Nanomechanical modeling of materials with defects and microstructure using gradient theories

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The aim of the current project is the further systematic development of gradient theories and their concepts, for the efficient modeling of materials with defects and microstructure at small scales, obtained in the first part of the project (sign removed). Materials with defects and microstructure play a fundamental role in materials science, engineering science, solid state physics, and nanomechanics. For this purpose, generalized continuum models should be developed and enhanced in order to describe physically meaningful and mathematically correct the behavior of such materials at small scales. The main focus lies on novel materials such as "smart materials", "advanced materials" or "hybrid materials". The aim is to investigate defects (dislocations, point defects, cracks) and the regularization behavior of generalized continuum theories (gradient elasticity theory, nonlocal elasticity theory, nonlocal gradient elasticity theory) for such promising materials. An important part of the project are modern continuum theories with internal characteristic lengths (such as gradient theories and nonlocal theories) as well as generalized continuum theories for new materials (quasicrystals) and their connection to atomistics. In particular, the modeling of quasicrystals by means of a gradient elasticity theory will be developed. In addition, a gradient electroelasticity theory including important effects like flexoelectricity and nano-piezoelectricity will be developed. Using analytical and numerical methods, predictions are to be made, which can be checked by experiments and simulations (in nanomechanics and advanced materials) and used as benchmark tests for numerical codes. Therefore, the project will provide an important contribution to the modeling of materials with defects and microstructure using enhanced gradient theories.