Hybrid particle methods in frictionless impact‐contact problems

Abstract

SUMMARYThe dual particle dynamic (DPD) methods which employ two sets of particles have been demonstrated to have better accuracy and stability than the co-locational particle methods, such as the smooth particle hydrodynamics (SPH). The hybrid particle method (HPM) is an extension of the DPD method. Besides the advantages of the DPD method, the HPM possesses features which better facilitate the simulation of large deformations. This paper presents the continued development of the HPM for the numerical solution of two-dimensional frictionless contact problems. The interface contact force algorithm which employs a modified kinematic constraints method is used to determine the contact tractions. In this method, both the impenetrability condition and the traction condition are simultaneously enforced. In the original kinematic constraints method, only the former condition is satisfied. A new formulation to find stress derivatives at stress-free corners by imposing stress-free boundary conditions is also developed. The results for 1-D and 2-D contact problems indicate good accuracy for the contact formulation as well as the corner treatment when compared to analytical solutions and explicit finite element results using the commercial code LS-DYNA.

Moving least-square interpolants in the hybrid particle method

“…Stress histories are tracked at both the stress and motion points, respectively. A step-by-step solution algorithm for the governing equations within a time-step is described in Reference [13] in detail and is briefly reviewed in this section. The field variables at the time instant t n are known and are advanced to the time instant t n+1 based on the central difference method.…”

“…In the process of computing stress derivatives at motion points located on the boundaries in the HPM, the local co-ordinate system is oriented such that the local x-and y-axes are aligned, respectively, along the outward normal and the tangential direction of the surface at that motion point [13]. Once the derivatives of the stress components are found in this local co-ordinate system using the MLS interpolants, the computed derivatives are transformed back to the global co-ordinate system.…”

“…In Reference [19], this treatment has been shown to be sensitive to the boundary geometry when velocity points (similar to motion points in the HPM) are employed on the boundary. The second approach is implemented by imposing boundary constraints [13,20]. Unlike the ghost particles-based approach which is suitable for methods based on both kernel approximations and MLS interpolants, the boundary constraints-based approach is applicable only for those based on MLS interpolants.…”

“…Numerical schemes based on kernel approximations, such as the SPH [10,17], or moving least-square (MLS) interpolants, such as the HPM [13], have both been used for this purpose. However, for both schemes, special care needs to be given to boundary particles because of the one-sided distribution of neighbouring particles available at these particles.…”

“…Comprehensive reviews on these methods and their derivatives can be found in References [7][8][9][10][11]. The hybrid particle method (HPM) [12,13] is a recently developed particle method, and is based on the strong form of the conservation equations. This method employs two sets of particles, known as the motion points and the stress points, respectively.…”