The following chapter provides an introduction into the description of finite (large) deformations and hence abandons the common assumption made engineering mechanics of “small” deformations. Though elastic deformations of metals are commonly small3 , a general description of deformation without this restriction makes sense for several reasons:

1. The general formalism of describing deformations without any restrictions is pointed out, thus allowing for a later quantification of what is small;

2. Materials other than metals, e.g. elastomers, may show large elastic deformations;

3. The representation allows also for the description of large inelastic deformations as it is essential in fracture mechanics or metal forming;

4. Commercial finite element codes like ABAQUS, ADINA, ANSYS, MARC provide options for large deformations, so that some insight into the underlying theory helps avoiding to use these programmes as “black boxes”, only.

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