PSI - Issue 35

S. Karthik et al. / Procedia Structural Integrity 35 (2022) 173–180 Karthik et. al. / Structural Integrity Procedia 00 (2021) 000–000

180 8

(a)

(b)

Fig. 7. Damage parameter evolution: (a) PFM; (b) GED.

• The damage process in GED model is static type and the damage process in PF model can be static or quasi static type depending on the formulation. • GED model is suitable for large scale engineering problems and PF model is suitable for small scale problems due to its expense of computation.

References

Bazant, Z., Belytschko, T., Chang, T., 1984. Continuum model for strain softening. Journal of Engineering Mechanics ASCE 110, 1666–1692. Bazant, Z.P., Jirasek, M., 2002. Nonlocal integral formulations of plasticity and damage: Survey of progress. Journal of Engineering Mechanics ASCE 128, 1119–1149. Eringen, A.C., 1983. On di ff erential equations of nonlocal Elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics 54, 1703–1710. Forest, S., 2009. Micromorphic approach for gradient elasticity, viscoplasticity, and damage. Journal of Engineering Mechanics 135, 117–131. Ha, Y.D., Bobaru, F., 2010. Studies of dynamic crack propagation and crack branching with peridynamics. International Journal of Fracture 162, 229–244. Kachanov, L.M., 1958. On the creep fracture time. Izv Akad. Nauk USSR Otd Tekh. 8, 26–31. Karthik, S., Rajagopal, A., Reddy, J., 2021. Nonlocal phase field approach for modeling damage in brittle materials. Mechanics of Materials 157, 103797. Kasirajan, P., Bhattacharya, S., Rajagopal, A., Reddy, J., 2020. Phase field modeling of fracture in quasi-brittle materials using natural neighbor galerkin method. Computer Methods in Applied Mechanics and Engineering 366, 113019. Lemaitre, J., 1996. A course on damage mechanics. Springer-Verlag, Berlin, Heidelberg. Miehe, C., Hofacker, M., Welschinger, F., 2010. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199, 2765–2778. Murakami, S., Liu, Y., 1995. Mesh-dependence in local approach to creep fracture. International Journal of Damage Mechanics 4, 230–250. Peerlings, R.H., De Borst, R., Brekelmans, W.A., De Vree, J.H., 1996. Gradient enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering 39, 3391–3403. Pranavi, D., Rajagopal, A., Reddy, J., 2021. Interaction of anisotropic crack phase field with interface cohesive zone model for fiber reinforced composites. Composite Structures 270, 114038. Raghu, P., Rajagopal, A., Reddy, J.N., 2019. Thermodynamically consistent variational approach for modeling brittle fracture in thick plates by a hybrid phase field model. Journal of Applied Mechanics 87, 021002. Triantafyllidis, N., Aifantis, E.C., 1986. A gradient approach to localization of deformation: I. Hyperelastic materials. Journal of Elasticity 16, 225–237. Umesh, B., Rajagopal, A., 2018. Higher order continuous approximation for the assessment of nonlocal-gradient based damage model. Mechanics of Advanced Materials and Structures 26, 1671–1682.