These offer us a technique for linking length scales so that we can use physically based models of the mechanics of materials embedded within a conventional finite element package. They also offer the possibility of linking mechanical damage to changes in thermal conductivity and permeability. Professor Andrey Jivkov is leading these mathematical and scientific developments.
The projects include revisiting:
- micro-polar mechanics in the context of distributed cracking in rocks, Qingrong Xiong.
- plasticity in metals, Craig Morrison.
- cleavage fracture in steels, Andrew Abu-Muharib.
The work was carried out on multi-scale modelling of fracture to extend our earlier studies on local approaches to cleavage, ductile void nucleation, growth and coalescence. Again, the basis of the approach is the hybridisation of the non-linear finite element method with cellular automata. The finite element solution deals with the continuum response of the structure and the cellular automata determine the local, length scale dependent state of the material; that is whether it has cracked or not. We are currently integrating the procedures for performing these fracture simulations into Code_Aster.
Another example of blending analytical and numerical tools is the work of Rolls Royce supported EngD student supervised by Dr John Francis. The Green’s functions was used to model the heat source during narrow gap TIG welding, where the conventional Goldak heat source is inappropriate. The work will progress to integrating the Green’s function into a finite element model to provide better simulations of residual stresses and component distortion for this welding technique.