Stack Exchange Network

Stack Exchange network consists of 174 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 [elasticity]

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.

0
votes
2answers
27 views

Elastic potential energy and springs

The formula for elastic potential energy(for a spring) has been derived by assuming the following things: 1.Work done by a deforming force on a spring from a relaxed state (state where spring is not ...
0
votes
0answers
13 views

Kelvin solid and deformation in transverse direction with Poisson ratio

A Kelvin-Voigt material is a material with such a behavior : I'm wondering if there is a way to model in a similar way the deformation in the transverse directions $y$. Meaning we have for the ...
0
votes
1answer
30 views

Statics and dynamics in elasticity : how to add time in elasticity

In elasticity, there is are static relations of the form $R(\sigma,\epsilon)=0$. In fluid dynamics, there is a dynamics relation with the conservation of momentum leading to Navier-Stokes equation. ...
1
vote
0answers
21 views

impossible Poisson's ratio of Lennard-Jones potential type solid (cubic cristal for example), or any potential depending on $r$

We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus. Let's assume we have a ...
1
vote
1answer
37 views

How can Young modulus depend on the geometry of the item & Lennard Jones (question related to an older one)

In the question Young's modulus and geometry of test material, the answer was that it cannot play any role. Nonetheless, for the Lennard-Jones solid, in many places the Young modulus is given as : ...
0
votes
1answer
31 views

Relation between strain and velocity

The strain tensor writes $\epsilon_{ij}=\frac{1}{2}\Big(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_i}{\partial x_j}\Big)$ with $u_i$ the displacement in the $i$ direction. Then $\frac{\...
-2
votes
3answers
39 views

Elongation of rod [closed]

If a force is applied on a unconstrained body lying on a smooth floor ,will it elongate? My thoughts-as force is applied on body ,it moves with some acceleration,but as it is not constrained it will ...
1
vote
2answers
68 views

Pressure on a compressible solid, dynamics of the relaxation

I have a sphere made of a solid of bulk compressibility B, and of volumic mass $\rho_0$. The pressure around that sphere is $P_0$. At time $t=0$, we apply a pressure on the sphere $P=P_0+\Delta P$. ...
0
votes
0answers
22 views

'It can be shown that there is always an orientation of the axes for which the shear components become zero'. Why?

Picked this up from Introduction to the properties of condensed matter by Barber, Chapter 2.
0
votes
0answers
27 views

Can an absolutely unelastic object move faster than light? [duplicate]

When i emit a physical impulse on an object, the time it takes for this object to react to the impulse decreases the higher its elasticity is - but wouldnt that mean that if an object has an ...
0
votes
0answers
13 views

Displacement of Point Particle in Infinite Linear Elastic Medium Subjected to Steady-State Force

I am attempting to develop an equation that will model the displacement of an infinitesimally-small point particle embedded in a linear elastic medium of infinite extent when a steady-state force is ...
0
votes
1answer
12 views

determine the shear stress and bending moment of the next axis

I have problems to raise the equations. They could recommend me a text to be able to solve it.
0
votes
0answers
37 views

How does hardening / tempering steel affect it's stress-strain curve?

Does hardening / tempering steel only scale it's stress-strain diagram horizontally (meaning it takes more strain to achieve the same stress) or does it also change the shape of the diagram (for ...
0
votes
2answers
28 views

What decides ductility of a substance- youngs modulus or the plastic limit of the substance? [closed]

Given two materials A and B such that a has higher young modulus as well as plastic limit than B , which of the two is more ductile?
0
votes
1answer
48 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 ...
3
votes
1answer
44 views

Hooke's Law and Overstretched Springs

Recently been working with Hooke's Law at university. My experience of real springs tells me that stretching to a certain point causes the spring to lose "springiness". (Not sure if "elasticity" is ...
0
votes
2answers
67 views

Terminology for how bendable an object is and what affects the bendable-ness of an object

I was wondering what the term is for how bendable an object is. Also, does this feature vary depending on the thickness of the object? Say, for example, I want to know how bendable a ruler is. Does ...
3
votes
1answer
84 views

(I-beam vs rectangular beam) Which sword blade cross section is less likely to break?

