Yield functions failure criteria for isotropic materials

A new yield function formalism is developed for isotropic materials. A spectrum of forms are inclusive to the general form that has two yield parameters. One parameter is that of a scale type involving uniform expansion or contraction of the yield function. The other is a non-dimensional shape parameter that controls the shape of the function in stress space. Thus the entire range of different behavioural types is accessed by varying a single parameter, the shape parameter. At one extreme of the behaviour is the usual Mises form involving distortional control. At the other extreme is a highly dilatant type of behaviour strongly influenced by mean normal stress. An intermediate range of behaviour is identified as being fracture controlled. The overall forms apply to the initial yielding of materials as well as to strength type behaviour where appropriate.