Questions tagged [solid-mechanics]

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65 views

Solid Mechanics -$\nabla\times\nabla\times\varepsilon = 0$ - having trouble with Einstein notation

Note: this is not an assignment for a grade, just me trying to improve my solid mechanics. The task at hand is to show that the compatibility condition $$\nabla\times\nabla\times\varepsilon = 0$$ ...
2
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4answers
255 views

Are rocks and other solid objects just very slow moving fluids?

Will a rock or other solid object under the influence of gravity, given enough time, behave like a fluid and slowly flatten out? Or do the properties of matter that make it solid prevent it from ever ...
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2answers
2k views

Jaumann deviatoric stress rate

Background about terms in this question: Hookes law and objective stress rates From my understading, the Jaumann rate of deviatoric stress is written as: $$dS/dt = \overset{\bigtriangleup}{{S}} = {\...
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1answer
66 views

Organs & Oscillations: An Analysis on the Temperature Dynamics of Solids

Does temperature have an influence on the frequency of an oscillating organ pipe?
2
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1answer
795 views

Why are rebar grooved?

Just what the title states, please. Iron reinforcement bars used to provide the framework over which concrete solidifies always appear to bear grooves. Do the grooves behave as the thread of a screw ...
2
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2answers
98 views

How derive a spring constant of a helically turned helix based on elasticity of the material and the geometry? [closed]

The structure has helicities on two levels and looks like the tungsten wire in an incandescent light bulb: How, if at all, can the spring constant be derived from elastic properties of the material, ...
2
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1answer
53 views

Why does $\sigma = E\cdot\frac{\Delta l}{l} = E\cdot\frac{\partial \xi}{\partial z}$?

When deriving the wave function ($\frac{\partial^2\xi}{\partial z^2}\left(z,t\right)=\frac{1}{c^2}\cdot\frac{\partial^2\xi}{\partial t^2}$) for longitudinal waves in a solid body we use Hooke's law $\...
2
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2answers
129 views

What happens to matter when there's distortion in space

This is all hypothetical, but if you had control of space (to do distortions to space as very heavy objects do), what happens to the matter in the space? To have a concrete example, let's say that you ...
2
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1answer
71 views

$D$-dimensional analogue of perpendicular axis theorem

In the paper $D$-dimensional moments of inertia by Bender and Mead (1995), the authors show that the moment of inertia about an axis through its diameters is $\frac{D-1}{D+2}MR^2$, whereas that about ...
2
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1answer
56 views

Physics of bursting balloons?

This is a reference request for a theory of bursting balloons: Let's say I have a balloon and this balloon has an impurity along a small strip. Let's assume for example the balloon had a hole there at ...
2
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1answer
53 views

Catenary shape of transmission lines

When flexible metal transmission lines are hung between two poles, the shape they assume to minimize the action of gravitational and tensile forces is a called a catenary. While assuming that shape, ...
2
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2answers
324 views

True strain, engineering strain, strain gauges

I've been somewhat confused over the concepts of true and engineering strain, and I just want to see if I am understanding this correctly. Let us denote true and engineering strain as $\epsilon_t$ ...
2
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1answer
174 views

Rigidity and superflow

In the book "Introduction to Many-Body Physics" by Piers Coleman, it is argued (page 406) that a momentum supercurrent (superflow) corresponds to sheer stress in a crystal. What would be a simple ...
2
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1answer
182 views

What is the stress on the cube?

In a problem, it is given that a mass of 10.2 Kg is resting on a cube made out of a particular material. Assuming that the x-axis is vertically upwards, what is the stress on the cube. (We can say ...
2
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2answers
1k views

Why is deflection at the boundary 0 for the given statically indeterminate beam problem?

I have been trying really hard to understand the boundary condition applied to the indeterminate beam problems.. although i am citing a particular problem, i have been finding the same approach in ...
2
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1answer
986 views

What is the spatial derivative of strain tensor?

I'm looking for a metric that contains enough information of a 3D solid's deformation: stretch, bend and twist, etc. Stretch, bend and twist may be ambiguous for a 3D solid, since unlike a rod, it ...
2
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0answers
16 views

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 ...
2
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0answers
61 views

Why the material time derivative of a material field $F$ equals to the directional derivative of $F$ in the direction of the velocity vector $v$?

