Some necessary implications for the time-discrete integration of finite deformations will be discussed together with particular schemes, when the geometrical structure o [...]

The paper raises a question whether the logarithmic time derivative, expressed in specific coordinate system, is the Zaremba-Jaumann time derivative, and if not why. In [...]

Stepwise integration of a finitely deformed body is based on an incremental kinematics of a medium under initial stress / strain conditions. As usual in continuum mechan [...]

Solution of finite deformation problems is sought in the space of all deformation tensor fields. Representation of a deformation process here as a trajectory makes us p [...]

The paper discusses the logarithmic strain in one dimension (1D) from the geometrical point of view to highlight the nature of problems when generalizing it to more dimen [...]

On the space of all symmetric positive definite matrices (the space of deformation tensor fields) one can introduce a Riemannian geometry, so that the matrix exponentia [...]

Large deformations are exposed from a viewpoint of differential geometry. This enables to formulate kinematics of continua in a compact, coordinate-free way with clear ge [...]