Questions tagged [solid-mechanics]

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Deflection of a composite beam of two materials

When I encounter a single cantilever beam with a uniform load, I know what to do. When I know the uniform load, I can calculate the deflection of the end of the cantilever beam. Now, I have a ...
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135 views

Rotating solid element

Sorry for boring you, my friends. Recently, I am haunted by a stupid question. It is probably a physics course question rather than a technique one. Finite element method is now a very popular tool ...
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Can displacement, stress, and strain fields be piece-wise twice differentiable?

I have an elasticity problem where the stress field is smooth everywhere except at two isolated points. QUESTION: To have a well-posed elasticity or solid mechanics problem, can the displacement, ...
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589 views

What is elastic thickness?

I read the article about Flexural rigidity, it says Flexural rigidity of plates is defined as $D=\dfrac{Eh_e^3}{12(1-\nu^2)}$ and $E$ is the young's modulus, $\nu$ is poisson's ratio. And I can't find ...
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276 views

where does deformation take place in a shaft subjected to a torsion?

If we rotate a shaft about an axis it is said to be under torsion. It is also said that there will be a deformation. What I'd like to know is will the shaft actually WARP during the process? If not ...
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781 views

Solid Mechanics book recommendations

I'm searching for a book on Solid Mechanics that explains the topics intuitively (similar to Kline explanations on Calculus: An Intuitive and Physical Approach). Also the book should have the ...
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Understanding incompressibility in continuum plasticity

I am a beginner in continuum plasticity and wondering physical meaning of incompressibility in continuum plasticity. Referring to MIT OCW link the consequence of incompressibility condition is (eq ...
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What is physics of Collision between solid and liquid (or gas)? [closed]

My mind has been busy recently by this question: What is physics of Collision between solid and liquid (or gas)? What is Conservation law's of such Collision? Why, when we drop a solid object in ...
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232 views

Does 'maximum principal stress fracture criteria' only apply in tensile loading?

I'm working on 3d simulation of solid fracture, primarily for graphics applications. I have one question about the Rankine fracture criteria, which is widely used in the computer graphics community. ...
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432 views

Deformation due to isostatic compression

When loading a solid material in the shape of a cylinder in isostatic compression, what is the relationship for the change in length versus change in diameter? For example. If I know that when I ...
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491 views

Why are momentum balance equations formulated in terms of net stress rather than net force?

In engineering, a steady state equilibrium force balance is typically expressed as $$\nabla\cdot \sigma=0$$ where $\sigma$ is the stress (force per unit area) applied at a point. It seems more ...
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228 views

what to use for mass in a 2D FEM simulation

I am trying to find the energy of a wave travelling through a solid material in a 2D Finite Element Method (FEM) - Simulation. As a general approach I would try to use $E_{kin}=\frac{1}{2}mv^2$ at ...
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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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22 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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92 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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31 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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14 views

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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9 views

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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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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24 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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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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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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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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43 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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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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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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38 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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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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1answer
78 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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229 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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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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28 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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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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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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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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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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32 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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120 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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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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323 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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111 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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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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How to determine the increment term of normal and shear stress in infinitesimal cube ?

Consider a solid body, if it is in equilibrium then every infinitesimal part of the body is in equilibrium so i take an infinitesimal cube with side lengths, $dx$, $dy$ and $dz$ and try to write the ...
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139 views

What is the use of a reaction frame?

Many experiments I did in the structural mechanics lab had instruments placed inside a frame. For example, for verifying maxwell's reciprocal law, the instrument (that contained hydraulic pistons for ...
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80 views

About the stress acting on the material

I have considered a steel rod of cross section area A and a force of p acting on the two ends along the axis.Now my doubt is whether the internal stress force is p or 2p? My approach is if the length ...
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Volume of cubes thrown in a container

I am trying to calculate how many lego bricks I can fit in containers of a given sizes. Basic 1x1 lego brick is 8 x 8 x 9.4 mm so it has a volume of ~600 mm² Then we have a container of size 192 x ...
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Which material has the lowest Young's modulus?

I guess some foams or elastomers would be the candidates. We are looking for materials with Young's modulus lower than 1 kPa. I also wonder how small it can be theoretically?
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556 views

Are there any examples of hyperelastic materials?

I found the definition of hyperelastic materials, but I can’t find any examples of them. So, are there any hyperelastic materials in our lives?
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geometrical stress dependence for a solid cylidrical body subjected to a uniform pressure load?

Suppose a solid, right-circular, cylindrical body has a long axis of length $L$ and end-faces each having a diameter $D$ was placed fully submerged into a fluid having a hydrostatic pressure of $p$, ...
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Pressure of a sphere against the ground

So we all know that the pressure of a force applied to an area is defined like this: $$P:=\frac{F}{A}$$ Where $F$ is the magnitude of the component of force applied orthogonal to the Area $A$ Now ...