I am reading the book Nonlinear Solid Mechanics A Continuum Approach for Engineering by Gerhard A. Holzapfel, Chapter 2.3 and find one equation confusing, which is displayed in the pitcure. Here in ...
2
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0answers
80 views

Best location for supports of a horizontal beam?

What are the best locations for placement of $y$ supports for a beam of length $x$? This seems like a very basic physics question, but I have been unable to find the answer. Perhaps I am not sure ...
2
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0answers
44 views

Why bicycles' rims are bent after winter? [closed]

I've noticed that the rims of many bicycles which are parked in the street during the whole winter are heavily bent. I'm wondering what causes this deformation? Typically, this happens to rather cheap ...
2
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1answer
682 views

How does the grain size effect on permeability and resistivity of a material?

If the grain size of a material varies, what does happen? Are the permeability and resistivity of the material changed with the variation of that grain size? If they do, how they do?
2
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0answers
98 views

Eigenfrequency of a beam?

How would you calculate the eigenfrequency of such a cantilever? This is what I found so far, but I don't know how to apply it to this specific geometry: http://iitg.vlab.co.in/?sub=62&brch=175&...
2
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1answer
161 views

Force acting on the surface during aspiration of elastic body into the pipe

Assume we have a pipe and a spherical elastic body Fig. 1 suspended in incompressible fluid. Due to the pressure difference, the sphere is partially sucked into the pipe so there is an equilibrium ...
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0answers
772 views

What is “Accumulated plastic strain rate” in Current yield Norton law?

I'm doing FEA of steel under high strain rates and using Elasto-ViscoPlastic material model, with Von-mises yield criterion along with Isotropic hardening. The strain rate sensitivity is addressed by ...
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2answers
3k views

How to formulate pin joints in finite element modeling of solid frames

In frame analysis with finite element every node can be assumed with 6 Degree of Freedom (3 translation DoF and 3 rotational DoF). There are formulations over the web for creating stiffness matrix etc....
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0answers
73 views

Simple model of fiber interaction for pressurized braided tubes

I am trying the understand the failure modes of braided tubes containing high pressure gas. Here is an example of such a braid with a variable radius: The tubes have an internal liner for sealing ...
2
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0answers
731 views

Mechanics of Materials (pressure and temperature)

A solid right cylinder of rock core is surrounded by four rods made of mild steel (all-thread rods). The rods are placed equidistantly around the core in a square formation. The tops and bottoms of ...
2
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4answers
453 views

Helical motion of a rigid body

I want to show that a rigid body, with two components of its angular velocity vector and one component of its linear velocity vector, in the absence of external forces and torques, has helical ...
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2answers
133 views

Force required to Stop a Cone made by Paper from Flattening Out

Suppose a paper cone is made with height equal to its radius, only the two straight sides just touch each other and are not glued together. It is kept on a frictionless table and a vertical force is ...
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3answers
102 views

Z-shaped lever balance

The goal is to find out whether a Z-shaped lever will fall over due to gravity. See diagram below (sorry for MS Paint): The bottom edge $x$ is resting on a flat surface. All three edges, $x$, $y$, ...
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1answer
4k views

Relation between transverse velocity of sound and Young's modulus in solids

There is a relation which holds in solids: $$v_{t}=\sqrt{\frac{E}{\rho}}$$, where $v_t$ is the the velocity of sound (transversal elastic waves) and $E$ and $\rho$ are Young's modulus and density of ...
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2answers
12k views

Why does fluid compression cool it up, unlike solids?

Why is it that solids on compression [As in striking a hammer etc.] heat up, but liquids and gases on compression [Pressurizing liquids causes them to freeze or gases to liquify] cool down?
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3answers
131 views

What exactly is Hooke's law defined for?

I used to think that Hooke's law was a relationship between how much a bar under uniaxial loading deformed and the internal force (per unit area) that developed within that bar. But this clearly isn't ...
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1answer
215 views

Why is the continuity equation hardly used in solid mechanics when it is essential in fluid mechanics?

