# Tagged Questions

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.

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### Prove Poisson's Ratio is 0.5 [closed]

Poisson's ratio is the negative ratio of the transverse strain (_T) to the axial strain (_A). For an incompressible (density doesn't change), homogeneous (everything is the same molecule), isotropic (...
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### Degree of anisotropy of crystal tensors

Does there exist a scalar that can describe how anisotropic the elasticity of a crystal is? What about other tensors such as the permittivity or susceptibility? I found a Wikipedia article that was ...
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### How to define the heat current in an isotropic continuum material

I'm doing a FDTD (finite difference time domain) simulation of an isotropic continuum material. And I have several questions. How do you define the energy transferred through an isotropic continuum ...
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### Divergence of Cauchy Stress Tensor

On the wikipedia page for the Cauchy Momementum Equation, it's stated that the equation can be written as $$\rho \frac{D\,\textbf{v}}{D\,t} = \nabla \cdot \sigma + \textbf{f}$$ Where $\sigma$ is ...
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### Confusion in Euler-Bernoulli beam theory

Euler-Bernoulli beam equation is given by $$EI \frac{\mathrm d^2 u}{\mathrm d x^2} = M'(x) \\ EI \frac{\mathrm d u}{\mathrm d x} = xM'(x) + C_1$$ Where, $E$ is modulus, $I$ is second moment of area,...
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### Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation (I'...
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### How many atoms exist within a continuum body?

Materials, such as solids, liquids and gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have cracks and discontinuities. However, certain physical ...
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### Tensorial version of Hooke's law

It is well known that $${\boldsymbol F} = k {\boldsymbol x}$$ for isotropic media. Also, according to Wikipedia $$F_k = k_{jk} x_j$$ for some elastic tensor $k_{jk}$. I'm a bit confused as to how ...
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### Physics of Wrinkling: Understanding inextensibility condition

I'm reading this very cool paper on the formation of wrinkles in elastic materials. The key result of the paper is a set of scaling laws for the amplitude and wavelength of wrinkles based on the ...
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### What is the functional shape assumed by a flexible rod?

Be L a flexible rod. Say that it is very difficult to significantly stretch it, so that we can uniquely identify a point on it by a parameter $l \in [0, L]$ where $L$ is its length. Be $C$ a set of ...
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### 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? (...
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### 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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### buckling of tube - shell thickness vs. momentum of inertia optimum

is there any simple formula (perhabs semi emperical, or aproximatively derived model) for buckling of tube under axial compression load given its crossection and wall thickness? ( and naturraly ...