# Questions tagged [solid-mechanics]

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79 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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### Interpretation of Hooke's Law

I often see people interpreting Hooke's Law $σ=Eε$ as, "The deformation $ε$ that occurs when you subject a material to a stress $σ$." This makes it sound like stress is an external ...
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### Superposition for deformation of a bar

I had a question on applying the superposition principle for a bar subjected to an external load and a temperature change. According to Wikipedia, "for all linear systems, the net response caused ...
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### General plane motion and freely floating rigid body

Consider a rigid rectangular plate of length $l$, width $w$ and thickness $t$ which is at rest and is floating freely in space (no gravity). The center of the plate is at $O_L$ with respect to global ...
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### Slip boundary conditions for solid-solid interactions?

If the no-slip conditions are mostly considered for fluid-solid interactions, so what about solid-solid? Apart from the slip (zero-normal velocity) conditions, are there another consideration that we ...
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### Applied load on a Stapler [closed]

I'm trying to do a finite element analysis on a stapler I created in Solidworks. In order to do this I have needed a set load being applied to the top of the stapler. Any ideas on how I would go about ...
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### Brillouin Zones as diffraction zones for a crystal lattice

Diffractions usually occur when planar waves strike a gap that has less than or equal to the size of the wavelength. Is it correct to assume that Brillouin zones are the gaps in the crystal lattice ...
91 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, ...
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### Principal Stresses in large deformation

Do you know if the principal stresses are invariant to the true (Cauchy) stress and undeformed (2nd Piola-Kirchoff) stress? I mean should i use always cauchy even the body deformations are significant?...
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### Why do ribbons curl when we stroke them with scissors?

I have recently learnt how to make quilling swirls [also called paper filigree] ,one of the methods to curl the paper strips is to quickly run your fingernail on the underside of the strip you want to ...
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### Simplification using Newton's second law

I am not sure if my simplification works in this problem: Problem: I have a beam which is strap around with cargo straps. First picture presents section through second picture. So applying Newtons ...
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### What machine element can we estimate a bicycle rim to be? [closed]

In mechanical terms, what machine element can we consider a bicycle rim to be? Like can we design it based on the assumption that it is a curved beam/ a hoop?
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### Weight exerted by two blocks of metal [closed]

Can 2 blocks, composed of different metals, have the same masses but different volumes and still have the same weight if hung on a spring balance?
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### Calculating bond energy per molecule [closed]

I'm currently going through a book on material science, a field of which I have little background knowledge. One of the questions asks me to calculate the bond energy per molecule when given the ...
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### Mathematical definition of elastic materials

Physically, elastic materials are materials which return to their original state upon complete removal of applied mechanical loads under isothermal conditions. In the book "Mechanics of ...
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### Is bending stiffness reduction a good model for beam wear and tear?

I'm working with the 1-dimensional Euler Bernoulli beam described by the PDE: I am wondering if reducing $EI$ as my time-advancing scheme solves the equation is an acceptable model of wear and tear (...
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### Name of the product between Young's modulus and coefficient of thermal expansion (CTE)

In solid mechanics, and especially thermo-elasticity, there are relationships with both the Young's modulus, $E$, and coefficient of thermal expansion, $\alpha$. Let's take the partitioning of strain ...
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### Constitutive relations and strain energy in finite strain viscoelastic solid mechanics

I'm an applied math graduate student, and my research is straying into hyperviscoelastic models of materials. I've had trouble finding an answer to this question I have about the mathematical theory ...
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### How mechanical Strain developed in metal bar at molecular level?

If I have metal bar fixed to a support at one end while I apply a tensile force at the other end, the bar elongates while its cross sectional area decreases. I want to know How strain is developed at ...
121 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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### 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 ...
101 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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### Confusion between statically determinate and indeterminate beams

Why is it that statically determinate beams can take some degree of misfits without any generation of strains or stress, but not statically indeterminate beams?
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### How does sound imparts vibrations to molecules in solids

How does sound imparts vibrations to molecules in solids which are tightly bounded. I understand the molecular bounding is very strong that is why it is solid and tough. So how does mere a tap on a ...
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### Why is the extension of a uniformly tapered round bar greater than that of a uniform cylindrical bar?

A round bar, of Length $L$ and young's modulus $E$, tapers uniformly from radius $r_1$ to radius $r_2=2r_1$. The extension produced by a tensile axial load $P$ is equal to $\frac{PL}{2\pi E r_1^2}$. ...
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### What is single mode approximation in fluid solid interactions?

Before redirecting me to the other questions, I am asking this with respect to fluid solid interactions. In order to obtain an understanding between the fluid - solid interactions, governing equations ...
136 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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### Is there a scale at which all solids can be treated as fluids?

I was answering an Earth Science SE question that involved the reasons why Earth has an equatorial bulge, and wanted to make an offhand comment such as "Real planetary constituents aren't this strong; ...
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### Second sound in superfluids and solids

I am trying to get a handle on the phenomenon of second sound. It most famously occurs in superfluids at finite temperature. Here, according to Landau, superfluid phonons (which exist at zero ...
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### What are the partial differential equations for Solid Stress Analysis?

When using Finite Element Analysis for Fluids we solve the Navier Stokes Equation and continuity equation, when solving for temperature we solve the heat equation and fouriers law, when dealing with ...
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### Resource recommendation for studying Elastostatics and Elastodynamics using Lagrangian and Hamiltonian formulation

I've been self studying Elastostatics and Elastodynamics from Kip S. Thorne's Modern Classical Physics (Chapter 11 & 12). The whole topic is discussed based on Newtonian mechanics, vector & ...
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### 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 \$\...