On the finite element prediction of damage growth and fracture initiation in finitely deforming ductile materials Original Research Article

This paper discusses some aspects of the finite element prediction of damage growth and fracture initiation in finitely deforming ductile solids. The material presented is of particular relevance to the simulation of industrial metal forming operations characterised by the presence of extreme deformations and strains, often resulting in localised material deterioration with possible fracture nucleation and growth. In this context, we focus on the crucial issues of constitutive modelling, low order finite element technology for near-incompressibility and adaptive mesh refinement. Constitutive modelling is treated within the framework of continuum damage mechanics. The effect of micro-crack closure, which may dramatically decrease the rate of damage growth under compression, is incorporated and its computational implementation is discussed. The use of low order elements in the presence of high nearly-isochoric plastic strains is addressed with the introduction of a methodology whereby the volumetric constraint is enforced over patches of simplex elements. This allows the effective use of simplex tetrahedra––for which intricate contact conditions as well as mesh generation over complex evolving geometries can be easily treated––without the volumetric locking typically associated with conventional low order displacement-based elements. With the aim of achieving an effective and robust adaptive strategy for this class of problems, it is important to design a damage-based error indicator which represents the essential features of the physical phenomena under consideration. The underlying idea is to correlate the adaptive procedure with the failure mechanism. The effectiveness of the resulting framework is demonstrated by the solution of relevant problems.