For any continuum, fluid or solid, we can express mass conservation through the continuity equation $$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 ,$$ where $\rho$ is density ...
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3answers
115 views

Localization of stress in tensile test specimen

I'm studying the mechanical (tensile) properties of metals, and my textbook (Introduction to Materials Science for Engineers by James Shackelford) says this: The smallest area region, referred to ...
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1answer
139 views

Rigidity of a material with respect to its structure

Suppose I have some material like graphene that I shaped in some structure (honeycomb, triangular lattice), then it would have a different rigidity according to the structure. My question is, how can ...
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2answers
152 views

System rigidity

What is the meaning of system rigidity in mechanics? I can't understand how to classify the system as rigid or not, and what is the effect of rigidity on the whole system. If you know anything about ...
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1answer
47 views

Is it possible to use the Navier-Stokes equation for solid simulation?

I had a PhD interview yesterday. One of the faculty asked me if it is possible to use a modified version of the Navier-Stokes equation for solid simulation, knowing that both are derived from Newton's ...
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2answers
186 views

Does pressure exist at the center of a solid Sphere? [closed]

If it does , can heating an object cause change in it? How can the relation between change in temp and internal pressure be derived?
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1answer
26 views

Antiplane shearing: singularities of $\vert\nabla\Phi\vert$

Suppose we wish to find the displacement field $(0, 0, \Phi(x,y))$ in an antiplane shear problem with a fracture along $0 < x < k, y = 0$. Then, according to my notes, $\vert \nabla\Phi\vert$ ...
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2answers
651 views

Relationship between Young's modulus and Bulk modulus

I recently came across a statement in a publication "The Young's modulus and Bulk modulus are independent of each other for a uniform isotropic material". Is this valid considering the two are ...
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1answer
96 views

Can an ideal rigid body be treated as hole in space? [closed]

Wikipedia defines ideal rigid body as "In physics, a ideal rigid body is an idealization of a solid body in which deformation is neglected. In other words, the distance between any two given ...
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1answer
279 views

how the form factor (stress - torque) is derived?

I am working on an experiment of rheology and I need to calculate shear stress in order to calculate the viscosity. After some research I found that for the type of viscometer I will be using (cone-...
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1answer
987 views

Measuring speed of sound in a solid specimen

Let's say I have real-life specimens of isotropic solid materials I want to investigate some properties of. Through my setup I'm able to send mechanical wave pulses into one cylindrical bar of the ...
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2answers
743 views

What is the meaning of pre-tension for a stiff membrane?

On one hand, I know that the tighter a drum head is stretched, the higher its natural frequencies. This relation is given by: $$f_{ij}=\frac{k_{ij}}{2\pi R}\sqrt{\frac{T_0}{h\rho}}$$ where $k_{ij}$ ...
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2answers
3k views

Volumetric and Deviatoric Strain Equation in 2D

Strain is defined as $$\epsilon=\frac{1}{2}\left( \nabla u + \nabla u^T\right).$$ I found a formula for the strain tensor in 3D decomposed into volumetric and deviatoric components: $$\epsilon= v + ...
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1answer
114 views

Modeling elastic moduli as a continuous function in space for a single solid material

I've read a number of solid mechanics papers where a single material is modeled with constant elastic moduli (lame parameters $\lambda$, $\mu$). I've also seen composite materials modeled with ...
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0answers
26 views

Strange pattern on fast spinning CD

In the following youtube video and timestamp: http://www.youtube.com/watch?v=zs7x1Hu29Wc&t=6m51s one can see a cd spinning very quickly, in slow motion, just before it breaks. I'm not sure I ...
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0answers
79 views

Deformation of a piece of plastic inside a box

I wanted to know the final form of a solid, for instance a surface. We have a rectangular elastic material of horizontal length equal to L, for example a piece of plastic (top Figure). We put this ...
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0answers
68 views

What kind of tensor is the stress tensor?

I have a lecture on solid mechanics that introduced the stress tensor as a bunch of indices squeezed into a matrix (my point isn't that the indices aren't justified). What I'm trying to understand is ...