Peridynamics damage model through phase field theory

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

“…Miehe et al [361] proposed a gradient damage formulation with two independent length scales to regularize the plastic response and crack discontinuities to ensure that the damage zones of ductile fractures remain inside plastic zones. Roy et al [362] presented a rephrased phase-field theory of continuum damage in a peridynamics setup and showed promising results of mode II delamination. Farrahi et al [363] demonstrated that under mode I crack growth and proper calibration of parameters, PFM always agreed with Griffith's theory.…”

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

“…Miehe et al [282] proposed a gradient damage formulation with two independent length scales to regularize the plastic response and the crack discontinu-ities to ensure that the damage zones of ductile fractures remain inside of plastic zones. Roy et al [283] presented a rephrased phase-field theory of continuum damage in a peridynamics setup and showed promising results of mode II delamination. Farrahi et al [284] demonstrated that under mode I crack growth and proper calibration of parameters, PFM always agreed with Griffith's theory.Alessi et al [285] demonstrated that macroscopic responses assimilable to brittle fractures, cohesive fractures, and a sort of cohesive fracture, including depinning energy contributions by tuning a few key constitutive parameters such as relative yield stresses and softening behaviors of the plasticity and damage criteria.…”

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

“…The gradient damage model (Pham and Marigo, 2010;Aslan et al, 2011), physical/mechanical community-based phase-field fracture models (Karma et al, 2001;Hofacker and Miehe, 2012;Borden et al, 2012) that traces back to the reformulation of Griffith's principle in Griffith (1921), and peridynamics (Piola, 1846;Silling, 2000;dell'Isola et al, 2015), which may be regarded as generalized non-local continuum mechanics, fall within this category. Replacing partial differential equations in the phase-field model by integrals in peridynamics frameworks allows for topologically-complex fractures such as intersecting and branching to be handled in both two and three dimensions (Roy et al, 2017). Coupling smeared and discrete crack approaches, for example, the element deletion method (Song et al, 2008), the combined non-local damage and cohesive zone method (Borst et al, 2004;Della Corte et al, 2017), and the thick level-set method in Bernard et al (2012) have also shown promising results in modeling fracture.…”