# Tagged Questions

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### Chromatic confocal microscopy (CCM) and stylus probe

I read research that compared between chromatic confocal microscopy (CCM) and stylus probe in wear test but the research didn't clearfield what is chromatic confocal microscopy and what is the stylus ...
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### Derive equation for shear modulus $G=E/(1+2v)$

Shear modulus, G Young's modulus, E and Poisson's ratio, v: $G=E/(1+2v)$ I have always wondered how this relation is derived, but have never found a derivation that I could follow online. I assume ...
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### Is Young's Modulus a Lorentz Scalar?

If a spring is at rest and lies along $X$ axis in a frame $O$ with a spring constant $k_{0}$ then its spring constant in a frame $O'$ which is moving with a speed $v$ at an angle $\theta$ with the $X$ ...
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### Normal reaction [closed]

Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H? I don'...
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### 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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### How does the shattering of an amorphous solid change in lower gravity?

This is a question that's been bothering me for a while. If I were to stand on the moon, holding a pane of glass, what would happen if I smashed it? Glass is an amorphous solid, which is why it is ...
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### 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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### how the form factor (stress - torque) is derived?

I am working on an experiment of rheology and I need to calculate shear stress in order to calculate the viscosity. After some research I found that for the type of viscometer I will be using (cone-...
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### Pressurizing a circular toroidal shell

Consider a toroidal elastic, isotropic, homogeneous shell with a circular cross-section that is initially not pressurized. Under an internal pressure $p$, the shell might become more straight, but the ...
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### Does frequency of a vibration wave of a cantilever depend on its deflection?

cantilever= a beam fixed at one end only deflection is the initial displacement of the free end. the beam is let go when the free end reached its position it will vibrate, does the frequency of ...
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### Measuring speed of sound in a solid specimen

Let's say I have real-life specimens of isotropic solid materials I want to investigate some properties of. Through my setup I'm able to send mechanical wave pulses into one cylindrical bar of the ...
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### Question regarding the use of the Green-Naghdi Objective Stress Rate

The equation for the Green-Naghdi Stress Rate reads: $\boldsymbol{\sigma}^{GN} = \dot{\boldsymbol{\sigma}} + \boldsymbol{\sigma}\cdot\boldsymbol\Omega - \boldsymbol\Omega\cdot\boldsymbol{\sigma}$ ...
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### How is a unidirectional lamina transversely isotropic?

What I don't understand specifically is that if there happen to be more fibers in the $x_2$ direction than the $x_3$ direction, wouldn't that make the material properties in those directions different?...
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### compound bars in series

Compound bars 1 and 2 have lengths L1 and L2, areas A1 and A2, Young moduli E1, E2,thermal expansion coefficient a1 and a2. subjected to a change of temperature T. Two ends of the bar are fixed. The ...
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### Composite bar in series paradox

2]2 Here is the progress and the problem that I encounter. I can calculate the tensile force but it seems like the force cannot exist in the first place ? P/s: I am sorry because I can only pose the ...
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### Is it a law of physics that all machines will break?

The question sounds kinda dumb when I say it out loud but at the same time I'm very curious. When things break, is it solely due to an intrinsic design flaw or is it due to entropy? And is the ...
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### Plastic deformation energy dissipation due to inelastic collision

I have been attempting to determine an analytical expression for the coefficient of restitution (or any similar collision parameter) for an inelastic collision. So far, I've looked at Hertzian contact ...
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### What is “Accumulated plastic strain rate” in Current yield Norton law?

I'm doing FEA of steel under high strain rates and using Elasto-ViscoPlastic material model, with Von-mises yield criterion along with Isotropic hardening. The strain rate sensitivity is addressed by ...
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### What is the stress on the cube?

In a problem, it is given that a mass of 10.2 Kg is resting on a cube made out of a particular material. Assuming that the x-axis is vertically upwards, what is the stress on the cube. (We can say ...
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### Incremental dynamic analysis of an elastic structure with multyple DoF

Consider a linear finite element model of a solid structure like image below: this structure does have a stiffness matrix K, a mass matrix M and a damping matrix C and each of these matrices are ...
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### Energy-Mass Equivalence applied to governing equations

To start off with this is an extremely general (vague) questions, and as such I expect vague answers. I've recently been studying the Navier-Stokes equations which govern fluid motion. These ...
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### Equilibrium and constitutive relation

The constitutive stress-strain relation, say $\sigma=Y\epsilon$ where $Y$ is the Young's modulus, gives you stresses. At equilibrium, force balancing (say, with respect to a internal pressure $p$) ...
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### Stress profile of pressurized bent shell

