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14 views

Strain calculation for complex sampe

When performing tensile tests samples must have constant crossection alongside the axis. Then two marks are made and we can define engineering stress $\sigma=\frac{F}{A_0}$ and engineering strain $\...
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1answer
25 views

Understanding stress-relaxation for viscoelastic materials

I'm studying a viscoelastic material with a cylindrical geometry and I read that for fixed strain(i.e. fixed elongation), I should observe decreasing strain over time. Given that stress $= F/A_0$ ...
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1answer
35 views

Understanding stress-strain calculations

I'm trying to compute the stress-strain curve for an elastic material with cylindrical geometry subject to an increasing uniaxial load. I understand that this requires: stress = $F/A_0$ where $A_0$, ...
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0answers
22 views

Stress on a fixture [closed]

How to determine the stress at point B and C and how can i calculate the maximal weight section A must be able to withstand?
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1answer
30 views

Studying dynamic elasticity for finite deformations

this is not a question asking for help with a problem but one asking for help where to begin serious study of elasticity, particularly that applied to dynamic systems. Most textbooks about elasticity ...
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1answer
42 views

Why does viscosity effect the normal component of stress in a Newtonian fluid?

The constitutive law for a Newtonian fluid is $$ \boldsymbol{\tau} = 2\mu \mathbf{D} + \lambda\left(\nabla\cdot\mathbf{v}\right)\mathbf{I}$$ where $\mu$ is the dynamic viscosity. Assuming we have a ...
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0answers
36 views

Give a strain state which describes a purely spatial change of volume [closed]

In a problem, I am asked to provide a strain state (strain tensor) that describes a "purely spatial change of volume". I am unable to understand what is meant by this. Does it mean that there is ...
0
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0answers
50 views

Derive equation for shear modulus $G=E/(1+2v)$

Shear modulus, G Young's modulus, E and Poisson's ratio, v: $G=E/(1+2v)$ I have always wondered how this relation is derived, but have never found a derivation that I could follow online. I assume ...
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1answer
26 views

Young's modulus and geometry of test material

When measuring Young's modulus in a material, does the geometry of the material actually matter? I have seen several references recommend that I use cylindrical pieces. But, wouldn't the tests work ...
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0answers
10 views

eccentrically loaded bolts in which the plane of loading is parallel to the bolt plane

This are eccentrically loaded bolts in which the plane of loading is parallel to the bolt plane.When deriving an equation to this particular problem almost all books start by assuming that $$\frac{F_{...
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0answers
31 views

What is Lamè mode?

I am trying to read some of the articles that says Lamè mode. But I can't find in google that describes Lamè mode. Can anyone quote good reference for this term?
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1answer
14 views

Trasversal wave on a rod velocity

What is the velocity of a trasversal wave on a metal rod? Does it depend on the shear modulus $G$ $$v_{t}=\sqrt{\frac{G}{\rho}}$$ Or on the tension $T$ of the rod? $$v_{t}=\sqrt{\frac{T}{\rho}}$...
4
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1answer
72 views

Breaking strength of wet paper/cloth

In the Hollywood movie, Shanghai Knights (pardon me for the non scientific citation), Jackie Chan states that 'wet cloth' does not break easily. How true a fact is this ? We know from common ...
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0answers
12 views

High pressure vs low Mises

I have two high Young modulus materials, and a small layer between them which material have a low Young modulus. I apply constraints on one side and make a compression. Analysis gives me low von ...
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1answer
38 views

For a cantilever beam, is bending stress linearly proportional to elastic deflection?

Let's say I have a cantilever beam (a beam with a fixed support on one end only) and introduce a downward point force (by hanging a weight on it or something) at some constant distance from the ...
0
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1answer
26 views

Poisson's ratio and change in volume

The Poisson's ratio $\nu$ is always less than $0.5$. A traction force ($\Delta L >0$) can cause an increase in volume, while a compression force ($\Delta L <0$) can only decrease the volume. $$...
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0answers
23 views

Absolute maximum shear stress due to combined loadings

In a prismatic beam subjected to 2D loadings, Is it possible that absolute maximum shear stress occurs at the point due to maximum bending stress (due to stress transformation)? Or that absolute ...
1
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1answer
35 views

