Questions tagged [stress-strain]

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Nickel gauge factor and why is it so quirky?

Hi so I've been researching the piezo-resistance effect and experimenting with finding different metals' gauge factors by applying stress on a wire and measuring the change in resistance however I can'...
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How to obtain nodal forces from stress tensor?

I am working on a FEM code in which I need to obtain the force vector on each node of a triangular linear element from the stress tensor in 2D. I have the shape functions, and the stress is constant ...
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Maximum tensile strain at a point on a standing wave

Objective: To find the maximum tensile stress on a wire (of length l) at a point x which has a standing wave on it having equation y=f(x,t); 0 $\le$ x $\le$ l My work: When the wire is at rest, the ...
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Equilibrium and constitutive partial and algebraic equations describing stresses and deformation of an axisymmetric elastic thin shell over a hole

I want to design a vacuum table to clamp down a very thin plate and I want to know the stresses and deformations due to the atmospheric pressure. Consider the simplified model below: ...
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What would be the Stokes hypothesis in a 1D flow?

In this paper, the author derives the Navier-Stokes equation for a Newtonian fluid starting from the Cauchy equation: $$\rho \frac{D\mathbf V}{Dt} = \rho \mathbf{f} + \nabla\cdot\mathbf{T}$$ where $\...
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In stress-strain diagrams, why is the dependent axis ($y$) used to represent stress and the independent axis ($x$) to represent strain?

why this convention is used despite the fact that strain is influenced by stress (cause -> stress, effect -> strain)
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Volumetric Strain In a Thin Spherical Pressure Vessel

Consider a thin spherical pressure vessel with a fluid inside at a gauge pressure of P. The normal stress developed in the pressure vessel is given by $$\sigma = \frac{Pd}{4t}$$ where t = thickness , ...
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Interpreting stress at the ends of a bar

Consider a bar loaded in tension by distributed loads applied on its ends as shown in the figure. The stress at any cross section of this bar will be $$\sigma = \frac{P}{A}$$ From what I know about ...
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Stress without strain [duplicate]

Suppose there are two rigid walls with some gap between them and a steel rod is placed within that gap firmly attached to both the walls(no strain can occur). If the temperature is increased by $T$,...
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Opposing uniform pressures/forces

If I have a vertical plate, with a uniform pressure of $10\,\text N/\text m^2$ acting on the left hand side, and a uniform pressure of $6\,\text N/\text m^2$ acting on the right hand side, can I treat ...
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Which part of a massless wire will break at the breaking stress?

Consider an ideal massless wire of length $L$, uniform cross-sectional area $A$, Young's modulus $Y$ suspended from the ceiling, with a load of weight $W$ suspended at the end. There is no variation ...
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Does this work to reduce eyes strain? Enlarge the PC monitor with a lens

I have an idea to reduce eyes strain, but don't know if it works. I work by looking at PC monitor all day long and I believe my myopia condition is getting worse and eyes strain occurs are due to ...
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Why is viscous stress a tensorial quantity?

In an incompressible fluid, the viscous stress (in Cartesian) is defined by \begin{align} \tau_{ij} = \eta(\partial_i v_j + \partial_j v_i) \end{align} for dynamic viscosity $\eta$ and velocity field $...
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Rate of deformation tensor in cylindrical coordinates

A question regarding the rate of deformation in cylindrical coordinates. The rate of deformation tensor, $D_{ij}$, is the symmetric component of the velocity gradient tensor, i.e. $D_{ij} = (\frac{\...
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Which occurs first: stress or strain? [duplicate]

Of stress and strain, which is the cause and which is the effect? Is stress a cause of strain, or is stress an effect of strain, or do they occur together (by applying Newton's third law)?
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Homogeneous strain-Atomic position in deformed state

I encountered today an equation in a quite old paper, which I am not able to derive. For the notation they define $\vec{\mathring{x}}$ as the reference position for any material point and $\vec{x}(\...
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Stress in a rigid body

Consider two bars one rigid and the other deformable, acted upon by two equal and opposite point loads P as shown. In either of the cases, if we cut the beam from an imaginary section, then, to bring (...
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Stress tensor between spatially separated layers

If I have an interface between two bodies (1 and 2). I would expect that the stress tensor is such that $\boldsymbol \sigma_1\cdot \hat n=\boldsymbol\sigma_2\cdot \hat n$ at the interface, where $\hat ...
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Why is this basic assumption leads incorrect answer?

A thin cylindrical uniform metallic rod of Length 'L' and radius 'R' rotates with an angular velocity "omega" in a horizontal plane about a vertical axis passing through one of its end . The ...
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Shear stress vs normal stress in incompressible solid

According to my current understanding, if a non compressible solid cube is subjected to a uniaxial compressing force, it will essentially be flattened - it will get shorter along the axis that is ...
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What is the interpretation of the symmetric stress tensor in laminar flow?

The strain rate tensor $D_{ij}$ is defined as $$ D_{ij} = \frac{1}{2}\left(\frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i} \right) $$ For a Newtonian fluid the stress tensor $\...
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The state of a Stress element isolated from a beam

Consider a beam subjected to an arbitrary loading, where the loads are only present in the plane of bending. The x-y plane is the plane of bending. If I take a stress element in the beam, there will ...
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What type of tensor is the stress tensor?

