Thermodynamically consistent linear-gradient damage model in Abaqus

Commercial finite element software follow cautiously the numerical methods developed by scientific community. Even though phase-field method is not a default option in Abaqus, code proposes unique way to implement and test complex, extraneous models. In last five years, fracture models Abaqus have gained unbelievable popularity among scientists engineers alike. However, most implementations are based on quadratic crack representation function, which easy solve but has no elastic threshold. Various solutions been proposed as workaround linear damage however, none of them obtain consistent results original Griffith solution when length scale reduced zero. This paper presents an energetically gradient model Abaqus. The bound constrained optimization achieved using Lagrange multipliers additional degree freedom. We show that necessary energy corrections applied, simulations agreement with analytical mechanics. Furthermore, through elaborate benchmark tests, we verified our experimentally demonstrated validity implementation.