Confused about shear elasticity and complementary shear stress

I am a self learner of continuum mechanic. I am confused about simple shear stress in situation similar to figure 1, in case $F_\textrm{ext}$ is caused by external perturbation by i.e., human, what ...
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0answers
40 views

Phonon softening explanation

Is there a simple, intuitive answer of why phonons soften with strain? I am aware of the Grüneisen parameter but it just tells us there is a negative sign.
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1answer
61 views

Momentum equation in a Lagrangian configuration

When writing the momentum equation in a lagrangian configuration is the the stress tensor used the first Piola-Kirchhoff stress tensor or the nominal stress tensor (which is the transpose of the 1st P-...
0
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1answer
30 views

An expression for stress power

I have seen it written that for a continuum undergoing deformation, if we ignore body forces and heat transfer, the work done is equal to stress power: $\cfrac{dW}{dt}=\sigma_{ij}D_{ij}$, where $D_{...
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2answers
73 views

What causes tensile stress to decrease after a material/wire reaches its ultimate tensile stress?

I was reading the AQA A Level Physics revision guide by Jim Bretihaupt, and in the Materials chapter in the section to do with plastic deformation, it says: Beyond the ultimate tensile stress, the ...
3
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0answers
16 views

physical significance of the 'time of relaxation ' and 'time of observation'

Deborah number (used frequently in rheology) is defined as the ratio of the time of observation to the time of relaxation. In his article The Deborah Number, M. Reiner the man who coined the term has ...
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2answers
50 views

young's modulus factors

is young's modulus of a material different for various diameters of that material? I would assume it does, but I cannot find a reference. Is the young's modulus of 1mm thick steel the same with 10mm ...
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2answers
112 views

Extension in a vertically hanging rod [closed]

Consider a vertical rod hanging from a ceiling. Neglect lateral contraction and frictional forces and air resistance and change in value of $g$ with height. Case 1: In the absence of gravity, a rod ...
3
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2answers
79 views

What is the purpose of the Maxwell Stress Tensor?

In the calculation of the forces acting on a charge/current distribution, one arrives at the Maxwell stress tensor: $$\sigma_{ij}=\epsilon_0 E_iE_j + \frac{1}{\mu_0} B_iB_j -\frac{1}{2}\left(\...
0
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1answer
72 views

How to model analytical expression for spring constant $k$ for certain structure?

In the deflection of beam, I learned that $$ \delta y=\frac{FL^3}{3EI} $$ where $$ I=\frac{h^3w}{12} $$ Together they comprise $$ F=\frac{Eh^3w}{4L^3}\delta y $$ How do I apply to four beams? is ...
3
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1answer
36 views

determining the stress of a beam

I have a question regarding a beam. I first consider a force applied to both ends of a rectangular beam which is perpendicular to its cross section with dimensions w (width) and h (height). The length ...
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0answers
42 views

Axial loaded bars problem

I completely disagree with the following calculations: Based on my understanding, there is no force either internal or external applied to the Green bar, so it should be 0N. The reaction (internal) ...
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0answers
12 views

Flow Curve - Plotting Shear and Strain Rates at Different Pressures and Flow Rates in a Capillary

So I'm not really asking for a solution but more clarification on this type of problem since I'm kind of confused on the concept. So i have two capillaries of a different diameters and lengths. Im ...
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0answers
37 views

Why is the Elastic Modulus of concrete smaller than that of steel?

I am trying to get a basic feel for what the Modulus of Elasticity means for different materials. My understanding is that since E = stress / strain, a higher E ...
0
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0answers
37 views

Linear vs non-linear (finite) strain

I have a somewhat non-specific question regarding strain in materials. What I understand currently -Linear elasticity or infinitesimal strain theory is an approximation of finite strain theory that ...
1
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1answer
42 views

Which area to be considered in calculating stress?

