Discontinuous Galerkin Method for Frictional Interface Dynamics

Abstract

A stabilized discontinuous Galerkin (DG) formulation is presented for transient small deformation contact problems involving friction with application to the modeling of bolted lap joints. The method is an extension of derivations from the quasi-static context, whereby the numerical flux terms acting at the contact interface are consistently derived using variational multiscale concepts. This transient primal formulation naturally accommodates nonconforming meshes and stratified materials such as geological faults. Also, the numerical flux terms involving the stress field at the contacting interface provide a natural mechanism for embedding friction models. Numerical results for nonsmooth transient problems confirm that the DG interface approach does not introduce artificial features into the physical response.

Variational coupling of non‐matching discretizations across finitely deforming fluid–structure interfaces

“…These attributes of the traction jump term were investigated in Masud et al, 33 and generalized to general classes of problems in Truster and Masud 34 . Mathematical attributes were further investigated in the context of interfacial frictional problems 42 where this term was employed for embedding constitutive models for friction and for imposing frictional stick–slip relation at the interface. Its significance in the context of incompatible meshes in coupled thermomechanical problems with interfacial kinematics was established in Chen et al 36 Remark For the degenerate case of nodally matched meshes with continuous interpolation along , the continuity of the velocity field and its weighting function wipes out the interface terms in (71), and the method reverts to the underlying continuous formulation. Remark The time increment in the interfacial stabilization tensor (53) and the variation of the traction (73) emanates from the linearization of the equations for the solid with respect to the velocity field.…”

“…These attributes of the traction jump term were investigated in Masud et al, 33 and generalized to general classes of problems in Truster and Masud. 34 Mathematical attributes were further investigated in the context of interfacial frictional problems 42 where this term was employed for embedding constitutive models for friction and for imposing frictional stick-slip relation at the interface. Its significance in the context of incompatible meshes in coupled thermomechanical problems with interfacial kinematics was established in Chen et al 36 Remark.…”

A Lagrangian DG-Method for Wave Propagation in a Cracked Solid with Frictional Contact Interfaces

“…A unifying analysis of the DG method applied to elliptic problems is contained in [17]. Recently, Truster and Masud [42] developed a stabilized DG interface method for transient contact with Coulomb friction that extends their previous work on interphase damage modeling [43]. To overcome the non-smoothness of the Coulomb friction model, they used an elasto-plastic regularization technique (see Simo and Laursen [18]).…”

Variational multiscale method for fully coupled thermomechanical interface contact and debonding problems

“…Fully coupled thermomechanical problems with interfaces have attracted considerable interest for various engineering applications. For instance, the heat transfer across the interface of two contacting bodies plays an important role in metal forming processes (Khoei et al, 2006), structure crashworthiness (Rieger and Wriggers, 2004), powder compaction (Truster and Masud, 2016), frictional contact problems between bone and tissue in biomechanics (Shi et al, 2019), and interfacial debonding failure of carbon nanotube composites (Shu and Stanciulescu, 2020). Studies show that the interphase between the constituents, where the transition of the material properties is rapid, is often the site of crack initiation (Truster and Masud, 2013) and dominates the failure mechanism owing to the rapid change in temperature.…”

“…In this method, consistent variational formulations that render an improved conditioned system matrix with small scalar factors are particularly convenient for time-dependent problems (Seitz et al, 2019). The method maintains the size of the original algebraic system of equations compared with the Lagrange multiplier method (Brezzi, 1974;Hansbo et al, 2005;Hirmand et al, 2015;Simo and Laursen, 1992), without introducing multiplier fields to enforce the continuity conditions (Truster and Masud, 2016); however, user-defined parameters such as the penalty parameters and flux coefficients must be predefined.…”