# on 10-May-2021 (Mon)

#### Flashcard 5525573864716

Tags
#continuum-mechanics #has-images
Question
Define body, region, particle and configuration of the body "more formally".
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More formally, in continuum mechanics a body $$\mathcal B$$ is a collection of elements which can be put into one-to-one correspondence with some region $$\mathcal R$$ of Euclidean point space. An element $$p \in \mathcal B$$ is called a particle (or material point). Thus, given a body $$\mathcal B$$, there is necessarily a mapping $$\chi$$ that takes particles $$p \in \mathcal B$$ into their geometric locations $$y \in \mathcal R$$ in three-dimensional Euclidean space:

$$y = \chi(p) \quad \textrm{where} \quad p \in \mathcal B, \mathbf{y} \in \mathcal R.$$

The mapping $$\chi$$ is called a configuration of the body $$\mathcal B$$; $$\mathbf y$$ is the position occupied by the particle $$p$$ in the configuration $$\chi$$; and $$\mathcal R$$ is the region occupied by the body in the configuration $$\chi$$. Often, we write $$\mathcal R = \chi \left( \mathcal B \right)$$.

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#### Parent (intermediate) annotation

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More formally, in continuum mechanics a body $$\mathcal B$$ is a collection of elements which can be put into one-to-one correspondence with some region $$\mathcal R$$ of Euclidean point space. An element $$p \in \mathcal B$$ is called a particle (or material point). Thus, given a body $$\mathcal B$$, there is necessarily a mapping $$\chi$$ that takes particles $$p \in \mathcal B$$ into their geometric locations $$y \in \mathcal R$$ in three-dimensional Euclidean space: $$y = \chi(p) \quad \textrm{where} \quad p \in \mathcal B, \mathbf{y} \in \mathcal R.$$ The mapping $$\chi$$ is called a configuration of the body $$\mathcal B$$; $$\mathbf y$$ is the position occupied by the particle $$p$$ in the configuration $$\chi$$; and $$\mathcal R$$ is the region occupied by the body in the configuration $$\chi$$. Often, we write $$\mathcal R = \chi \left( \mathcal B \right)$$.

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