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This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of classical tensors, this approach allows gathering the usual mechanical entities - mass, energy, force, moment, stresses, linear and angular momentum - in a single tensor. Starting with the basic subjects, and continuing through to the most advanced topics, the author's presentation is progressive, inductive and bottom-up. He begins with the concept of an affine tensor, a natural extension of classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics - torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.
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Galilean and relativistic mechanics. In the follow-up, we shall detail only the applications to classical mechanics and thermodynamics.
As a valuable reference source, this book presents a detailed and complete ...
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