Implicit gradient elasticity based on laplacians of stress and strain

• Applicant: Professor Dr.-Ing. Charalampos Tsakmakis
• Subject Area: Mechanics
• Term: from 2016 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 323258122

Real materials exhibit a substructure (microstructure) which can be addressed by characteristic material internal length. The microstructure can strongly effect the macroscopic response in many applications. Such phenomena have been observed in statics in form of a stiffening effect in the material response and in dynamics in form of non-classical dispersion relations. The examples cover, among others, in the microscopic range thin films, nanotubes, micro sensors,adhesive joints etc. and in the macroscopic range the response of earth plates, lining of tunnels in soil, capillarity effects, etc. . The observed phenomena can be addressed adequately by constitutive laws of gradient elasticity. In the first part of this project it has been shown that models of so-called implicit gradient elasticity can be derived either as particular cases of micromorphic elasticity or within the framework of non-conventional thermodynamics. In the second part we continue the investigations about implicit gradient elasticity by modelling poroelastic material behaviour combined with implicit gradient elasticity and by discussing several examples. The examples concern problems in statics (straight prismatic bar under static uniaxial tensile loading, bending of Bernoulli-beams, study of plane circular inhomogeneity with imperfect interface, FE-analysis of a crackin a thin film) and in dynamics (propagation of plane waves, reflection and scattering of waves, causality of the models). These problems will help to compare implicit gradient elasticity with standard Gradient elasticity and with classical elasticity.

• DFG Programme: Research Grants