Questions tagged [solid-mechanics]

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12 views

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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18 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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16 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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24 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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24 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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58 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
38 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
40 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
34 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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19 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
72 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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69 views

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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29 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
62 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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48 views

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
50 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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47 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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25 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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25 views

Total stress and total strain in thermoelasticity

For a solid undergoing thermoelastic deformation, we can write the total stress as $$ \sigma_{total} = \sigma_{mechanical} - \sigma_{thermal} $$ Where $$ \sigma_{mechanical} = C:\epsilon_{mechanical} ...
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20 views

Calculating physical quantities (cohesive energy, elastic constants etc.) for fcc/bcc metal directly from an (EAM) interatomic potential

I am of mathematical background and am currently doing some background reading on what is done 'in practice' when modelling atomistic crystalline systems. In particular, I want to understand how, ...
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1answer
27 views

Why does squashed clay 'hug' the press rather than spreading out?

In this demonstration a piece of clay (or clay-like material) is squashed under a press. The lump of clay initially spreads out under the ram of the press. But once it reaches the edge of the ram ...
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28 views

Why does brass fracture at a 45° angle?

These images were from a demonstration of a brass sample exposed to intense longitudinal (axial) pressure. Initially it was squashed resulting in some bulging outwards and sideways distortion, but ...
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3answers
53 views

Bending of a metal plate

If I have a stiff metal plate, and several forces acting on it at specific points, how would I calculate the resulting shape? What information, besides the forces acting on it, would I need?
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138 views

Law of the lever - Explained Physically

Thanks for reading. I've seen the "Archimedes Proof" of the law of the lever, and many similar ones, but...at the end of the day, all they're doing is getting observations about the way rotating ...
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27 views

How to calculate the tensor of inertia in this problem?

I have the following geometry for my problem: I'm asked to calculate the tensor of Inertia: $\stackrel{\leftrightarrow}{I}_{O}=\left[\begin{array}{ccc}{I_{11}} & {-P_{12}} & {-P_{13}} \\ {-...
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77 views

Gibbs free energy: reduction from elastic solids to thermodynamics

The book on elastic solids that I'm reading defines the Gibbs free energy per unit mass as $g = e - Ts - \frac{\mathbf{P} : \mathbf{F}}{\rho_0}$, where $e$ is the specific internal energy, $T$ ...
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21 views

How to increasing the swing frequency/speed of pendulum with hollow sphere enclosing small solid sphere?

When a small solid sphere is enclosed inside a hollow sphere, for a pendulum. How it will change the swinging nature of the pendulum? How can we increase the swinging frequency/speed of the pendulum?
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2answers
265 views

Why are springs spiral-shaped? [duplicate]

I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question. I've had a lot of physics experiments involving springs, unintentionally ...
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0answers
17 views

Accion response calculation on tilt steering kick board scooter

Hi I am designing a home made kick board scooter, need to understant the behaviour between the board angle and the turn angle. In a classic sakateboard the foot action is transformed to turn angle, ...
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3answers
93 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
212 views

Elastic potential energy per unit volume,stress-strain and strain-stress curve

From what I understand, when we calculate elastic potential energy per unit volume of a material which extends linearly, we calculate the area under the graph of stress- strain OR strain- stress graph,...
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16 views

Viscoplastic Anand Model of Solder Alloy

I have found some data of viscoplastic Anand model for the SAC305 solder joint of electronic devices in the literature. Does this data depend on the thickness, length and width of the joint? I mean ...
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1answer
60 views

Stress acting at an internal point of a suspended rod [closed]

I've come across a question that asks to calculate the stress acting at the midpoint of a uniform rod (mass $M$, length $l$ and area $A$) suspended at one end: I know that the basic definition of ...
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1answer
30 views

Strains when one vertex of a 2 dimensional square element is pulled up

ABCD is a square and C is pulled up by a small amount(say x) keeping other vertices else fixed, what are the strains in the element. I assumed it would be same as pulling CD up by x/2 and then ...
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4answers
336 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
512 views

Poisson's ratio in analytical beam deflection equations

After looking at some of the analytical expressions for analyzing beams, I noticed that none of the equations depend on the material's Poisson ratio. Some analytical expressions can be found in https:/...
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100 views

Converting the deformation gradient from Cartesian to Cylindrical

Suppose I have a Cartesian deformation gradient tensor F for a domain $\Omega_0$. This tensor deforms $\Omega_0$ into a new domain $\Omega_1$. Also assume that I know the values for each entry of F at ...
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2answers
218 views

Deflection in beams — which material properties are most influential?

I am modeling a beam made of an orthotropic material. The beam's length is aligned with the x-direction, and the force is applied in the y-direction (it is a 4 point bend experiment that I am modeling)...
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0answers
43 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 ...
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1answer
772 views

Why is the partial derivative of strain energy function with respect to strain equal to stress

In Elasticity, we have a strain energy function , $W$, that is a function of strain tensor, $E$. Then the cauchy stress tensor, $T$ can be determined by: $$T_{ij}=\frac{\partial W}{\partial E_{ij}} \...
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2answers
210 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 $\epsilon_t$ ...
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1answer
466 views

How can we theoretically calculate the dependence of torsion constant of a wire on it's length and radius?

Is there a way to calculate how the torsion constant depends on the length and radius of a uniform wire without doing the experiments? Also do mention if we require value of any kind of property of ...
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1answer
57 views

Why does the stress strain curve depend upon strain rate?

I was going through this website :https://www.tf.uni-kiel.de/matwis/amat/iss/index.html where it answered a question: Why is the maximum of the (nominal) stress-strain curve and the beginning of ...
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1answer
210 views

Coefficient of thermal expansion tensor

This question pertains to the general coefficient of thermal expansion (CTE) tensor, with no assumption about isotropy. The CTE tensor is $\alpha_{ij}$. Is it possible for $\alpha_{ij}$ to be non-zero ...
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1answer
875 views

Young's modulus and shear modulus relation - temperature effect

Young's modulus and shear modulus are related by $E=2G(1+\nu)$ (for isotropic and homogeneous materials), $E$ is Young's modulus, $G$ is shear modulus and $\nu$ is Poisson's ratio. I can do experiment ...
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1answer
346 views

von Mises yield criterion when all 3 principal stresses are equal and in tension

Based on the von Mises yield criterion, a material begins to yield at a point when the state of stress at that point is such that the scalar known as the von Mises stress, exceeds the yield strength ...
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18 views

Stress state in an elastic half space with uniform constant body force

Is there a closed form expression for the stress state in an elastic halfspace subject to a uniform constant body force? I know that the Green's function for this problem is given by Mindlin's ...
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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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30 views

2D plane stress problem: a bent rod with one curved side squeezed

Consider a bent rod (i.e., a sector of an annulus) of angle $\alpha$ and inner and outer radii $R_i$ and $R_o$. Now, we squeeze in azimuthally the lower face by an amount $\Delta$ (see the image below)...
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1answer
66 views

What should be the characterisitc dimension for angled entry of cylinder in water?

I am working on problem for angled entry of cylindrical object in water (30 degrees and 60 degrees), for that I need to calculate the characteristic dimension of the cylinder to calculate the impact ...