During the calculation of longitudinal stress, we say that stress is equal to the magnitude of applied force divided by area of cross section. However, is this area of cross section, the cross-...
0
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1answer
81 views

3D beam deflection

How can you get formula for 3-dimensional beam deflection at the free end of horizontal cantilever due to the cantilever's own gravitational load? I assumed E= 160GPa, $\nu=0$, $\rho=2330kg/m^3$, ...
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0answers
26 views

Atomic Stress (Virial Stress) and Harmonic Springs

The general context here is polymer physics. The stress tensor in a bead-spring simulation can be easily computed using the Virial Stress (which may be named the Kirkwood formula, or the Doi-Edwards ...
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0answers
29 views

Pressure vessel analysis of transversely isotropic multilayer material

Suppose I have a transversely isotropic, hyperelastic material with known strain energy that is a fibrous composite. I am interested in an explicit formula for the displacements (so I can get the ...
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2answers
898 views

Why do chocolate bars usually break at the cleavages?

Why do chocolate bars usually break at the cleavages? The chocolate bar is less thick at cleavages. How can we relate thickness and fracture point of chocolate bar?
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0answers
51 views

Question regarding the use of the Green-Naghdi Objective Stress Rate

The equation for the Green-Naghdi Stress Rate reads: $\boldsymbol{\sigma}^{GN} = \dot{\boldsymbol{\sigma}} + \boldsymbol{\sigma}\cdot\boldsymbol\Omega - \boldsymbol\Omega\cdot\boldsymbol{\sigma}$ ...
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0answers
84 views

Why is maximum shear stress at 45 degrees instead of near 0?

I think I might havr an immensely stupid question but it's really bothering me so please be patient. I am not physicist smart. Look at this guy's question: https://www.physicsforums.com/threads/mohrs-...
2
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1answer
46 views

Are hardness, strength and toughness of materials not the same thing in a way?

I had to look through several videos and re-read Wikipedia statements about these material properties several times before I could even begin to differentiate them. However, now that I have found out ...
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0answers
8 views

Equation Governing Small Lateral Deflections z of a Uniform Membrane

The equation governing small lateral deflections z of a uniform membrane subjected to a lateral (dimensionless) pressure p is given by $$ \frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\...
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0answers
38 views

Do stress and strain contradict each other?

According to the book Engineering Physics by R.K Gaur and S.L Gupta Strain: Strain is a fractional deformation produced in the body when it is subjected to set of deforming forces. Stress: The ...
0
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0answers
32 views

From in-plane strain to Poisson ratio

I have recently been trying to simulate a graphene cantilever and thus I need to know the Poisson ratio, Young's modulus, and density. From literature it is easy to find the Young's modulus and ...
1
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1answer
52 views

Can a magnetic field weaken aluminum?

I'm wondering if there is any reason to suspect that applying a magnetic field to a piece of solid aluminum would weaken it structurally in any way. The application is that I would like to put a stir ...
1
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1answer
51 views

Elastic properties of materials at low temperature

It is common knowledge that materials are more brittle at low temperature. But does it apply also on elastic deformations or is it just matter of plastic deformations? Practically: Is it possible to ...
3
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1answer
68 views

Cauchy stress tensor in different coordinate system

The general form of the cauchy stress tensor is given by the dyadic decomposition $$\boldsymbol \sigma = \sigma_{ij}\,\,\mathbf{e}_i \otimes \mathbf{e}_j$$ I want to know how this can be expanded in ...
4
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0answers
72 views

Cauchy stress tensor for a spherically symmetric problem [closed]

Given a sperically symmetric problem, I am asked to show that its Cauchy stress tensor, in spherical coordinates will assume the form: $${\overline{\overline{\sigma}}}=\sigma_{RR}(r)\overline{e_r}\...
1
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0answers
30 views

Stuck with physics tensile strength problem

So this was a question in my exam. I am not asking for the solution rather some help at a step. A glass spherical shell of radius $R$ has a point source of monochromatic light of wavelength $\...
2
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2answers
163 views

Elongation and tensile strength of rubber

I want to do some experiments on a neoprene rubber sheet (ex. supplier). When I went to order the sheet I was confused because the listed elongation and tensile strength for all sheet sizes (with ...
2
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1answer
38 views

Calculate the applied force associated with uniform distortion of an area

I am exploring Hooke's Law and considering how it might apply to an arbitrary area (perhaps as a slice of some volume). Since $$ F = -kx $$ Would it be correct to calculate the force, $F$, ...