Mathematical modelling of mechanics of nonsingular defects in elastic and electro-elastic materials at small scales using gradient-enhanced continuum field theories

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The study of modern materials like smart, advanced or novel materials is of great importance in materials and engineering sciences, applied mathematics, solid state physics and nanomechanics receiving continuously growing interest due to their numerous applications in new and emerging technologies. To the main characteristics of such materials belong their complex microstructure, electro-elastic coupling effects as well as the presence of defects. For the physically realistic description of various phenomena occurring in these materials, generalized continuum field theories of higher-order are required, since they are able to capture phenomena at small scales where classical continuum theories are not valid leading to unphysical singularities and for this reason they are significant. On the other hand, the complexity of the mathematical modelling is increased due to the higher-order terms demanding the use of rigorous mathematical methods. The aim of the project is providing an efficient mathematical modelling of mechanics of materials with defects, microstructure and electro-elastic coupling effects at small scales developing systematically, extending and assessing, if necessary, gradient-enhanced continuum field theories. The focus of this project lies on gradient-enhanced elasticity, electroelasticity and plasticity continuum theories with internal characteristic lengths important for the description of effects such as flexoelectricity and nanopiezoelectricity, which do not appear in classical theories. This project will provide a unique, innovative and important contribution to the modelling of mechanics of materials at small scales where defects, the underlying microstructure and electro-elastic coupling effects play an essential role, using and developing gradient-enhanced continuum field theories valid down to the Ångström-scale with promising applications in nanotechnology.