Gradient-enhanced ductile fracture constitutive modeling in implicit two-scale finite element analysis

In the field of damage modeling for ductile materials, numerous models have successfully addressed various fracture responses, as well as the need for robust algorithms and solutions to computational challenges. This study developed a damage model based on continuum damage mechanics. It addresses mesh regularization, a primary computational issue in macroscopic structural fracture analysis through a gradient-enhanced damage model using micromorphic theory and incorporating damage hardening variables. To provide a physical explanation for the characteristic lengths associated with the gradient-enhanced term, an extended “two-scale” computational homogenization approach was employed to define the length scale between the macro- and microscale. This microvariable within a micromorphic extension can be utilized to model the damage hardening mechanism, which cannot be fully captured via high-resolution localized characterization. In duplex microstructures, the length scale can be defined by the microstructure size relative to the width of the micro-shear band. This explains the damage overlapping phenomenon between the two-scales.