UMAT

A straightforward numerical technique for finite element implementation of non-local gradient-dependent continuum damage mechanics theories. This paper presents a direct algorithm to implement non-local gradient-enhanced damage mechanics theories in the existing finite element codes with minor modifications and without the need to formulate a higher-order element. This method extends the algorithm of R. K. Abu Al-Rub and G. Z. Voyiadjis [Int. J. Numer. Methods Eng. 63, No. 4, 603–629 (2005; Zbl 1140.74545)] to gradient-dependent damage theories and to three-dimensional (3D) problems. The presented algorithm is implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The potential of the proposed numerical algorithm for non-local gradient-enhanced damage theories in eliminating mesh-dependent simulations is validated by conducting various numerical tests of the localised damage