A co-rotational floating node finite element for geometric non-linear fracture modelling of composite structures

Abstract

Fibre-reinforced composites have become increasingly attractive for many engineering applicationsin the last decades. A very interesting aspect of these materials is that their mechanical properties canbe tailored for optimum strength and stiffness by controlling the orientation of the fibers embeddedin the matrix material. Composites are characterized by high strength properties, strong corrosionresistance, improved damage tolerance and can lead to considerable weight and cost reduction whencompared to their metallic counterparts. However, accurate modelling of damage in composites is stillan active research topic, as their progressive failure involves the interaction of various intra- and inter-laminar damage mechanisms, which often lead to complex fracture paths. To this regard, the FloatingNode Method (FNM) proved to be particularly suited for the modelling of complex cracking scenarioswithin a finite element. However, its use has so far been limited to geometric linear analyses, wheredeformations and rotations are small enough and the conventional linear FEM formulation is used. Thisthesis work investigates the modelling of geometric non-linear fracture problems in composites usingthe Floating Node Method. A co-rotational approach is proposed as a convenient, conceptually simpleway to include geometric non-linear effects in problems characterized by large rotations but smalldeformations. This approach allows re-use of the conventional linear FEM formulation by separatingrigid body and purely deformational motions at the element level. The co-rotational procedure, firstimplemented and validated on a linear solid brick element, is subsequently applied to the FloatingNode (FN) element. Finally, a demonstration of the element’s potential in capturing geometric non-linear effects is offered, addressing the modelling of crush and impact loading on composite laminates.