Total Lagrangian SPH Numerical Framework for Large Deformation and Collision Simulations

Min Jun Kim; Gil Ho Yoon

doi:10.7734/COSEIK.2026.39.5.319

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2026 Vol.39, Issue 5 Preview Page Next Page

Research Paper

Total Lagrangian SPH Numerical Framework for Large Deformation and Collision Simulations 대변형 및 접촉 시뮬레이션을 위한 Total Lagrangian SPH 수치 해석 프레임워크 구축

31 October 2026. pp. 319-326

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Abstract

In this study, a Total Lagrangian Smoothed Particle Hydrodynamics (TL-SPH) framework was developed for collision and large-deformation problems of elastic solids. The total Lagrangian formulation was applied to stress evaluation and time integration, whereas contact forces evaluated in the current configuration were coupled to the reference-frame equations of motion. To handle collisions, a penalty contact model with a surface-aware penetration depth and Coulomb friction model were coupled to the TL-SPH equations of motion. The surface-aware measure computes the contact forces only when the surfaces penetrate, removing the non-physical repulsive force that conventional SPH produces from kernel overlap before contact. The framework was verified through three benchmarks—a 2D oscillating cantilever plate, an elastic cylinder on an inclined plane, and the collision of two rubber rings—verifying convergence, agreement with analytical solutions, and energy conservation.

Keywords

total lagrangian SPH

contact force model

large deformation

energy conservation

본 논문에서는 탄성체의 접촉과 대변형 거동을 해석하기 위한 Total Lagrangian SPH(TL-SPH) 기반 수치 해석 프레임워크를 제안한다. 응력 평가와 시간 적분에는 초기 기준 형상 기반 정식화를 적용하고, 현재 형상에서 평가한 접촉력을 이에 결합하였다. 접촉 처리는 표면 인식(surface-aware) 침투 깊이 기반의 페널티 접촉 모델과 쿨롱 마찰 모델로 수행한다. 이 표면 인식 방식은 표면이 침투할 때만 접촉력을 계산하여, 기존 SPH에서 접촉 이전의 커널 중첩으로 발생하던 비물리적 반발력을 제거한다. 2D 진동판, 경사면 접촉･마찰, 고무 링 충돌의 세 가지 벤치마크 문제를 통해 프레임워크의 정확성, 수렴성, 에너지 보존 특성을 검증하였다.

키워드

total lagrangian SPH

접촉력 모델

대변형

에너지 보존

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 39
No :5
Pages :319-326
Received Date : 2026-06-01
Revised Date : 2026-06-22
Accepted Date : 2026-07-01
DOI :https://doi.org/10.7734/COSEIK.2026.39.5.319

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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