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Questions tagged [solid-mechanics]

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Beam Deflections of a simply supported beam in terms of forces acting on the beam

I came across this formula for the bending moment of a simply supported cantilever beam with a point load added in the center: M=WL/4 I am currently investigating the effect of distance between the ...
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51 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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12 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
108 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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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
66 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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9 views

why the percentage of Umklapp scattering is exp(-Θ/2T) in low temperature?

Regarding the heat conduction by fonon, why the percentage of Umklapp scattering is exp(-Θ/2T) in low temperature? Θ is Debye temperature. In this book p.184, he says the number of electron that has ...
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1answer
66 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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15 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
48 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
26 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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Finding a function that maps one surface to other. Deformation fields

I have a isotropic viscoelastic material, under a certain deformation I would like to find displacement field so I can find the strains and stresses eventually. The initial surface is a rectangle ...
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72 views

Horizontal displacement profile of a simply supported beam

I am modeling a simply supported beam, with 2 symmetric loads on the top surface as shown in the below figure. A linear elastic model is used. The second figure shows the horizontal displacement ...
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4answers
251 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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Proving co-rotated time derivative is objective

So I need to show that: $$ \mathring{u}^+ = Q\mathring{u} $$ My progress is thus far, since a vector is objective (i.e. $u^+=Qu$): $$ \mathring{u}^+= (\mathring{Qu}) = \dot{(Qu)}-w(Qu)=\dot{Q}u+Q\...
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Linear elasticity boundary conditions

I came across this post from the computational science board: https://scicomp.stackexchange.com/questions/26495/well-posedness-of-elasticity-boundary-conditions I agree with the posted answer, but I ...
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2answers
121 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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67 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
59 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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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
305 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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23 views

Is there a “solid dynamics” and are there optimal shapes for it?

I am interested in designing an object that can move swiftly through a more solid medium like rock or dirt. Is there any particular kind of mechanical shape (besides a conventional drill) like a ...
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20 views

What component of the strain tensor is a strain gauge measuring in a bend test?

I am studying a bend test of a beam. The beam is set up like a 4 point bend. The force is applied at 2 locations on the top surface, and 2 locations on the bottom surface are fixed in place. It is ...
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2answers
113 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
278 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
51 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
95 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
144 views

Extensible string on a pulley

Suppose we have an extensible massless string satisfying Hooke's Law, tied to a wall at one end and going over a 'fricional pulley'. Now if we tie the other end with a mass 'M', the total length of ...
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1answer
544 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
222 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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17 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
24 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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29 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
65 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 ...
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0answers
80 views

Phonons to solve solid mechanics problems?

From what I understand, phonons can be used to solve acoustics or optics problems, but can we used phonons to solve a solid mechanics problem? The first answer I expect is :"Acoustics wave are solid ...
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4answers
81 views

Does the pressure-volume-temperature realation of gases also work on solids?

I've read about the Combined gas law which said: The ratio between the pressure-volume product and the temperature of a system remains constant. My question is: Does this law also works on ...
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0answers
90 views

Existence of solid mechanics problems that cannot be solved through Lax-Milgram approaches

Very often, solid mechanicians employ finite-element analyses to solve problems in linear solid mechanics. This approach is guaranteed to work because the Lax-Milgram theorem, along with some ...
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1answer
51 views

Why shear stress is developed only in the two set of planes for a rotating pressurized solid cylinder? Why not in the third set of plane?

In case of a rotating pressurized solid cylinder,why shear stress is not developed in the $ABCD\ \& \ EFGH$ planes while the other two set of planes are having shear stress component?
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1answer
220 views

Taylor series expansion for stresses on an element vs equal stress values on opposite faces

I only recently realized this "confusion" despite having cleared all my exams long ago. Consider these 2 diagrams: and 2. Clearly they yield different equations. I have seen both in different ...
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1answer
27 views

Pressure to stress

If you are considering a material that is just sitting on a table, is this material subjected to stress due to the standard pressure (1ATM) of the air around it?
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1answer
175 views

Linear elasticity governing equation

Transient linear elasticity is governed by the following hyperbolic PDE: \begin{align} \frac{\partial^2(\rho \boldsymbol{u})}{\partial t^2} - \nabla \cdot \boldsymbol{\sigma} = \boldsymbol{F} \end{...
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1answer
175 views

How do you compute the stiffness tensor for anisotropic linear elasticity?

The stiffness tensor for anisotropic linear elasticity stiffness tensor consists of 36 elements, but only 21 are unique. Are there equations for these elements as a function of the material ...
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1answer
53 views

Surface Tension— Sessile drop

For background :- Surface tension and capillarity I was reading the above answer. Particularly the sessile drop thing. I understand that as water is being pulled into the solid(assuming it is ...
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2answers
596 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
104 views

Periodic motion, Rotatory motion, and uniform circular motion, are these same or should be considered different?

In a job interview, I was asked that question: are the periodic, rotatory and uniform circular motions are same and are simple harmonic motion? As for as my knowledge is concerned, every rotatory ...
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58 views

What is the maximum tensile stress of Atomic Layer Deposition (ALD) $Al_2O_3$?

I am looking for the maximum tensile stress of ALD (Atomic Layer Deposition) Al2o3, but I have only found this paper, where they found the maximum tensile strain: https://doi.org/10.1063/1.3567912 ...
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16 views

Diameter cutting x Center mass

I'm trying to set the ratio between the variation of the diameter cutting in the region lower a sphere with respect to distance from the center of mass with the center of the radius of the sphere. ...
3
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1answer
56 views

Wave equation on Air- Solid interaction

Suppose that there is, due to an explosion $h$ meters above the ground, a wave in the air with high density, velocity and pressure, capable of inducing an elastic wave on the earth's surface. How does ...
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3answers
64 views

Why solid objects create a sound if you tear them apart?

For example, if you are strong enough to tear apart a piece of plastic - it will make a distinctive sound. If you break it - it too makes a sound. Even if you tear apart paper - it makes sound. But ...
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1answer
371 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?