Questions tagged [stress-strain]

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What physics could be applied to accelerate a person from zero to 8000 m/s if you want to: a) Minimize the time, and b) Not kill or hospitalize them? [closed]

My thoughts on this are that you would: Immerse the person facing forwards in a neutral buoyancy fluid, Slew the acceleration up and down just enough to avoid shock waves in their body, Increase air ...
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1answer
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Formal definition of Wall Shear Stress (WSS)

I am looking for the formal definition of the scalar wall shear stress for an arbitrary fluid in 3D. Here, I hope to find a definition that allows both positive and negative scalar values. My ...
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2answers
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How can I have 0 strain and non-zero stress?

Suppose I pull a bar at both ends and there’s no movement in the bar. Now strain in this case is 0. But I know the stress is nonzero (right?) However strain is linearly related to stress, implying ...
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Young's Modulus as a function of temperature

Is there a formula that relates Young's Modulus as a function of temperature? From Wikipedia, there is this formula in section 3.3: https://en.wikipedia.org/wiki/Young%27s_modulus I tried my best to ...
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Deformation convert stresses to others

Elastic instability (also known generically as buckling) can be interpreted as the phenomena in which deformation converts axial stress(compression) into bending moment. OK. Also, if we deform an ...
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Is there any possible scenario where a human could directly sense gravitational waves (preferably without being destroyed)? [duplicate]

Merging black holes radiate enormous amounts of energy - several solar masses worth! Unlike most astrophysical happenings, this happens on very human timescales. Most of the energy is released in the ...
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1answer
35 views

Relation between strain and displacement

Consider a vertical prismatic bar fixed at top end, it elongates due to its self weight. Stress and strain at top are non zero and the two are related by hooke's law, but the vertical displacement of ...
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3answers
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Can there be strain without stress (e.g. Thermal Expansion)?

In here The solution says that strain is 0 in thermal expansion? Doesn't this sound weird and contradictiory? by taking two infinitesimally closer points the stress could be zero but in a article of ...
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1answer
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Work conjugate pair of stress and strain and $pV$

I am trying to understand the role that the work conjugate pair of stress and strain plays in the enthalpy: $H = U - V_0\mathbf{P}:\mathbf{F}$, where $\mathbf{P} = J\sigma\mathbf{F}^{-T}$ is the 1st ...
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Visualizing Tensors in the simplest possible way

Is there any easy way to visualize tensors (such as stress) using paper and pencil with the help of a matrix? If it is possible, kindly post a picture of that tensor.
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Does the strain induces stress or does the stress induces strain? Or is it both ways?

I have thought intuitively that when a force is applied on a material, the material responds by stress which is the internal force. And then, because of this internal force, the material undergoes ...
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1answer
48 views

In terms of compressive stress $F/A$, what is the cross-sectional area of a sphere?

Any physics textbook chapter on stress-strain curves will generally mention that stress is force acting upon an area, and when a shape is three-dimensional, that area is the cross-sectional area. ...
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Why are the transformation equations of strain tensor only dependent on the tensor components and angle of rotation?

https://www.continuummechanics.org/principalstressesandstrains.html Whether its stress or strain tensor, when calculating strain or stress at a given plane making an angle with the global coordinates, ...
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1answer
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Why do we have to divide strain engineering components to use them in the strain tensor?

I understand the reason of dividing them is in order to correctly perform coordinate transformations on strain tensors. But it feels to me as if we are tricking ourselves. Strain tensor should ...
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Why is a force distributed over an area? Why couldn't the stress be directly equal to the force?

So, my question might seem silly. I know in real life when we apply a force with our hand and push on lets say a cylinder , we know the force will be distributed over the cross section of the area, so ...
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Stress in a bar subjected to unequal forces [duplicate]

A bar is subjected to force P at one end and 3P at other end, what is the stress developed in the bar and will it vary along the length of bar ? Is there any stress due to inertia force? According to ...
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2answers
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Stiffness of a Cantilever Beam

I was wondering that for a Cantilever beam subjected to point load at extreme end. Does the stiffness goes on changing as the deflection of free end changes? Logically it should provide more ...
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2answers
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Intuition for Stress and the Cauchy Stress Tensor

I'm struggling to get an intuitive understanding of what exactly Stress is, particularly the "direction" associated with it. In the case of a 1 dimensional bar with just uniaxial loading, ...
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1answer
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Does the expansion of the Universe cause internal stresses in solids (and other substances with similar internal resistance forces)? [duplicate]

Is my understanding correct? Weren't it for the internal resistance forces between particles in a solid object, the expansion of the Universe would continuously increase the distances between all of ...
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1answer
55 views

How do objects deform if we apply pressure at a single point?

