COMPLAS 2023

An improved material point method for frictional contact problems involving phase field fracture

  • Kakouris, Emmanouil (School of Engineering, University of Warwick,)

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Study of dynamic fracture resulting from the impact of materials has gained significant attention due to the constant need for optimum design of structural components. The complex nature of dynamic fracture, which can occur in response to and factors, has led to a need for improved numerical methods for simulating e.g. crack curvature, branching, merging etc. To accurately simulate the behaviour of materials under impact, it is necessary to consider factors such as frictional contact, complex continuum constitutive response under severe deformation, and 3-D fracture branching and merging. Phase field damage models provide a practical approach for simulating failure while avoiding the complexity of explicitly tracking fracture surface interactions. To this extend, a novel Phase Field Material Point Method (PF-MPM) has been recently introduced [1] for robust simulation of dynamic fracture in isotropic and anisotropic materials. However, MPM-based methods are generally facing three main challenges in impact related problems which yield to severe stress oscillations in the contact surface: (1) cell-crossing errors emerge when particles move from one grid cell to another, (2) contact occurs when material points in two bodies share the same grid node, leading to an early (less realistic) contact, (3) inaccurate numerical integration when a particle just crosses a grid cell. Taking these into consideration, this research work proposes an improved MPM contact algorithm enriched with phase field damage models to address the previous challenges and increase the accuracy of in impact-fracture problems. Cell-crossing and numerical integration errors are treated with the recently proposed Extended B-Splines [2]. The early contact numerical issue is addressed by utilising a penalty method-based contact algorithm which tracks boundary materials points of the solid bodies making it independent on the fixed computational grid. A series of comparative analyses are conducted to ascertain the significance of the proposed frictional contact algorithm. [1] Kakouris E.G., Triantafyllou S.P., Phase-Field Material Point Method for dynamic brittle fracture with isotropic and anisotropic surface energy, Computer Methods in Applied Mechanics and Engineering, Vol. 357, 112503, 2019. [2] Yamaguchi Y., Moriguchi S., Terada K., Extended B-Splines-based implicit material point method, International Journal for Numerical Methods in Engineering, Vol. 122, pp. 1746-1769.