Abstract
An exact solution to the problem of tension of a one-dimensional chain formed by harmonic oscillators is found, and the results obtained are used to derive the relationship for the Young’s modulus as a function of the number of particles on the scale of averaging. It is revealed that, in the case of quasi-static loading, a nonuniform temperature distribution is formed in a material. The temperature distributions are calculated for different types of loading. The dynamics of a one-dimensional chain of nonlinear oscillators interacting through the Lennard-Jones potential is investigated numerically. It is demonstrated that the dynamics is chaotic in character and leads to an ill-conditioning of the model.
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