Microscopic approaches to the nonlinear mechanics of driven defect-rich crystals

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We will investigate the elastic and plastic properties of hard and soft matter crystals in the nonlinear and non-equilibrium regime for large stresses and large deformations. Bringing together three research groups, allows us to consider three different complementary approaches starting from microscopic principles in order to calculate elastic and transport coefficients of these systems and to derive the macroscopic equations for elastic, plastic, and transport phenomena in defective crystals. These approaches are (1) statistical mechanics concepts with projection operators, (2) classical density functional theory, and (3) efficient computer simulations. It is well known that the elastic and plastic properties are strongly influenced by dislocations which are topological defects of the crystal lattice and are highly mobile. However, less is known about the effect on elasticity and transport arising frompoint defects which do not change the lattice structure and which correspond to vacancies, interstitial particles, or several particles on a single lattice site. While on a macroscopic level standard elastic theories describe seven modes (sound waves and diffusive heat transport), two seminal works by Martin, Parodi, and Pershan and by Fleming and Cohen have shown already more than forty years ago that there must be an eighth mode which describes the diffusion of point defects. Little is known about this eighth mode and its coupling to strains on the microscopic level. Recent interest results from the discovery of crystals with giant defect densities, where each particle experiences on average close to one defect among its neighbors. For this reason, our project will mainly focus on point defects and elaborate a microscopic understanding for their diffusive motion and their influence on the elastic and plastic properties of the material in the nonlinear and the non-equilibrium regime. We will especially consider soft crystalline materials and cluster crystals which are defect-rich and are expected to show strong effects.