Original question Assumption: i made several swords with different cross sections (lenticular, single broad fuller as in viking swords, diamond, hollow ground diamond) the blades are made using the ...
0
votes
1answer
33 views

Relationship between strain energy function and strain or stress

How one can get the strain or stress from the strain energy function ? And if one cannot do it, what is the use of that function ?
1
vote
2answers
42 views

Is the Young's modulus the same for compressive and tensile test?

I want to know the Young's modulus for a compressive test, but I have just a tensile test. Are they of the same value?
2
votes
0answers
47 views

Fixing the Poisson equation to match the deformation of elastic sheet with experimental observation

I am working on the calculation of the deformation of a circular elastic sheet with radius $R=1.2~m$ when a plate with mass $M$ and radius $r_0 = 4~cm$ is sitting in the center of the sheet. I used ...
1
vote
1answer
51 views

Helfrich energy derivation

The Helfrich elastic energy of membranes is given by $F = \int dS (\kappa H^2 + \kappa_G K)$ where $H$ is the mean curvature and $\kappa_G$ is the Gaussian curvature. The derivation in the original ...
1
vote
2answers
52 views

Collision between two non-deformable objects

Let say we have a non-deformable object and we release it into free fall and it hits the non-deformable floor. What would happen? Here is the way I think. Since the floor and the object are both ...
1
vote
0answers
14 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 ...
0
votes
2answers
56 views

Can I use $v_{final}=0$ when I calculate impulsive force?

If a 1kg ball strikes a wall with 10m/s and it rebounds with 10m/s, the time of impact being 0.2s, what is the impulsive force? I know that the initial velocity is 10m/s but can I state that the final ...
1
vote
2answers
61 views

Is $\sin\left[2\alpha\right]\cos\left[2\alpha\right]\ge0$ a valid restriction on the angles of the principal stresses in 2D elasticity?

This question pertains to Elasticity: Tensor, Dyadic, and Engineering Approaches By: Pei Chi Chou, Nicholas J. Pagano, Section 1.4. The objective under discussion is to find the directions of ...
0
votes
2answers
42 views

Spring strain vs fractional extension

How do I show that the strain tensor $$\epsilon_{ij}=\partial_i u_j + \partial_j u_i$$ in the case of a one-dimensional spring is reduced to $$\epsilon= \frac{x-L}{L},$$ where L is the initial ...
1
vote
2answers
42 views

Does the resonance frequency of a cantilever beam depend on whether it is bending in-plane?

What is the in-plane resonance frequency equation for a single-beam cantilever of rectangular cross-section that is fixed on one end and has a mass M attached to the other end? Below are the only ...
0
votes
2answers
54 views

Why the resultant spring constant different in the following two cases?

In these two cases in the first case my book The Physics Of Waves And Oscillations by NK Bajaj says: That the restoring force exerted ...
3
votes
3answers
85 views

Why does different part of a spring having mass expand proportional to their distance while the spring has some mass hanged in the bottom?

Why do different parts of a massive spring expand proportional to their distance while the spring has some mass hung on the bottom which is comparably very less than the mass of the spring? If we take ...
1
vote
1answer
40 views

Motion along length of a spring [closed]

What's relation between velocity of each part of a massive spring undergoing Simple Harmonic Motion.
1
vote
0answers
23 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)...
0
votes
2answers
80 views

Stress/strain within an object experiencing a single applied force

If I push an object in space, will any strain/stress happen within the object, though there is only 1 force rather than a pair of opposite forces on the object? Can be any (even if trivial) stress/...
0
votes
1answer
48 views

Spring Constant of Two-Sided Fixed Beam [closed]

Let's suppose I have a two-sided fixed beam: ...and I want to find the equivalent spring constant... can I do the following: I know that the maximum deflection (at the center is): $$\delta =\frac{...
-1
votes
2answers
89 views

