Interfaces, such as those between polymers and metals, often provide a decisive definition of the macroscopic behaviour of a composite material. Knowledge of their properties is therefore vital for this collaborative research group, SFB. For this reason, a material model will be developed within project B3, in order to demonstrate the mechanical behaviour of these interfaces by taking their underlying atomic structure into account. This model shall depict the macroscopic mechanical interactions via so-called traction-displacement-laws (for example, stress vs. crack-opening relationship). Although these laws are already widely applied today, their connection with the atomic structure of an observed material has so far been dealt with inadequately.
A macroscopic description of interfaces based on atomistic models shows significant advantages over conventional "ad hoc" methods, i.e. that the macroscopic mechanical properties may specifically be improved and/or optimised by, for example, changing their charge density. Hence the project B3 pursues a multi-scale approach that connects atomic and macroscopic models by means of the following 3 key schemes:
Prediction of interface properties via density functional theory
Macroscopic modeling of interfaces via traction-displacement laws (cohesive zone models [1], [2])
Coupling of the different models using homogenisation methods
The ab-initio based modeling enables the quantitative modeling of mechanical properties as a basis for continuum mechanical simulation. The quantum mechanical method is not limited to certain classes of systems. Hence it can be used to obtain the material parameters for virtually all types of materials relevant to the SFB. The macroscopic modeling of interfaces will be carried out via traction-displacement laws (cohesive zone models). Important features of these potential-based models are variational and thermodynamical consistency. Both of these classes of models for the description of interfaces exhibit characteristic advantages. Suitable homogenisation strategies shall be developed in order to couple the scales of density functional theory and of the macroscopic models of continuum mechanics both for reversible and irreversible processes.
The above sketched multi-scale approach combining the characteristic advantages of atomistic and macroscopic methods is illustrated in the following figure.
References
[1] J. Mosler, I. Scheider: A thermodynamically and variationally consistent class of damage-type cohesive models, J. Mech. Phys. Solids 59 (2011) 1647-1668.
[2] J. Mosler, L. Stankovic and R. Radulovic: Efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach, Int. J. Numer. Meth. Eng. (2011) in press, DOI: 10.1002/nme.3210.
[3] J. H. Rose, J. R. Smith and J. Ferrante: Universal features of bonding in metals, Phys. Rev. B. 28 (1983) 1835-1845.
