Questions tagged [solid-mechanics]

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3answers
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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2answers
177 views

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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25 views

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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5answers
198 views

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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0answers
14 views

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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1answer
21 views

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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1answer
21 views

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 ...
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2answers
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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0answers
7 views

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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1answer
80 views

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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2answers
82 views

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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1answer
23 views

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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1answer
37 views

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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2answers
36 views

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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4answers
52 views

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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2answers
20 views

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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1answer
42 views

Question on elasticity of materials [closed]

What I did: The force applied here is its weight F$=$mg, while m=$\rho l$A, where A = area of cross-section of the wire. $$\text{Y}=\frac{\text{stress}}{\text{strain}}=\frac{\text{$\rho l$A}/A}{\text{$...
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2answers
73 views

Kleppner problem 6.33 Confusion [closed]

A cone of height $h$ and base radius $R$ is free to rotate around a fixed vertical axis. It has a thin groove cut in its surface. The cone is set rotating freely with angular speed $ω_0$, and a small ...
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0answers
27 views

Cycles to failure

$$ \text{Ramberg-Osgood equation:} \hspace{41mm} \varepsilon_{tot} = \underbrace{\frac{\sigma}{E}}_{\text{elastic}} + \underbrace{\left(\frac{\sigma}{K}\right)^{\frac{1}{n}}}_{\text{plastic}}$$ $$ \...
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0answers
23 views

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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23 views

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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2answers
31 views

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 ...
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2answers
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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1answer
74 views

Why are the principal planes where principal stresses occur perpendicular to each other?

Equation of principal angles: $$\tan 2\theta_p=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}$$ Equation of principal stresses: $$\sigma_{max}, \sigma_{min} = {\sigma_{xx} + \sigma_{yy} \over 2} \pm \sqrt{ \...
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1answer
71 views

Is this book correct?

I'm currently reading this book on flight dynamics but I'm having some trouble getting my head around the way the author derives some equations of motion. He starts by showing the body in the first ...
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0answers
42 views

How to prove $\operatorname{div} \mathbf{A}=\operatorname{Div} \mathbf{A} \mathbf{F}^{-\mathrm{T}}$?

I recently focus on solid mechanics and I am reading Nonlinear Solid Mechanics A Continuum Approach for Engineering by Gerhard A. Holzapfel. However, I was confused by a mathematical formula eq(2.49), ...
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1answer
57 views

Self-deformation due to own weight [closed]

The goal is to calculate the total deformation due to self-weight. I understand the calculation that is shown in the picture. I forgot to include that $x$ is the length of the object's portion under ...
4
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1answer
146 views

Why isn't there a “parallel” Pressure as there is a parallel or shear Stress?

I had this question while I was reading the differences between pressure and stress. As I have read: Pressure is the intensity of external forces acting on a point, and it always act normal to the ...
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1answer
30 views

Why $curl\textbf{u}$ is twice the axial vector $\omega$ of the skew part of tensor $grad\textbf{u}$

I met a problem in Nonlinear Solid Mechanics: A Continuum Approach for Engineering by Gerhard A. Holzapfel. This is the problem and the solution given bu the author. My question is WHY $W_{ij}=\...
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1answer
117 views

Tensor Product between Nabla operator and a vector or tensor field

I am recently studying solid mechanics and I met a problem regarding Nabla operator. I am trying to prove the following relation: $$\nabla \otimes\textbf{u}=\frac{\partial\textbf{u}}{\partial x_{i}} \...
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0answers
52 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 ...
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1answer
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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29 views

Non conservative torque and lagrangian formalism

I have a system I would like to describe with a Lagrangian formalism. I model friction on my system with a torque ($\tau$). Having non conservative forces and torques, I use equation: $$ \frac{d}{dt}\...
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0answers
20 views

Strains in a homogeneous isotropic linear elastic porous body

I am trying to understand a claim made in many papers (Geertsma, 1957a; Rice, 1976) and textbooks (Jaeger and Cook; Zimmerman) related to mechanics of porous media. Consider an isotropic linear ...
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0answers
25 views

Advanced wind electricity generation

Well, when it comes to electricity generation it is important to design units to be scalable enough. With wind turbines becoming popular nowadays it is very important. As you know, currently wind ...
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0answers
42 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 ...
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0answers
61 views

Design an Experiment based on Castigliano’s Theorem to Determine Young’s modulus of the Unknown Member

The question states: "You need to design an experiment based on Castigliano’s theorem to determine Young’s modulus of the vertical member (unknown material) without destroying the structure." Is ...
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1answer
48 views

Dispersion relation with damping force

We consider a linear chain of atom connected by springs with constant $K$. We have the usual elastic force and we add damping force such that the dispersion relation is: $$ \omega = 2\sqrt \frac K m \...
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2answers
45 views

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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1answer
121 views

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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41 views

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 ...
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2answers
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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0answers
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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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0answers
33 views

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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1answer
131 views

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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0answers
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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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1answer
52 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 $\...
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0answers
49 views

Kinetic energy of a solid

Considering an inertial reference frame with origin O, the first part expresses the angular momentum of a system as the sum of the angular momentum of the center of mass and the angular momentum ...
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0answers
26 views

Good references for Fluid/Solid physical properties

I need good references for Fluid (Equation Of State, Heat capacity, thermal conductivity, radiation properties...) and Solid (Elasticity modulus, stress-strain data, heat capacity, thermoelasticity, ...

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