Questions tagged [solid-mechanics]

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Solid material thermophysical properties database

Can anyone suggest me a reliable source for solid material (isotropic/anisotropic) thermophysical properties database ? Thanks
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1answer
51 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 ...
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19 views

Find a reference frame for a straight line rigid system

A body reference frame is a reference frame moving with a rigid body. So any rigid system has at least two points $P$ and $Q$ and these are such that $$ \vec{QP}\,\cdot\,\vec{QP}=\text{constant} $$ by ...
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25 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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1answer
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Why doesn't the Stress Power in the theorem of the expended mechanical power contribute to the kinetic energy?

The following is the formula of the expended mechanical power: $P(t)$ $=$ $\frac{d}{dt}$ $\int \frac{1}{2} \rho\ v^2 dV$ $+$ $\int \sigma \colon d\ dV$ where $P(t)$ is the mechanical power entering ...
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1answer
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How to derive Infinitesimal Strain Tensor in Cylindrical Coordinates [closed]

How can I obtain the below formulas of infinitesimal strain in cylindrical coordinates using matrix calculation given the first formula? I find it hard to study them because I still don't know how to ...
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45 views

Bouncing capsule (ellipsoid) can have COR (coefficient of restitution) higher than 1?

So I originally saw the problem in last year's IYPT. (#15 https://www.iypt.org/problems/problems-for-the-34th-iypt-2021/) A spherical ball dropped onto a hard surface will never rebound to the ...
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29 views

Should transmission lines be manufactured to have a catenary shape?

When metal transmission lines are hung between two poles, the shape they assume to minimize the action of gravitational and tensile forces is a catenary. While assuming that shape, the line undergoes ...
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74 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
62 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 ...
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3answers
99 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
187 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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28 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
240 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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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
27 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
95 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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1answer
115 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
84 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
38 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
48 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
55 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
23 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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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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37 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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38 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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26 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
131 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
121 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
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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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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
152 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
34 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
163 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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60 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
172 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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32 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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30 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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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
66 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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66 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
71 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
48 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
208 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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