I am having some problems identifying the what type of tensor the stress tensor is. Say we have two bases $B = \{\mathbf{e}_i\}$ and $\bar{B} = \{\mathbf{\bar{e}}_i\}$ that are transformed according ...
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Stress tensor and equality of normal stresses on opposite faces

Consider a body arbitrarily loaded as shown, At a particular point in the body, I take an element and show all the stresses acting on its faces. To specify a plane I will be using the the axis which ...
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Relation between strain and displacement (virtual works)

I am a little confused about the expression of the strain in virtual work equations. The small strain tensor can be defined as followed: $\boldsymbol{\epsilon} = \frac{1}{2}(\nabla \textbf{u}+(\nabla \...
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Why is the stress tensor contravariant?

The stress tensor relates the traction $\vec{t}$ (force per area) on a surface with surface normal $\vec{n}$ usually written as (when disregarding co- and contravariance) $$ t_j = \sigma_{ij} n_i.$$ ...
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Is the Young's Modulus different for Compressive and Tensile Stress?

My textbook says that the magnitude of strain produced is the same whether the stress is tensile or compressive. So the Young's modulus, which is the ratio of (tensile or compressive) stress to the ...
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Why is the divergence of Cauchy stress equal to zero in the reference domain?

Below are three configurations of a body: The current one, the reference, and the natural one. The natural reference is when the configuration is pre-stressed. Why is the divergence of Cauchy stress ...
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Why does the stress of fluid depend on rate of deformation unlike stress of solid that depends on deformation itself?

So as stated in the picture above, stress behavior in fluids and solids isn't the same. Why is it physically that way?
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Why do I get different Euler-Almansi strains depending on how I calculate them?

I'm trying to calculate the Euler-Almansi strain for a simple bar with one end fixed (see drawing below). I know that the Almansi strain can be calculated by either directly using the displacement ...
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Stress-strain relationship for linear viscoelastic solid

I am a bit confused about the definition of a linear viscoelastic (isotropic) solid. Following Landau and Lifshitz (Theory of Elasticity, section "viscosity of solids"), I would say that in ...
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Stress, Residual stresses [closed]

From a mechanics book http://goriely.com/wp-content/uploads/Pages-from-Interdisciplinary-Applied-Mathematics-45-Alain-Goriely-auth.-The-Mathematics-and-Mechanics-of-Biological-Growth-Springer-Verlag-...
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Shear stress in Interstellar docking scene [closed]

The movie Interstellar has a scene where a huge spaceship (64 meter diameter ring) called Endurance is spinning out of control after an explosion. The protagonist slows its angular velocity down by ...
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Why are the components of elasticity tensor 21?

I know there's a duplicate but I didn't understand the whole answer which was: A 6×6 matrix has 36 different components. When you reduce it to a symmetric case it has 1+2+3+4+5+6=21, where we are ...
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If a wire undergoes longitudinal stress and there is significant change in area. Is the stress Force/old area or Force/ new area?

Supposed a wire undergoes longitudinal stress and its diameter changes non negligibly, how is the stress calculated, is it Force/old area or Force/new area. Please comment if my question is inadequate....
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Why is stress invariant under a change in coordinate system?

Since stress is represented by a tensor, it should be invariant under a change in coordinate system. For something like a position vector $\mathbf{r}_{P/O}$ which is also invariant under a change in ...
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Force field lines in surface ice

The question Melting ice pattern shows a single hole melted in ice. The picture below shows multiple holes of the type described in that question, and there are lines in the ice between the melted ...
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Why are stress components on opposite faces identical?

The stress tensor stores information about the stress on each of the faces of an infinitesimal volume of material. But I am confused as to why the stress components on opposite faces should be equal. ...
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How would one calculate the electric field produced by a piezoelectric device in response to a sound wave?

So the governing equations of piezoelectricity are: Where E is the electric field, D is the displacement field, S is the strain, and T is the stress. Say I have a piezoelectric device where the ...
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1 vote
1 answer
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Elastic Potential Energy Of Elastic Wire: Two contradictory methods [closed]

Suppose a wire of length $L$, cross sectional area $A$, density $\rho$ and Young's Modulus $Y$ is suspended at one of its ends from a ceiling, then find its total elastic potential energy due to its ...
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Deformation/Fracture from Impact

What equations predict the deformation from two objects colliding? Such as dropping a heavy ball onto a plate of metal. Source references would help, I havent found much anything yet.
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How the bulk modulus and Lamé coeffiencts are connected in the book of Theory of Elasticity by Landau?

In the book of Theory of Elasticity written by Landau and Lifshitz (published in 1970), they make a connection of bulk modulus $K$ and Lamé coeffiencts, which are $\lambda$ and $\mu$, at the section 1....
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"A diamond baseball bat would be very easy to break compared to a wood baseball bat." Is this true? If so, why?

In a previous question, someone mentioned that a diamond baseball bat would be very easy to break compared to a wood baseball bat. Is this true? If I could create a baseball bat that is made out of ...
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2 votes
1 answer
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Difficulty in proof of relationship between $Y$, $B$, $\sigma$

On internet, I was looking for the proof regarding the following relationship between $Y$ young's modulus,$\sigma$ poisson's ratio, and $B$ bulk modulus: $Y=3B(1-2\sigma)$, and I came across the ...
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Why non-elastic deformations of solids are time dependent?

I'm learning the properties of viscoelasticity, and it is a common fact that non-elastic deformations are time dependent. However, I don't understand what physically happens to the molecules that take ...
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Is there a generally followed "convention" regarding the signs of the diagonal components of the stress tensor?

The question pure compression or pure traction? is very similar to what I wish to ask. One answer to the referenced question includes the sentence: "It is also matter of convention." My ...
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Force applied per unit area

I am having difficulty in understanding what force applied per unit area means. For example consider a mass $m$ attached to a cylindrical string. When we define stress, we take it to be $\frac{mg}{\pi ...
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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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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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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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