A Surface-to-Surface Finite Element Algorithm for Large Deformation Frictional Contact in febio

Abstract

This study formulates a finite element algorithm for frictional contact of solid materials, accommodating finite deformation and sliding. The algorithm uses a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints in a nonmortar surface-to-surface approach. Use of a novel kinematical approach to contact detection and enforcement of frictional constraints allows solution of complex problems previously requiring mortar methods or contact smoothing algorithms. Patch tests are satisfied to a high degree of accuracy with a single-pass penalty method, ensuring formulation errors do not affect the solution. The accuracy of the implementation is verified with Hertzian contact, and illustrations demonstrating the ability to handle large deformations and sliding are presented and validated against prior literature. A biomechanically relevant example addressing finger friction during grasping demonstrates the utility of the proposed algorithm. The algorithm is implemented in the open source software febio, and the source code is made available to the general public.

Total Knee Replacement: Subject-Specific Modeling, Finite Element Analysis, and Evaluation of Dynamic Activities

“…where the constants G and λ are material coefficients, I 1 = trC is the first invariant of the right Cauchy-Green deformation tensor C, and J is the determinant of the deformation gradient tensor. Equation ( 1) is solved by FEBio, and the material properties given will be Young's modulus E and Poisson's ratio v, where E = 2G(1+v) and λ = 2Gv/(1−2v) (Zimmerman and Ateshian, 2018). Thereafter, no other parameters need to be specified except linear parameters, such as Young's modulus and Poisson's ratio.…”

“…Moreover, a sliding-elastic contact was defined between the two deformable parts of the FE TKR model, namely the femoral component and tibial insert. Sliding contact interfaces at the femoral component-tibial insert interface permits sliding between the two geometries but prevents them from penetrating each other (Maas et al, 2012;Zimmerman and Ateshian, 2018). The user must specify the two contacting surfaces' faces, namely the femoral component and tibial insert.…”

A Formulation for Fluid–Structure Interactions in febio Using Mixture Theory

“…13. The interface C s between X s adv and X s adt was modeled as a tied contact interface [28]. The displacements of the walls of the adipose tissue were fixed.…”

“…The rollers and pump casing were modeled as rigid materials; the casing was modeled as a rigid body with fixed degrees-of-freedom and the rollers were combined into another rigid body whose angular velocity was set to x, and all other degrees-of-freedom fixed. A frictionless elastic sliding contact interface [28] was prescribed between the tubing outer wall and the pump casing; a similar contact interface was prescribed between the tubing outer wall and the rollers such that the tubing could be compressed and constrained within the pump casing. Backflow and tangential stabilization schemes were prescribed for both the inlet and outlet boundaries of the tubing (b ¼ 1).…”

“…It can describe biological tissues with mixture theory, accounting for interstitial fluid and solute flow in a porous deformable solid matrix, also accommodating chemical reactions [21,25]. It includes robust contact algorithms that handle large deformations and sliding, with or without friction, for elastic, biphasic, and multiphasic materials [26][27][28].…”