Consider a pressurized cylindrical shell of radius $r$ and pressure $p$, which at equilibrium has a nonvanishing in-plane stress components $pr/2$ and $pr$. This result is generically found by force-...
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Background about terms in this question: Hookes law and objective stress rates From my understading, the Jaumann rate of deviatoric stress is written as: $$dS/dt = \overset{\bigtriangleup}{{S}} = {\... 2answers 94 views ### Solid Mechanics book recommendations I'm searching for a book on Solid Mechanics that explains the topics intuitively (similar to Kline explanations on Calculus: An Intuitive and Physical Approach). Also the book should have the ... 2answers 143 views ### How does stress change through a bar that sharply increases in diameter? I am looking to analyse the stress through the following bar: The bar is of circular cross section, homogeneous in material, that is of a certain diameter on one half, and a large diameter on the ... 1answer 227 views ### Understanding incompressibility in continuum plasticity I am a beginner in continuum plasticity and wondering physical meaning of incompressibility in continuum plasticity. Referring to MIT OCW link the consequence of incompressibility condition is (eq ... 1answer 860 views ### How to determine plastic strain rate Equivalent plastic strain rate is defined as$$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$Where,  \dot{\bar{\epsilon}} is equivalent plastic strain ... 1answer 731 views ### Meaning of boundary conditions in solid mechanics The Question is: A uniform horizontal beam OA, of length a and weight w per unit length is clamped horizontally at O and freely supported at A. The transverse displacement y of the beam is ... 2answers 484 views ### How to formulate pin joints in finite element modeling of solid frames In frame analysis with finite element every node can be assumed with 6 Degree of Freedom (3 translation DoF and 3 rotational DoF). There are formulations over the web for creating stiffness matrix etc.... 0answers 32 views ### What is the boundary of restorable thermal expansion? As every book indicates, thermal expansion is a linear process \frac{\Delta L}{L}=\alpha \Delta T. Upon heating an object the result is thermal expansion. If we cool it down it is restored its ... 2answers 300 views ### Is there a way to calculate strain energy based on stress and deformation gradient? We know that we can obtain stress from strain energy density and deformation gradient, for example:$$\mathbf P=\frac{\partial W}{\partial \mathbf F}$$However, is there a way to calculate W from ... 1answer 34 views ### Stresses in materials depend on co-ordinate system of choice, true or not? I was studying stresses and strains and my professor told me that they depend on the co-ordinate system we choose to represent, he also said that as we rotate the co-ordinate system, shears that were ... 2answers 345 views ### Why is deflection at the boundary 0 for the given statically indeterminate beam problem? I have been trying really hard to understand the boundary condition applied to the indeterminate beam problems.. although i am citing a particular problem, i have been finding the same approach in ... 2answers 259 views ### What is the meaning of pre-tension for a stiff membrane? On one hand, I know that the tighter a drum head is stretched, the higher its natural frequencies. This relation is given by:$$f_{ij}=\frac{k_{ij}}{2\pi R}\sqrt{\frac{T_0}{h\rho}}$$where k_{ij} ... 0answers 37 views ### Can an axisymmetric solution produce antisymmetric eigenfunctions? I'm solving a vibrating membrane. In order to simplify my calculations, it's tempting to assume axisymmetric behaviour. If I solve an axisymmetric problem, am I going to lose all the antisymmetric ... 3answers 4k views ### Why rubber is incompressible material? Why rubber is incompressible material? I know its Poisson's ratio is nearing to 0.5. So I don't understand physically, what it means by 0.5 Poisson's ratio and incompressibility. When I tried ... 0answers 70 views ### Are there any known (closed form even if approximate) solutions to problems in relativistic elasticity? There are several useful known solutions to the EFE with relatively simple / trivial stress-energy-momentum tensor, such as the Schwarzschild solution. Despite the idealizations made therein they are ... 2answers 508 views ### Why plane stress condition is taken for thin plates Why plane stress is taken for thin plates? It says in the books that the stress variation is small for thin components and is close to zero. Why is that so? Also why stress at free surface is zero? (... 1answer 532 views ### Hookes law and objective stress rates Often, in papers presenting updated Lagrangian simulation methods for solid dynamics, the following procedure for updating the (Cauchy) stress tensor is presented: First, the Cauchy stress tensor is ... 0answers 172 views ### Creep of materials at atomic/molecular level under stresses Do the viscoelastic materials creep at the same rate under three types of fundamental stresses, viz.- TENSION, COMPRESSION and SHEAR??? My intuition tells me that the answer is no. But, I can't get ... 1answer 665 views ### Volumetric and Deviatoric Strain Equation in 2D Strain is defined as$$\epsilon=\frac{1}{2}\left( \nabla u + \nabla u^T\right).$$I found a formula for the strain tensor in 3D decomposed into volumetric and deviatoric components:$$\epsilon= v + ...
Is there the formula (if someone already has discovered it) or what is the algorithm (if a particular formula was not deduced), to calculate the critical pressure of thick-walled spherical shell $−$ ...