Questions related to the Continuum Mechanics Division of Elasticity. The bending of beams, deflection of rods, or in general, applications of Hooke's Law generalized to three dimensions.

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1answer
632 views

effect of object mass in coeficient of restitution

I know the coefficient of restitution depends on the velocity before and after the impact of a bouncing ball. How does the mass affect it. Can't figure it out. v ...
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1answer
522 views

Confusion In solving a problem related to Elasticity?

This the question given in my textbook A thin, uniform rod of length $l$ is rotated with constant angular speed $\omega$ about an axis passing through it's one end and perpendicular to one end of ...
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1answer
820 views

Calculation of a bending moment

I'd like to calculate the bending moment of a cantilever, fixed at its base, and submitted to a certain stress on a specific spot, but I can't find the proper definition of this bending moment (first ...
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1answer
240 views

Simplifying some math for an ant-on-rubber-band problem

OK, I've been doing this problem for fun (it's a great problem, BTW!): http://www.physics.harvard.edu/academics/undergrad/probweek/prob76.pdf Here is the solution: ...
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2answers
272 views

Stress and strain

Let us consider a rod having a young's modulus $Y$. Let it be of length $l$, and suppose it is suspended from a point P. Let us pull the rod with a force $F$ at a point Q which is at a distance $2/3l$ ...
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15 views

Energy losses of a ball, hitting the ground due to elastic and accelerating processes

There is a question about gravitational force and irreversibility. In my answer I pointed towards the phenomenon of photon emission during accelerations and by this of energy loss. My last sentence ...
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0answers
11 views

What is our most complete microscopic theory for the elastic-plastic transition point?

I suppose its all stated in the title. What is our most successful description of the microscopic behavior of material at the elastic-plastic transition point. My condensed matter physics prof was ...
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1answer
27 views

Predicting contact time and COR (coeff of restitution) for a cricket ball and pitch

For real world application, COR --> Bounce produced by pitch, for both spinners & seamers; Contact time --> grip provided by pitch, mainly for spinners Assuming cricket ball to be a sphere and ...
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15 views

Infinite elastic half-space with point load (Mindlin's problem)

What is the equilibrium deformation of an infinite half-space (that is, an isotropic and homogeneous linearly-elastic three-dimensional medium, with a single planar surface) produced by a force which ...
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1answer
9 views

Biot coefficient as function of porosity

Can the Biot poroelasticity coefficient $\alpha$ be approximated as a function solely of porosity $\phi$, and if so then how (and under what conditions)? I've read (e.g. 2.02-3 here) that it can, ...
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0answers
23 views

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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2answers
29 views

Realtion of acceleration and deformation [duplicate]

What will happen if I apply 10N force to a body's one end and 11N to it's others end? Which force will accelerate it, which force will deform it? Why?
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4answers
244 views

Hooke's Law is valid upto what limit?

My textbook states: " the extension produced in the wire is directly proportional to the load applied,within elastic limit." But my Physics professor said that it is valid upto only proportionality ...
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0answers
23 views

Why don't we consider net force while calculating elongation in an object?

I have been studying elasticity in mechanics . Most of my books while solving problems where we have to calculate the elongation in an object due to an external force don't take into account the net ...
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1answer
60 views

Ball suspended on elastic string (finding tension)

A ball (of mass $m$) is suspended by an elastic string. It accelerates upwards with an acceleration $a$. Find the tension in the string. Taking upwards as positive, we have $$T - mg = ma \iff T = ...
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0answers
36 views

Formulae for Elastic Hysteresis of rubber

Being a school student, I'm pretty sure we don't need to explicitly learn any formulae helping us evaluate the energy dissipated by mechanical internal energy in a hysteresis loop. But I was wondering ...
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1answer
43 views

Deformation of a rubber ball between planes

I want to know the shape of a rubber ball when it is sandwiched between two (not necessary parallel) plane. If two plane is parallel, I think it is possible to approximate the ball as spheroid and ...
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1answer
28 views

pulmonary physics: balloons in closed chambers

Imagine we have an expanded balloon with radius $R_1$ and an internal pressure of $+20$ atm, in an room at $0$ atm of pressure. The system is at equilibrium. Now, I drop the pressure in the room to ...
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0answers
34 views

