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4 views

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 ...
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1answer
30 views

Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
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0answers
11 views

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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1answer
36 views

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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1answer
63 views

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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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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0answers
61 views

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 ...
2
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1answer
35 views

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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0answers
7 views

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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0answers
24 views

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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0answers
29 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 ...
0
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1answer
177 views

Jaumann deviatoric stress rate

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}} = ...
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2answers
73 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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2answers
96 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 ...
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1answer
117 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 ...
2
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1answer
476 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 ...
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1answer
484 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 ...
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2answers
253 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 ...
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0answers
30 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 ...
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2answers
210 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 ...
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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 ...
2
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2answers
264 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 ...
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0answers
108 views

Area moment motivation

I have some intuition about the (second) moment of inertia, and there is some motivation to define this concept if we think about the $KE$ of a rotating body or the torque $\tau$ applied, for example, ...
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2answers
197 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 $k_{ij}$ ...
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0answers
33 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 ...
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3answers
2k 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 ...
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0answers
67 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 ...
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2answers
429 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? ...
2
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1answer
410 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 ...
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0answers
166 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 ...
0
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1answer
427 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 + ...
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0answers
38 views

What is the criterion of stability of thick-walled spherical shell?

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 $−$ ...
2
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1answer
126 views

Out-of-Plane Phonons

I am trying to derive the out-of-plane phonon dispersion relation for a membrane. As far as I can tell, one of the simplest ways to do so is with a Lagrangian of the form: ...
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2answers
220 views

Potential energy of an infinitesimal length of elastic rod

I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area A. The picture shown below is an element of the rod that has ...
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3answers
474 views

Continuum limit for solid mechanics

Is there a rigorous derivation of the limits for continuum properties in solid mechanics? For instance, the stress-strain relationship may be linear for large samples (the slope being the Young's ...
2
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1answer
1k views

Limits of Poisson's ratio in isotropic solid

For an isotropic solid, Poisson's ratio can be expressed in terms of stiffness constants as: $$\sigma = \frac{c_{11} - 2c_{44}}{2c_{11} - 2c_{44}}$$ Alternatively we may express Poisson's ratio in ...
2
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0answers
54 views

Simple model of fiber interaction for pressurized braided tubes

I am trying the understand the failure modes of braided tubes containing high pressure gas. Here is an example of such a braid with a variable radius: The tubes have an internal liner for sealing ...
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2answers
2k views

Compression and expansion

Why is it that solids on compression [As in striking a hammer etc.] heat up, but liquids and gases on compression [Pressurizing liquids causes them to freeze or gases to liquify] cool down? Can ...
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0answers
108 views

Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ...
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1answer
116 views

What is the $n$ in the formula in Solid Mechanics? [closed]

The formula is about the critical force for the elastic beam that is supported by its joints: $$ P_{cr} ~=~ n^2 \pi^2 \frac{EI}{ L^2} $$ It should be based on the book Parnes - Solid ...
0
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1answer
390 views

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 ...
2
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0answers
391 views

Mechanics of Materials (pressure and temperature)

A solid right cylinder of rock core is surrounded by four rods made of mild steel (all-thread rods). The rods are placed equidistantly around the core in a square formation. The tops and bottoms of ...
0
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1answer
124 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. ...
3
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2answers
509 views

Determination of mass density distribution of an object

This is a follow-up to a previous question How can you weigh your own head in an accurate way?. My purpose is not to restart the flurry of more or less humorous jokes (which are not such a bad thing ...
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1answer
231 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 ...
2
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1answer
40 views

Organs & Oscillations: An Analysis on the Temperature Dynamics of Solids

Does temperature have an influence on the frequency of an oscillating organ pipe?
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0answers
2k views

Materials with Zero Poisson Ratio

Poisson's ratio is defined as negative ratio between transverse and axial strain. So, a material with zero poisson ratio must necessarily exhibit no transverse strain. After checking the wikipedia, ...
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1answer
97 views

Modeling elastic moduli as a continuous function in space for a single solid material

I've read a number of solid mechanics papers where a single material is modeled with constant elastic moduli (lame parameters $\lambda$, $\mu$). I've also seen composite materials modeled with ...
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2answers
689 views

Interpretation of lame parameters in solid mechanics

I think I have a pretty good understanding of the physical interpretation of young's modulus $E$ and poisson ratio $\nu$ in solid mechanics. However, I often find in mathematical papers that the ...