Suppose, we have a large solid object and we apply a pressure to it a single point (let say, with a finger, or a needle). How does the deformation of the surface depend on the force with which we ...
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1answer
40 views

Why does an elasticity approach for an adiabatically compressed bubble give a different answer?

Problem (inspired by this question): a bubble of ideal gas at pressure $P_0$ and volume $V_0$ is adiabatically compressed to conditions $P_1, V_1$ such that its radius $r$ is reduced by $a$, where $a\...
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1answer
56 views

Inelastic strain and stress

In a viscoelastic medium, the total strain is the sum of elastic strain and inelastic strain: \begin{align} \mathcal{E}^t_{ij}= \mathcal{E}^e_{ij}+\mathcal{E}^i_{ij} \end{align} The elastic stress (...
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Why is the stress component in a tensor related to deformation along two dimensions

While trying to derive the constitutive laws of Newtonian fluids, I came across this equation: $$\tau_{ij} = \mu\left(\frac{\partial v_i}{\partial x_j}+\frac{\partial v_j}{\partial x_i}\right)$$ I ...
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2answers
87 views

Transformation matrix of a strain tensor

If the stress $\sigma_{xx}$ is applied to an isotropic, three-dimensional body, the following strain tensor results: $$\boldsymbol\epsilon=\left(\begin{matrix}\frac{1}{E}\sigma _{xx} & 0 & 0 \...
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1answer
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Transformation - strain tensor matrix

A question from a continuum mechanics beginner... If the stress $\sigma_{xx}$ is applied to an isotropic, three-dimensional body, the following strain tensor results: $$\boldsymbol\epsilon=\left(\...
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2answers
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How shear-strain is related to diagonals?

In two dimension the shear strain causes deformation of diagonals, But how the diagonals are deformed (means which stress is acting?
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209 views

Why have we taken different areas for both the cases?

My teacher had solved an example question related to stress and strain. The question is as follows: If a hollow glass sphere of inner radius $r$ and thickness $\Delta r ~ (\Delta r \ll r)$ is filled ...
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2answers
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How to obtain displacement from strain tensor? [closed]

I know the relation $$ \varepsilon =\frac{(\nabla + \nabla^T)}{2} u $$ to obtain strain tensor $ \varepsilon$ from vector field of displacements $u$. But, is it possible to obtain displacements from ...
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1answer
79 views

Deformation of a ball when it falls on a rigid surface

Suppose, we drop a rubber ball on the floor. The ball collides with the floor, comes to rest and often bounces back up to lower height. I'm trying to look at this from the force perspective, not ...
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1answer
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If we join multiple wires of different cross sectional area in series, then what will be same for the wires, tension or stress?

If we join multiple wires of different cross sectional area in series, tie one end to the wall and pull the other, then what will be same for the wires, tension or stress?
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1answer
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How to consider the reference point of a bending moment

When evaluating the relationship between shear force and bending moment, most books take look at the following bending segment with loading intencity of $q$: In equilibrium, sum of force: $qdx+(V+dV)-...
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1answer
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Higher order nonlinear stress definition

For the nonlinear case, I often find the following definition for the mechanical stress: $$ \sigma=E_2\epsilon+E_3\epsilon^2$$ The parameters $E_2$ and $E_3$ are called "elastic modulus" or &...
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2answers
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Stress developed in a Hoop due to rotation

In the given question with constant angular velocity. It asks us to find longitudinal stress at each of the positions. Now I'm not even sure what longitudinal stress is but here is what I tried as A ...
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1answer
65 views

Shear modulus with plastic deformation

The shear modulus $G$ gives information about the linear-elastic material behavior. How does it behave in the area of plastic deformation? With $ \tau=G\tan\gamma$, shear modulus should get smaller up ...
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2answers
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The Sign of the Strain Tensor Determinant and What it Means

Background I'm currently working my way through Milton's and Cherkaev's, "Which Elasticity Tensors Are Realizable?" as part of my research. I come from an electrical engineering background ...
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Can there be singular subtensors in the elasticity tensor and what would it mean in that case?

