Further consideration of a mathematical model for progressive fracture of a heterogeneous material

Abstract

Synopsis Uniaxial stress-strain curves are derived for a mathematical model designed to represent a heterogeneous material that fails in tension by progressive fracture. These results show qualitative agreement with the behaviour of real materials including mortars and concretes. The results suggest that the behaviour that occurs, after the peak stress has been achieved in a deformation-controlled test, is dependent upon the energy required to fracture the material. If this is sufficiently high, stable fracture propagation occurs. However, if the energy required for fracture is low, failure occurs by instability under reducing stress. The conditions for the occurrence of this instability are obtained in terms of the properties of the model material and the implications of this behaviour, for materials testing and the derivation of failure criteria, are briefly discussed.