Limits of structural mechanical models – Numerical method for identification, quantification and evaluation of parasitic residual stresses induced by non-compliance with model assumptions

• Applicant: Professor Dr.-Ing. Jens Wackerfuß
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 576718078

Due to rapid progress in the field of additive manufacturing, load-bearing structures with almost any geometry and topology can now be realized. However, with the increasing geometric complexity of individual structural members - and their connections to each other - it is becoming increasingly difficult to decide where within the structure, the structural-mechanical models (beams, plates and shells) can still be used for static and dynamic analysis. And if so, with which theory? As there are no appropriate methods for this yet, the process of modeling is associated with major uncertainties. +++ Each structural-mechanical model is based on specific assumptions that relate to the displacement and/or stress field and limit the deformability of the cross-section (e.g. keeping the cross-section flat). These model assumptions are no longer fulfilled in those areas of the structure where geometric and static discontinuities occur (cross-section jumps, connections, point supports and concentrated loads or in the case of inhomogeneous, anisotropic and inelastic material behavior). The project focuses on the model assumptions of the different beam theories. In comparison, the model assumptions of the plate and shell theories are special cases and are therefore not explicitly considered. +++ The aim of the project is to develop a novel method that will make it possible for the first time to identify, quantify and evaluate the parasitic residual stresses that are induced when modeling specific beam structures due to the non-compliance with the model assumptions. In order to be able to calculate these residual stresses directly, the beam structure is considered as a FE solid model on which the individual model assumptions of the beam theory under consideration are enforced by specific constraints. Local, stress-based error indicators are derived from the calculated residual stresses (separately for each assumption). These enable: a) explicit specification of the effective ranges of all static and geometric discontinuities occurring in the structure, b) automatic selection of a beam theory suitable for modeling the beam structure under consideration and c) quantification of the influence of each individual model assumption on the local and global load-bearing behavior of a beam structure. The focus is on beam-type structures with arbitrary geometry and topology as well as arbitrary bearing, load and deformation scenarios, taking into account geometric and material non-linearities. +++ With the error indicators introduced in the project, it is possible for the first time to validate the modeling process on the basis of quantitative criteria. In addition, these indicators also make an important contribution to future research activities in the field of adaptive methods or in the coupling of structural models with continuum models.

• DFG Programme: Research Grants