A Novel Bi-Penalty Method for Stable Contact-Impact Analysis

EasyChair Preprint 13575

Abstract

The contact-impact analysis focuses on the short period contact that results in a change in the direction of a body’s velocity. In the finite element method, an adequate expression of the contact stress for discretized spatial fields should be formulated to obtain accurate results. In general, the penalty method is a popular approach for fulfilling the impenetrability condition. It regularizes the impulsive response of the contact stress and generates the contact stress using nonphysical springs on the contact surfaces. Thus, an arbitrary stiffness parameter should be defined, and the simple representation of the contact stress can reduce the implementation difficulty and computational cost. The penalty method with a large stiffness penalty accurately constrains the contact conditions and reduces temporal potential energy loss by decreasing the penetration. However, in the explicit finite element method, the stability is pushed to its limit at the same time, and it requires a smaller time step to satisfy the stability condition. To alleviate this difficulty, the bi-penalty method was proposed and showed that the stability can be conserved by a mass penalty term in the one-dimensional contact case. This method is an extension of the penalty method, which utilizes the idea of the penalty method to the mass term. This study proposes a novel bi-penalty method for general contact-impact cases with conserved stability. The method is demonstrated to show and prove the effectiveness and stability in 1D, 2D, and 3D contact cases.

Keyphrases: Bi-penalty method, Contact-impact problem, Explicit time integrator, Penalty method, finite element method, stability

@booklet{EasyChair:13575,
  author    = {Yun-Jae Kwon and S.S. Cho and José A. González and Jin-Gyun Kim},
  title     = {A Novel Bi-Penalty Method for Stable Contact-Impact Analysis},
  howpublished = {EasyChair Preprint 13575},
  year      = {EasyChair, 2024}}