PSI - Issue 60

584 N. Khandelwal et al. / Procedia Structural Integrity 60 (2024) 582–590 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 3 Where is the length scale parameter measuring the width of diffusiveness, is the critital energy release rate

Diffuse crack

Sharp crack

Fig. 1. Elasto-plastic solid body with sharp crack and diffuse crack. In the formulation, a degradation function ( ) is applied on elastic and plastic energy to simulate the stiffness degradation in the material during crack propagation process as represented in Eq. (3). =∫ ( )[ ( ) + ( )] + ∫ 2 0 [ 2 + 0 2 | | 2 ] (3) Where ( ) , ( ) are elastic and plastic energy functional with total strain ( ) comprised of elastic strain ( ) and plastic strain ( ) . To arrest the crack growth in compression, elastic strain energy functional is devided into positive ( + ) and negative ( − ) parts in terms of the volumetric and deviatoric contributions [10] with + , accompanied with degradation functions ( ) as displayed in Eq. (4). =∫ ( ) + ( )+ − ( ) + ( ) ( )] + ∫ 2 0 [ 2 + 0 2 | | 2 ] (4) Application of variation priciple on Eq. (4) results in the following stress and phase field evolution equilibrium equation as per Eqs. (5) and (6) respectively. ∇. ( , )= 0 (5) ∫ {[( 0 ) + ′ ( )( )] + 0 ( 0 2 ). ( )} = 0 (6) Where ( , ) is the effective Cauchy stress tensor and is the history field variable introduced to enforce the irreversibility condition at time step ( ) as given in Eq. (7). =max ∈[ , ] [ + ( ( , )) + ( ( , ))] (7)