Questions tagged [solid-mechanics]

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154 questions
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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, ...
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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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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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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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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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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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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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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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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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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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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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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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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. ...
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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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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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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?
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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 ...
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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 ...
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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 ...