The Use of Peridynamic Virtual Fibres to Simulate Yielding and Brittle Fracture

Journal article, 2021

The forces in the ‘arms’ joining the particles in a peridynamic analysis depend upon the state of stress in the equivalent continuum and the orientation, length and density of the arms. Short and long arms carry less force than medium length arms as controlled by the weighting kernel. We introduce an intermediate step of imagining a mat of long fibres in which the fibre forces only depend upon the stress, the fibre orientation and the length of fibres per unit volume without the added complexity of the arm lengths. The effect of the arm lengths can then be considered as a separate exercise, which does not involve the continuum properties. The arm length is proportional to size of the particles and the separation of length from the state of stress allows for modelling of variable particle density in the discretisation of a problem domain, which enables computationally efficient accurate analysis. We then introduce the concept of arm elongation to fracture in order to model surface energy in fracture mechanics. This means that shorter arms have a larger strain to fracture than longer arms. The numerical implementation demonstrates that this produces a fracture stress that is inversely proportional to the square root of the crack length as predicted by the Griffith theory.