Questions tagged [solid-mechanics]
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262
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Computing Cauchy stress tensor in a static cube of uniform isotropic material
As the title says, I'm interested in explicitly calculating the value of the Cauchy stress tensor in a static (non-moving) cube of some material that has uniform density an is isotropic (e.g. concrete)...
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1
answer
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What's the difference between constitutive laws and equation of state?
While defining material properties in finite element modeling, when should we opt for constitutive models, such as Linear Elastic or Neohookean (that relate stresses and strains) over Equation of ...
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2
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Problem in thermal stress equation
I came across this derivation of thermal stress where the strain is given as $\frac { l_0 \alpha t}{l_0}$.
However, I believe it should be $\frac { l_0 \alpha t}{l_0(1+\alpha t)}$ to consider the ...
1
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1
answer
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In-plane stresses on the surface of a cylinder
The three principal stresses on the surface of a cylinder are the hoop, $\sigma_\theta=\frac{pR}{d}$, longitudinal, $\sigma_z=\frac{pR}{2d}$, and radial, $\sigma_r=-p$, stresses. However, what are the ...
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Infinite deflection on axially compressed beam
With $k$ proportional to the square root of the compression force, an axially loaded (and otherwise unloaded) beam has a deflection following the DE
$$
\frac{\partial^4}{\partial x^4}z + k^2\frac{\...
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Would anyone be able to provide a reference for the equations concerning plane strain and incompressibility?
I've been trying really hard to find a textbook or research paper that mentions the equations I mentioned in my question. Sadly, I haven't had any luck so far. Would it be possible for someone to ...
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The expression of elastic energy in this paper
Elastic properties of $\rm{Ni_{2}MnGa}$ from first-principles calculations
Hello,
I am reading a paper investigating the linear elasticity of a crystal. However, I am a little bit confused over the ...
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Why is the maximum stress of a uniformly tapered round bar lesser than that of a inverse uniformly tapered round bar?
Given two round bars with uniformly tapering radii, one from a smaller to a larger radius and one from a larger to a smaller radius, the former bar experiences greater maximum stress.
Since stress ...
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63
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Why are the shear stresses corresponding to adjacent faces of the stress element equal?
I am studying the definition of the stress element from the book Theory of Elasticity from S. Timoshenko and J.N Goodier. In page 3 it is shown that from taking the moment of forces acting on the ...
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1
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Rigid projectile penetrating a solid target at normal incidence
Let's suppose we have an equation that describes the minimum kinetic energy required for a rigid ogival projectile to perforate a target as a function of it's thickness T. Can we use this information ...
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Addition of forces on a rigid body instead of a point
When two forces act on a point mass,we add the forces like we usually do and i have no problem understanding that. When the same forces are applied on a rigid body,how are we able to add them the same ...
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Why does the torsion in a circular bar result in shear stress along the axial direction?
In the case of pure torsion, how does a differential area on cross-section of the cylinder with dx length undergo a shear force that is perpendicular to the cross-section ?
I can understand that a ...
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Mass conservation in a deformed membrane in cylindrical coordinates
This is clearly an obvious question but here is my issue.
Context :
We assume an axisymmetric deformation of a membrane, and work with cylindrical coordinates $(r; \phi; y)$. At time $t = 0$ we let $r$...
- 101
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Energy balance equation using Reynold's transport theorem
Hello everyone I'm trying to reach this equation:$\iiint \rho \frac{du}{dt} dV = \iiint \overrightarrow f\cdot \overrightarrow v dV +\iint \sigma\cdot \overrightarrow v\cdot d\overrightarrow S$ from ...
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What is the correct formulation of momentum balance for a body of continuum?
What is the correct form of the momentum balance equation
for a continuum body $\mathscr{B}$
whose particles are
fixed,
and occupies volume $V(t)$ at time $t$?
\begin{align}
&\frac{\mathrm{d}}{\...
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1
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What is the correct form of the conservation of mass equation?
What is the correct form of the continuity equation
for a continuum body $\mathscr{B}$
whose particles are
fixed, and occupies volume $V(t)$ at time $t$?
\begin{align}
&\frac{\mathrm{d}}{\mathrm{...
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2
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Simulating rigid body collisions in 3d
I have been reading about physics engines and I am confused on how one approaches simulating collision responses.
I read about the coefficient of restitution:
https://en.wikipedia.org/wiki/...
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Wave equation in two different forms (2nd order, 1st order): Which of the two should I use and when? [closed]
I am studying elastic waves in solids. Depending on paper or documents, the wave equation is written in two different forms.
The first form is in the second order PDE
$$ \rho \frac{{{\partial ^2}{\...
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1
answer
152
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Continuum mechanics cauchy stress
I have a question regarding the stress tensors. In a publication I found the following definition:
I havnt seen this equation before, and I am wondering how to get there. T is the Cauchy stress, Je ...
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When is the equation $\vec{L}=I\vec{\omega}$ not valid?
When is the equation $\vec{L}=I\vec{\omega}$ not valid?
Let me clarify, I've encountered a few problems where the angular momentum you obtained by integrating and the angular momentum you'd obtain by ...
user348222
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3
answers
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Do forces act on points or areas?
In a lot of situations we are taught about forces acting on points on solid objects (torque, point particles), and in other cases (axial stresses) we consider them as acting on an 'area', is this ...