Strain problem with diferent forces

Good day to everyone. I had a test a couple of weeks ago and just got it back, and I'm getting a little confuse with a certain question that I thought was answered correctly, so here is it: (roughly ...
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1answer
36 views

Calculate water pressure in a elastic material cavity

Imagine there is a ball-shape cavity made of elastic material. The diameter of the cavity is 1 cm so that the capacity of the cavity is $\dfrac{4}{3}\pi\approx4.19 \textrm{cm}^3$. Now we pump ...
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0answers
24 views

Elastic material with exponential behavior?

I know some constitutive models for elastic materials like Neo-Hooke or Mooney-Rivlin, which give a relation between elongation $\lambda=y/y_o$ (where $y$ and $y_o$ are the length of the elastic ...
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0answers
24 views

Negative Kinetic energy of normal modes in an elastic solid?

So I'm pretty stupid, admittedly, but I'm also pretty confused. I also fully realize this question is probably completely idiotic. The background is normal modes in linear elastic solids. Let the ...
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0answers
30 views

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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0answers
29 views

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 ...
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0answers
28 views

Mooney-Rivlin coefficients sign

I'm doing a fitting of uniaxial compression data of a isotropic polymer using the Mooney-Rivlin model: $\sigma=\left( 2C_1 + \frac{2C_2}{\lambda} \right )\left( \lambda ^2- \frac{1}{\lambda } ...
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0answers
29 views

Strain energy density (potential energy of elastic continua)

This question has to do with writing down the potential energy of an elastic body, which obeys a generalized Hooke's law [; \sigma_{ik} = \sum_{klm} \lambda_{iklm} u_{lm} ;] Where $\sigma$ is the ...
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0answers
26 views

Shear flow in J section type beam

What does the distribution of shear flow look like in a J section type beam. I'm only interested in a qualitative picture of it. I'm not interested in the calculations themselves. It is the top of the ...
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0answers
35 views

Specific form of Stokes's differential equation

Coming from a chemical background, I have next to no knowledge of the (as it seems to me) complex field of fluid dynamics, so bear with me here. I'm reading a paper written by seismologist Norman ...
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0answers
51 views

Coefficient Of Restitution of Two Balls With Different Elasticities

In a computer program, I need to simulate the collision of two balls with different elasticity values given between 0.0-1.0. I looked for a formula to derive restitution coefficient from elasticity ...
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0answers
19 views

Solution for elastic wave on plane of ideal contact between two half spaces of elastic, homogeneous, isotropic, linear solids

Please give the solution for elastic wave of arbitrary polarization incident at arbitrary angle on plane of ideal contact (meaning no slip, homothermal, nondissipative, and no transfer of material ...
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1answer
43 views

Can surface waves exist near a fixed surface

(I'll phrase this question in terms of waves in an elastic medium, but this is a more general question.) Surface waves are waves near the surface of a medium whose amplitude decreases as you go away ...
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2answers
46 views

Elastic behaviour of objects

If I strike my car with a wrench with enough force to make a dent in it, then it's obvious that I won't be able to produce any acceleration in the car. But I am applying an external deforming force. ...
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1answer
403 views

Diameter of after elongation of a cylinder

This is more Material Science than Physics, but I'm doing a research project right now in computational science that involves some additional information that is outside of my background. I've done ...
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1answer
47 views

Is an elastic, gravitating object stable?