Can the elastic tensor $C_{ijkl}$ describing the stress strain relationship as $$\sigma_{ij} = C_{ijkl} \, \varepsilon_{kl}$$ contain singular subtensors? In that case, what would it mean mechanically?...
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1answer
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Relation between ultimate stress and strain

I'm comparing the material properties of two polymers A and B and noticed that A has a lower stress at break, but a higher strain at break. Is it generally true of most polymer materials that when it ...
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1answer
42 views

Poisson ratio in plastic deformation area

Can the Poisson ratio of metals in the plastic deformation range be assumed to be constant? If not, are there any alternative modeling approaches?
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Resolved shear stress - direction

The shear stress in a crystal can be described as follows: $τ=R σ_{xx}$, where $σ_{xx}$ is the tensile load and R the Schmid factor. Can the shear stress now be assigned to a defined direction?
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Question on yield criteria

Consider a cubic body subjected to a hydrostatic pressure state where $$\sigma_I=\sigma_{II}=\sigma_{III}=X$$ and the definitions of the Rankine, Tresca and Mises yield criteria, given e. g. under: ...
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1answer
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Longitudinal Wave in 3D - strain/stresses

If a longitudinal wave is passed through a 3D isotropic body, the following strain tensor results [Reference]: This describes the strain in the x-direction while the strains in the y-and z-directions ...
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Taylor's series + Stress Equilibrium Equation (Cauchy's equilibrium equation)

I am now studying theory of plasticity and elasticity and I stumbled upon the derivation of the equation of stress equilibrium (or Cauchy's equilibrium equation) that I would like to have more ...
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How to find out resonance frequency of micro-resonators?

I am a student with a theoretical background, so I'm not well versed in the practicals. I have, on a silicon chip, a vacuum gap capacitor of Nb of 5 microns x 20 microns dimensions with 500 nm gap ...
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1answer
45 views

Find elongation of a rod of constant volume given Young's modulus, original length and load without assuming that cross-sectional area is constant

The usual formula for Young's modulus: $$ Y=\frac{FL}{A\Delta l}, $$ (where $F$, $L$, $A$ and $Δl$ are load, original length, and area over which force is applied respectively) can be rearranged to ...
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1answer
79 views

Green-Kubo relation for viscosity

I want to compute the shear viscosity of a system using Green-Kubo relation. I have the full stress-tensor evolution $P_{ij}(t)$ and the system is isotropic so I can write $$ \eta = \frac{V}{k_B T} \...
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1answer
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How does a materials modulus of elasticity (proportional zone ratio) relate to crystal defects?

I'm studying biomedical engineering and I'm about to take "Biomaterials" (basically materials science applied to medicine) final exam. In one recorded class, the professor mentions the ...
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von Mises yield criterion on 'pure' shear

I want to predict when a particular sample will yield using the von Mises yield criterion, which in 2D reduces to: $$ \frac{1}{\sqrt{2}} \sqrt{(\sigma_{11}- \sigma_{22})^2 + (\sigma_{22})^2 + (\sigma_{...
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How to find the longitudinal waves in an elastic bar hanging from the ceiling?

The vertical displacements $w(y)$ in a bar hanging from a fixed point, due to its own weight, compared with the unstressed configuration follow a quadratic equation, that solves: $$E\frac{\partial^2 w}...
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How can a physical quantity be neither vector nor scalar?

I was going through the definition of stress. I came to know that stress is a tensor quantity. When I checked the net about - 'What is a tensor quantity', I came to know that it is neither a scalar ...
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Mechanism of bending and breaking of a stick

We are to break this stick, by twisting our hands in opposite directions. What is the exact mechanism involved in the breaking of this stick? I understand that we are applying two opposite couples, ...

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