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.
Questions tagged [continuum-mechanics]
819 questions
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What is the material frame indifference/material objectivity principle exactly saying?
In classical continuum mechanics, equations of motion (balance equations) are Galilean invariant, i.e. they have the same form in all inertial reference frames.
The fact that these reference frames are inertial means that transformations between…
z.v.
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Explain $\rho_{0}\dot{e} - \bf{P}^{T} : \bf{\dot{F}}+\nabla_{0} \cdot \bf{q} -\rho_{0}S = 0$
I am trying to understand the balance of energy -law from continuum mechanics, fourth law here. Could someone break this a bit to help me understand it? From chemistry, I can recall $$dU = \partial Q + \partial W$$ where $U$ is the internal energy,…
hhh
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Saint Venant–Kirchhoff model
Why is the second Piola–Kirchhoff stress tensor $S$ equal to $\lambda$ $tr$($E$) $I$ $+$ $2$ $\mu$ $E$ $?$ Is there a derivation of it? By other means, from where does the assumption of strain energy density come from? Thank you.
Source of…
user134613
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Continuum mechanics - deformation gradient confusion
I have seen several different approaches to describing continuum mechanics that are all very similar, yet some differences (that I see, not sure if they are true) keep confusing me.
The picture that makes most sense to me is defining points living…
Hello
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Derivative of deformation gradient with respect to Green-Lagrangian strain?
For hyperelastic material, the elastic energy $\Psi $ is related to the deformation gradient $F$ and other internal variables (e.g. temperature $ \theta$).
However, in many literatures (including Malvern's and Belytchko's) the derivatives…
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Golf ball impact
A golf ball is said to be "compressed" when hit by a golf club and makes a characteristic "thwack-hiss" sound coming off of the club when impacted by professional golfers (whose impact conditions have been optimized). My question is, what changes…
Chris L
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Superior attachment of Möbius strip
In this DIY project, the Möbius strip is used to make a spill-proof coffee cup carrier. The author uses a Möbius strip as the handle of this carrier and says
If you attach a Möbius strip to an object, say a bowling pin, and
swing it around your…
shamisen
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Why infinitesimally close?
From AN INTRODUCTION TO CONTINUUM MECHANICS by J.N.REDDY
A rigid-body motion is one in which all material particles of the continuum
$\mathcal{B}$ undergo the same linear and angular displacements. However, a deformable body is one in which the…
lucas
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Basic difference in viscoplasticity and elastoplasticity
I am trying to create a Finite element based code to solve dynamic Plasticity problem. I recently started reading about Plasticity and I have come to understand that Rate-independent plasticity is also called elasto-plasticity and Rate-dependent…
CRG
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Is deviatoric strain associated with thermal effects?
Does temperature have any effects on deviatoric strain for a linearly elastic isotropic material?
gyeox29ns
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Uniqueness of a stress (only) boundary value problem
A static problem in linear elasticity is typically written as the following
boundary value problem:
find $\boldsymbol u$ and $\boldsymbol \sigma$ such that:
$\text{div} \boldsymbol \sigma + \boldsymbol f = \boldsymbol 0$ in $\Omega$,
$\boldsymbol…
KevMoriarty
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Can $U_{ij}$ or $v_{ij}$ in continuum mechanics be negative?
In continuum mechanics, we have the deformation gradient $\mathbf F$ to be:
$$d\mathbf x = \mathbf F d \mathbf X$$
And then, we do a polar decomposition (A good reference here would be http://www.continuummechanics.org/cm/polardecomposition.html),…
Shawn Wang
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Does a uniform loading of an elastic half space result in a uniaxial stress state or a uniaxial strain state?
Suppose for instance a soil is loaded by a building over an area of length $L$ (load is in the $z$ direction). In the neighborhood of a point at depth $h$, $h \ll,L$, in the soil under the loaded area, do we expect a uniform uniaxial $\sigma_{zz}$…
user8736288
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Why does the zero divergence of displacement field mean that a body's volume is conserved?
Why is the zero divergence of displacement field means that a body's volume is conserved?
I got this question while reading the research paper "ON THE DERIVATION OF ELECTRIC BODY FORCE,COUPLE AND POWER IN AN ELECTROELASTIC BODY" Author: Jiashi…
user134613
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What is the difference between the balance of linear momentum and Cauchys momentum equation?
I am currently working on a presentation about the Cauchy's momentum equation or (also known as?) Cauchy's first law. I need to base my presentation on an equation given by my professor: $ \rho \ddot{u} - \nabla \cdot P = f$. Where $\rho$ is the…
Ole
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