Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [solid-mechanics]

The tag has no usage guidance.

0
votes
0answers
6 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 ...
0
votes
1answer
47 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,...
0
votes
0answers
11 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 ...
-2
votes
1answer
41 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 ...
0
votes
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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
66 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 ...
2
votes
4answers
200 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 ...
0
votes
0answers
17 views

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\...
0
votes
0answers
10 views

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 ...
0
votes
2answers
43 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:/...
0
votes
0answers
40 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 ...
0
votes
2answers
39 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)...
2
votes
0answers
41 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 ...
0
votes
1answer
117 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}} \...
0
votes
0answers
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 ...
0
votes
0answers
18 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 ...
1
vote
2answers
93 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 $\epsilon_t$ ...
0
votes
1answer
200 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 ...
0
votes
1answer
41 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 ...
0
votes
1answer
45 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 ...
1
vote
1answer
101 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 ...
0
votes
1answer
336 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 ...
2
votes
1answer
160 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 ...
1
vote
0answers
16 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 ...
1
vote
1answer
23 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, $\vert \nabla\Phi\vert$ ...
1
vote
0answers
28 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)...
1
vote
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 ...
1
vote
0answers
71 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 ...
0
votes
0answers
62 views

Bloch theorem in Hofstadter problem

right now I'm dealing with the Hofstadter Butterfly. Currently I'm reading and trying to understand a paper. It's about the following paper: https://arxiv.org/pdf/cond-mat/9312088.pdf. Zabrodin, ...
0
votes
4answers
75 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 ...
4
votes
0answers
88 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 ...
0
votes
1answer
40 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?
1
vote
1answer
151 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 ...
0
votes
1answer
25 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?
0
votes
1answer
154 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{...
1
vote
1answer
133 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 ...
0
votes
1answer
43 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 ...
1
vote
2answers
550 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 ...
0
votes
1answer
79 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 ...
0
votes
0answers
55 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 ...
1
vote
0answers
14 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
votes
1answer
54 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 ...
4
votes
3answers
59 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 ...
2
votes
1answer
292 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?
2
votes
2answers
109 views

What happens to matter when there's distortion in space

This is all hypothetical, but if you had control of space (to do distortions to space as very heavy objects do), what happens to the matter in the space? To have a concrete example, let's say that you ...
-1
votes
4answers
121 views

What is the definition of a solid?

What is the definition of a solid? What is the most general definition of a solid? Are amorphous materials (which can creep) like window glass considered solids? Are colloidal substances like proteins ...
0
votes
1answer
2k views

Solid Mechanics — how to find pure shear stress state?

I have a question regarding Solid Mechanics and Mohr's circle. In my test today, we had a plane stress state represented in a Mohr circle which was not centered at the origin. The question asked to ...
0
votes
1answer
41 views

Understanding internal torques

I have having trouble with Q7: https://i.imgur.com/vsco1GW.png I don't understand how to find internal torque, the solutions say that the internal torque is equal to the external torque. So I can ...
2
votes
0answers
88 views

Eigenfrequency of a beam?

How would you calculate the eigenfrequency of such a cantilever? This is what I found so far, but I don't know how to apply it to this specific geometry: http://iitg.vlab.co.in/?sub=62&brch=175&...