The novel Incremental Sheet Forming (ISF) process allows producing complex threedimensional shapes from Computer Aided Design (CAD) models without specially designed forming tools. This process thus meets a demand for small batch production and rapid prototyping of industrial shell-like structures. The formability of a metal sheet subjected to this process is generally found to be much higher compared to traditional forming processes such as stamping and deep drawing. This thesis formulates an explanation for the remarkable formability on the basis of through-thickness shearing that occurs during ISF.

While in the study of many conventional sheet forming processes through-thickness shear (TTS) can be neglected, several numerical and experimental investigations presented in this work have shown that this assumption does not hold for ISF. The finite element method, a numerical tool for solving non-linear field problems, is adopted for the simulation of ISF processes. Models of different spatial refinement, determined by the mesh density, have been investigated, using various models for the material constitutive behavior. A non-negligible TTS is indeed predicted by models with a sufficiently large mesh density. Such fine meshes also allow proper modelling of the small contact zone in ISF, as well as an accurate prediction of the forming force. On the experimental side, a direct measurement method of the overall TTS is proposed, and statistically non-zero through-thickness shear angles are observed for a low carbon steel sheet. The accuracy of these measurements is however limited, and the method itself is questionable as a defect needs to be introduced. Another experimental verification of TTS is performed from christallographic texture measurements by X-ray diffraction. The deformation texture contains evidence of TTS during the ISF process, although only in a qualitative sense.

The Marciniak-Kuczynski (MK) model framework, which assumes an imperfection (groove) in an otherwise perfectly homogeneous sheet (matrix), is a commonly used analytical tool to predict the limit of sheet formability due to the onset of localized necking. An original extension to the MK model framework is presented in this thesis in order to explicitly account for TTS, which is usually disregarded in MK analyses. This is achieved by the introduction of additional force equilibrium and geometric compatibility equations that govern the connection between matrix and groove in the MK model framework. Furthermore, in order to integrate plastic anisotropy in the extended model featuring TTS, a material reference frame available in recent literature is incorporated, as well as a particular model for anisotropic yielding that relies on virtual testing of anisotropy (Facet plastic potential), since out-of-plane anisotropy related to TTS cannot be measured experimentally.

The extended MK model shows that TTS delays the onset of localized necking in case the TTS is applied to the sheet in the same direction as the incipient necking direction. The underlying mechanism is a stress mode change within the groove towards the plane strain yield point, which brings about additional hardening that stabilizes necking. From the comparison of formability predictions between an aluminum and a low carbon steel sheet, it is also clearly seen that anisotropy influences the amount of delay in necking that is due to TTS. The occurrence of TTS in the ISF process postpones the onset of localized necking and thus contributes to the high formability that is observed.