Contact framework for total Lagrangian smoothed particle hydrodynamics using an adaptive hybrid kernel scheme

Abstract

Total Lagrangian SPH (TLSPH) offers many advantages that can overcome instability and computational time issues. However, it is not naturally applicable to problems with contact. Many problems in solid dynamics and structural analysis require contact definition. In order to use the total Lagrangian formulation, further development for the contact algorithm is required. This research proposes an algorithm to implement inter‐particle contact in TLSPH using an adaptive hybrid‐kernel scheme for the first time. A combination of the updated and total Lagrangian formulations at the contact surface is introduced, in which the kernel type change automatically when particles from a different body are detected. In kernel change from the updated to the total Lagrangian formulation, the gradient correction cannot be performed using a common correction method because different frames of reference are used. Therefore, a hybrid‐kernel correction technique is proposed to maintain the zeroth‐ and first‐order completeness. Then, the contact force is obtained from the inter‐particle force using the conservation of momentum. The proposed method does not require a user‐defined parameter that makes the application straightforward. Based on the test, the proposed method agrees well with the data available in published literature and the finite element method. Compared with the contact method in classical SPH, the proposed TLSPH shows a significant stability improvement.