Using a penalty term to deal with spurious oscillations in second gradient finite elements

It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second-order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite...