On the Decomposition of the Deformation Gradient in Plasticity

Starting from the premise that the distances between points are the only measurable quantities, plasticity is placed into the more general context of the continua with a two-scale representation of the deformation. The Kröner-Lee multiplicative decomposition of the deformation gradient comes out to be incompatible with the geometry of such continua, while the Clifton multiplicative decomposition is compatible but geometrically irrelevant. On the contrary, an approximation theorem taken from the theory of structured deformations provides a measure-theoretic justification for the additive decomposition. It also leads to a decomposition of the strain energy into the sum of two parts, one for each term of the decomposition of the deformation.