Adaptive coupling of FEM and RKPM formulations for contact and impact problems

High strain rate contact-impact with accompanied fragmentation is one of the most challenging problems in computational mechanics. Although substantial effort has been made in recent years in the development of meshfree methods, such as the reproducing kernel particle method (RKPM), for alleviating difficulties associated with mesh distortion and regularity requirement in the numerical modeling of the said problems, issues such as spatial-temporal stability and computational efficiency remain unresolved. In this work, an adaptively coupled FEM-RKPM formulation is proposed and stability analysis is performed for modeling of contact and impact problems. Several FEM-RKPM coupling approximation and discretization are introduced, and an averaged consistent coupling formulation has been proposed to achieve desired accuracy with reduced oscillation near the coupling domain.;A unified stabilized conforming nodal integration (SCNI) for the evolving RKPM and FEM domains is proposed. As such, state and field variables transfer in the discretization transformation between FEM and RKPM is not required. The convergence of the FEM with SCNI domain integration is numerically studied. The results show FEM with SCNI exhibits higher accuracy and better convergence rate than FEM with Gauss integration.;The von Neumann stability analysis of the Lagrangian and semi-Lagrangian RKPM discrete equation of motion has been performed. The stable time step estimation for central difference temporal discretization and RKPM as well as FEM-RKPM spatial discretization with various domain integration methods are derived. The results show a favorable stability in SCNI over DNI and one-point Gauss quadrature. The stability analysis for semi-Lagrangian RKPM formulation also shows that the stability condition is inversely proportional to the local velocity gradient. Meeting this stability condition plays an important role in obtaining stable numerical solution in the contact-impact problems.;A new particle based kernel contact algorithm for multi-body contact-impact in proposed. The partition of unity contact detection approach is introduced to identify the potential contact particles. In this approach, the non-penetration condition is naturally achieved by kernel interaction of the contacting bodies. A frictional kernel contact constitutive law suitable for meshfree methods is proposed for modeling the stick-slip condition in frictional contact.;The gradient type stabilization, GSCNI, is proposed to improve the stability condition for RKPM with SCNI domain integration in transient problems. The eigenvalue analysis shows that with the additional gradient stabilization, the non-zero energy oscillatory modes in SCNI are removed.;The proposed methods are applied to model several earth-moving and fragment contact-impact problems. The reliability of the proposed methods is validated by comparison of some simulation results with experimental data showing reasonable agreement.