As I understand, an object can contract under its own gravitantional pull. Then as it does so, different parts of the object must move with some velocity. This in turn means that their relativistic ...
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1answer
50 views

Relation between area elements in finite deformation theory (continuum mechanics)

There are relations for the line and volume elements in continuum mechanics. For example: \begin{align} \ \ \ \ \ \ \ \ \ \ \ \ \frac{V}{V_0}&={\rm det}(F)\tag{1}\\ \lambda^2&=(F^TFe_1\cdot ...
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0answers
50 views

What's the relation between the type (Gender) of a balloon and its internal pressure

I'm working on a project about balloons and I need to know the relation between the gender of the balloon and its internal pressure. As far as I know, there are some parameters such as " Elasticity of ...
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0answers
39 views

Tricky question (physics) [duplicate]

I know this may not be the place for this question, by stackexchange physics has banned homework questions :( A piece of hair taken from a goat has a radius of $3.1\times 10^{-5}\text{ m}$. What ...
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2answers
363 views

Determining flexural modulus by performing 3 point bending test using hollow cylindrical tube

I would like to decide the flexural modulus of the material of plastic tube by performing 3 point bending test according to the ASTM D 790 procedure. In ASTM D 790, the form of the specimen is ...
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0answers
33 views

Role of the crystallographic point group on properties of tensorial elasticity

If a space point group for a crystal is known, does this automatically define the elastic tensor symmetry of the material? What further implications can be found? The crystallographic subgroups: ...
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0answers
66 views

Young elasticity modulus anisotropic media

Im studying anisotropic system composed by a elastic matrix (Young modulus $E_m$) filled with oriented rods. Given this filler orientation, the material is elastic-anisotropic, with Young elastic ...
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0answers
620 views

Caculating thermal stresses in a composite rod

The Question Between two rigid walls separated by a distance $l_1+l_2$, two rods of equal cross-section area $A$, and length, coefficient of linear expansion and Young's modulus $l_1, ...
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0answers
84 views

Internal Stresses in a Horizontal Rod

Suppose we havean uniform slender rod of dimensions : $L$( length) and $A$( cross sectional area). Now at different points on the rod we apply different forces. So, in this situation how are we ...
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0answers
83 views

What is the relationship between strain and electric current?

Strain or stress can be caused by different sources. I categorized theses sources as mechanical, thermal and electrical loads and formulated the total stress as follows: $$ \epsilon_{total} = ...
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1answer
166 views

Is there a difference between, static loading and fast loading of a polymer (non linear elastic material) in terms of elastic potential generated?

Imagine a non-linear elastic material such as a rubber band, nylon webbing or polyester webbing tensioned between two points. Scenario 1: A large mass is statically (no acceleration) loaded onto the ...
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0answers
481 views

Maximum Shear on a Beam - beam with fixed support on one end and hinge on other end

A beam $\displaystyle 3m$ long with fixed support on one end and hinge on the other end is subjected to a uniform load of $10\ kN/m$. What is the maximum shear of this beam? The solution is this one: ...
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0answers
727 views

Whats the contact area for elastic contact between a cylinder and a plane surface?

I am trying to determine the contact area between a cylinder and a plane surface of two different materials so that the plane lies tangent to the cylinder. There is elastic contact between the two ...
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0answers
515 views

How to solve fixed-fixed beam with finite difference method?

What equations to use on this system to form a matrix $A$ with dimensions $[n,n]$ and load vector $q$ with dimension $[n]$ ? I am trying to get vertical displacement $w$. $$w = A^{-1}\times q$$ ...
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168 views

Continuum mechanics and effects of stress

Going to word this question a bit more straightforward than I may have before. Also, I'm trying to use baby formulas so I can grasp exactly what's going on. Object A has an elasticity of ...
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0answers
94 views

Can a wave propagate in an elastic fluid in the absence of volume forces?

A motion (wave) $\mathbf{x}: \mathcal{B}_0 \times [t_0,t_1] \to \mathcal{E}:$ such that $q-o = \mathbf{x}(p,t)=(p-o)+\mathbf{a}_0 cos(\mathbf{k}_0\cdot(p-o) - \omega_0 t)$ can propagate in an elastic ...
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1answer
229 views

Determine the tensor of contraint and deformation of a cube under compression

We have a cube under compression with dimension l1*l2*l3, is put between 2 rigid plates in the axis 1 (two plates block the deformation of the cube in thí axis), the cube is also put on a rigid plate, ...