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Cyclic values inside stress tensor in given configuration
i have majored in mechanical engineering and implemented a fully working FEM-Solver for structural mechanical problems for 2 and 3-dimensional problems. I have lately been working on bringing this to ...
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What are the effects of Bravais lattices classification differences in 2D space on the physical properties of the crystals?
There are five possible distinct Bravais lattices in two-dimensional space.
For example, if crystal A is Monoclinic (M) and crystal B is Hexagonal (H), how will the difference in their 2D Bravais ...
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Movement of a rod submitted to a shifted torque
Suppose I have a rod of mass m initially at rest, for which a torque (F1, F2) is applied at the right side during a brief time $\Delta t$, as in the schema below. The rod is not fixed to anything and ...
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0
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What is the function of air cavity in drums?
I'm trying to understand the function of the air cavity inside drums.
I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This ...
3
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1
answer
424
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Is charge carrier density an intrinsic property of a material and is thus constant?
I was studying the equation $$I = nAvq$$
where $n$ = the charge carrier density, $A$ = cross-sectional area of the conductor, $v$ = mean drift velocity of the
charge carriers, and $q$ = the charge on ...
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292
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Can we prove the Hooke's law? [duplicate]
I was learning about stress and strain and my text book suddenly mentions about this law so called hooke's law.
It states that
$$\text{stress}\propto \text{strain}$$
Or,
$$ \text{stress}=k \times \...
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Absence of velocity in energy conservation
Here we see a rod at rest hinged about a point. We want to know the angular speed of the rod when it becomes vertical as shown in the figure.
The solution which is given in the books goes like this.
...
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Doubt in derivation of bending of beam, It's about derivatives and intergration
Radius of curvature of the beam in above picture is given as:
$$ \frac{1}{R} = \frac{d^2 y}{dx^2}$$
Please help me two points used as steps of a derivation in my book:
How was the radius of ...
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1
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Why two wires are used in railway overhead equipment? [closed]
While watching the train video's I came across this overhead wires. After searching on internet I found that both catenary and contact wires carry same voltage and connected by vertical wires called ...
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3
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Where does the stored potential energy in a bar go, when I reduce the load acting on it?
Consider a deformable bar, fixed at one end and acted upon by a load P (gradually increasing), as shown, through a rigid plate attached to its end. At the end of loading, potential energy is stored in ...
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Stiffness for helical spring under lateral bending force
The stiffness for a helical spring under axial loads is
$$k_\text{axial}=\frac{F_\text{axial}}{\delta_{axial}}=\frac{Gd^4}{8n D^3}\, ,$$
where $G$ is the shear modulus, $d$ the wire diameter, $D$ the ...
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In stress-strain diagrams, why is the dependent axis ($y$) used to represent stress and the independent axis ($x$) to represent strain?
why this convention is used
despite the fact that strain is influenced by stress (cause -> stress, effect -> strain)
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639
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Volumetric Strain In a Thin Spherical Pressure Vessel
Consider a thin spherical pressure vessel with a fluid inside at a gauge pressure of P.
The normal stress developed in the pressure vessel is given by $$\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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0
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How can the total torque of a body equal a "torque" at only one point?
I am trying to understand the solution to this problem.
Pictured is a rough sketch of a ball in which another, smaller ball of density $\rho_2 > \rho_1$, where $\rho_1$ is the density of the ...
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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)?
user331791
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1
answer
450
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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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1
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How to interpret a differential stress element with differing stress magnitudes on opposite faces?
The element is in equilibrium, but with different magnitudes of stress on opposing faces. What meaning does this have physically?
See attached image.
Thanks
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1
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Why the elastic limit of solid corresponds to a larger strain/extension than the limit of proportionality?
In all the force-extension graphs I saw, the elastic limit corresponds to a larger extension than the limit of proportionality. Is this true for all cases? If so, what are the underlying reasons?
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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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Is it possible to find Coefficient of Restitution without performing experiment? But only using mathematical equations?
I was finding empirical equations to find Coefficient of Restitution (COR) for two solid bodies undergoing collision. Seems like all have used experimentation to find COR. Is there any way to find ...
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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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Relation Between $Y, K, \eta$ and $\sigma$
How did we get the following relations between $Y, K, \eta$ and $\sigma$, where $Y$ is Young's modulus, $K$ is Bulk modulus, $\eta$ is Shear modulus, and $\sigma$ is Poisson's ratio? (Some books and ...
user324347
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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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How does pressure act evenly in all directions in interactions between solids?
Pressure is a scalar quantity, and I think I understand this in the context of pressures exerted by gases and liquids. However, I struggle to understand this in the context of solids. If I use a ...
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574
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Understanding Strain Energy Density
The strain energy density is:
$$\frac{1}{2}\sigma_{ij}\epsilon_{ij}$$
Where $\sigma$ is the Cauchy stress tensor ($\sigma_{ij}=T_j(\mathbf{e}_i))$ and $\epsilon^e$ is the infinitesimal strain tensor ($...
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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 ...
3
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1
answer
154
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Can a material generally score or cut itself by hand?
I'm wondering if a given solid material can, in general, score or cut the same material, when applied by (at most) human muscular strength.
I've tried searching for this online, but it seems like a ...
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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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