Abstract of a proposal for an FWF project entitled:
Computational Structural Mechanics of Strain Gradient Theory
Applicant: Dr. Martin Lederer
Theoretical framework
In recent years, strain gradient theory has attracted increasing interest for two reasons. Firstly, the theory includes an internal material length scale imposing a mechanical size effect. Secondly, at least some formulations of strain gradient theory have the capability of removing stress singularities, which appear in the conventional theory of fracture mechanics. This leads to a regularizing effect on continuum mechanics.
Objectives and hypotheses
The main objective of the intended reformulation of strain gradient theory is to improve the agreement between theoretical predictions and experimental results. In this context, the length scale parameters of the theory are of major importance. When the dimension of a small scaled sample approaches the intrinsic length scale of the theory, pronounced size effects of mechanical properties occur. However, the length scale parameters reported by different scientists are not always concordant. Working groups focusing on plane wave deformations derive length scale parameters in the nm range. On the other hand, length scale parameters obtained from numerical fits to bending experiments are in the range of µm. The here proposed project aims at the solution of this problem by considering a coupling term between strains and strain gradients, which is added to the elastic energy of the system. In conclusion, one obtains a theoretical formulation, which is in accordance with either deformation mode.
Approach and methods
This project also attempts to improve the numerical methods, which are used to implement strain gradient theory in Finite Element software. A novel formulation of mixed Finite Elements based on sequential interpolation will be proposed. Material parameters shall be obtained from numerical fits to experimental data. For this purpose, bending experiments with micro-cantilever beams will be conducted in cooperation with the Erich Schmid Institute (Leoben). Furthermore, experiments of fatigue notch sensitivity will be performed at TU Wien.
Level of originality and innovation
The use of sequential interpolation in context with mixed Finite Elements is a new method proposed by the applicant of this project. Furthermore, the reformulation of strain gradient theory explained in the full description of the project is a novelty.
Researchers: Dr. Martin Lederer (TU Wien), Dr. Mitra Delshadmanesh (TU Wien)
National Cooperation Partner: Priv. Doz. Dr. Megan Cordill (Erich Schmid Institute)