Oscillation of elastic rope hanging from the ceiling

I have to explore the problem of oscillations of an elastic rope hanging from the ceiling, which can move both in vertical and horizontal direction. I'm planing to solve this using a finite ...
0
votes
0answers
19 views

Euler Elastica with a bent rod

Here is a thought exercise. What would happen if one were to do Euler's Elastica with a naturally bent rod, i.e. one already with a spontaneous curvature? Consider two cases. First, put in on the ...
5
votes
2answers
44 views

Shape of a compressed wristband

What is the curve of the top part of this wristband after I squish the two ends closer? It's a curve of fixed length with given start $(x_1, 0)$ and end $(x_2, 0)$, and zero slope at these points, ...
1
vote
1answer
37 views

Strain compatibility

From this link, strain compatibility for 2D problem with strains as $$ \varepsilon_{11} = \cfrac{\partial u_1}{\partial x_1} ~;~~ \varepsilon_{12} = \cfrac{1}{2}\left[\cfrac{\partial u_{1}}{\...
0
votes
1answer
17 views

Are the curvature Frank elastic constants of the liquid crystal the no-zero elements of the 6x6 elastic (stiffness) matrix?

I was reading Landau's book on elasticity theory, and it raised this doubt. Can anyone help me?
2
votes
2answers
41 views

Calculating Elastic Potential Energy of a Stretched Sheet

Essentially, I'm trying to determine the amount of elastic potential energy stored in a thin, elastic sheet that has gone under some type of stretching (ex. A flag of stretchy fabric waving in the ...
1
vote
2answers
303 views

Conservation of energy when dropping a ball [duplicate]

If we drop a bowling ball from one meter above the earth's surface, we are converting its gravitational potential energy to kinetic energy. When it hits the floor, it transfers its kinetic energy to ...
0
votes
0answers
107 views

Shearing strain - difference between gamma-xy and epsilon-xy

What is the difference between $\epsilon$$_{xy}$ and $\gamma$$_{xy}$? How does the relation $\epsilon$$_{xy}$ = $\gamma$$_{xy}$/2 comes?
1
vote
1answer
64 views

Landau and Lifshitz argument for symmetry of stress tensor

In Landau and Lifshitz's book on the theory of elasticity (vol 7, theoretical physics series), specifically section 2 of the first chapter, the authors present an argument for justifying the symmetry ...
2
votes
1answer
87 views

Why do materials obey Hooke's law? [duplicate]

Why do materials extend proportionally to the force exerted on them (Hooke's law)? I thought that when materials are compressed or extended under force, their atoms become closer or further apart; ...
2
votes
4answers
178 views

Where is the Elastic Strain Energy per Actual Volume Gone?

I have a probably real stupid question, but I still can not wrap my head around it. The change in inner energy per unit volume $v$ of the actual state of a stressed crystal is given by the well ...
-3
votes
1answer
33 views

How to stack padding materials to pad an edge [closed]

This is about how to combine materials of various elastic and deformation properties as a stack to show different properties as a stack. A cardboard box has two holes punched in the side of the box ...
0
votes
0answers
19 views

Calculation of Young's modulus for a three-layer stacked material

I am currently working on three-layer stacked material and want to calculate the effective Young's modulus. The spring constant of the three layer material would need the effective Young's modulus ...
0
votes
1answer
139 views

Change of system of coordinates for the stress matrix

I have a stress matrix in cartesian coordinates : $\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix}$. How can I convert it to spherical coordinates ?
1
vote
1answer
53 views

Which Formula for the Internal Elastic Energy is Correct?

I am confused by the internal energy of a crystal. Lets say I have a isotropically stressed crystal. The total differential of the internal energy per unit volume V is defined as $$du = \sigma d\...
2
votes
2answers
187 views

Why a short rope takes more load than a longer rope?

The captain of a ship told me that it should be avoided to put a long rope next to a short one because the short rope takes most of the load and the long becomes relatively inactive, although both ...