and assuming the surface is a sphere around this particle: a) Find the net force on the particle (This part I...
  10. P

    The physical meaning of Maxwell stress tensor

    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...
  11. B

    Conformal Invariance of N=4 SYM Theory and the Yang-Mills Stress Tensor

    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...
  12. E

    Is the Stress Tensor Symmetric? Examining the Physical Meaning and Implications

    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}...
  13. T

    Exploring the Meaning of Curling a Stress Tensor

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

    Maxwell Stress Tensor: Solutions for Polarized Waves & Coulomb's Law

    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...
  15. C

    Understanding Stress and Inertia Tensors: A Comprehensive Guide

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

    Why is the Stress Tensor Symmetrical?

    Can someone explain to me why the stress tensor is symmetrical. I understand that Sij=Sji , but can someone give me the assumption or the physical reason why this is true. Thanks.
  17. D

    Understanding the Force on a Charged Hemisphere Using the Stress Tensor

    I'm having some trouble with an example in griffiths book about using the stress tensor. The problem is to find the force on the northern hemisphere of a uniformly charged solid sphere by the southern hemisphere. Charge Q, radius R. I understand that we will only need the zx, zy, and zz...
  18. M

    How Does Maxwell's Stress Tensor Apply to an Infinite Parallel Plate Capacitor?

    Consider an infinite parallel plate capacitor with the lower plate (at z=-d/2) carrying the charge density- \sigma and the upper plate (at z=d/2) carrying the charge density \sigma. Determine all nine elements of the stress tensor in the region between the plates. Display your answer as a...
  19. M

    Deriving the Maxwell Stress Tensor for a Spherical Charge Distribution

    Consider a spherical volume of radius R filled with a uniform electric charge density p(rowe) a) Use Gauss' law to calculate the electric field E in the interior of the spherical charge b) Use the expression for the electric field to derive an expression for the Maxwell stress tensor...
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