C h a p t e r 2
The paper examines alternative continuum descriptions of the degradation of strength. In particular we study recent proposals to regularize local strain-softening descriptions which introduce both spatial as well as temporal discontinuities in the solution domain. The formation of spatial discontinuity surfaces is normally accompanied by loss of ellipticity, which in turn is responsible for ill-posedness of the underlying initial boundary value problem. This results in extreme sensitivity of numerical solutions with regard to mesh size, and especially with regard to mesh orientation. Three regularization concepts will be interrogated, whether or not the formation of discontinuity surfaces will be suppressed: (i) the fracture energy concept of equivalent softening, (ii) the second order gradient formulation, and (iii) the Cosserat theory of polar continua. All regularization concepts are essentially local in character in spite of their characteristic length measures. The implications of the three degradation descriptions will be discussed at the oral presentation of the uniaxial tension problem, for which appropriate extensions of the Rankine maximum stress hypothesis and the ^-theory of maximum shear distortion will be examined.