Decomposition contact response (DCR) for explicit finite element dynamics

Abstract

SUMMARYWe propose a new explicit contact algorithm for finite element discretized solids and shells with smooth and non-smooth geometries. The equations of motion are integrated in time with a predictorcorrector-type algorithm. After each predictor step, the impenetrability constraints and the exchange of momenta between the impacting bodies are considered and enforced independently. The geometrically inadmissible penetrations are removed using closest point projections or similar updates. Penetration is measured using the signed volume of intersection described by the contacting surface elements, which is well-defined for both smooth and non-smooth geometries. For computing the instantaneous velocity changes that occur during the impact event, we introduce the decomposition contact response method. This enables the closed-form solution of the jump equations at impact, and applies to non-frictional as well as frictional contact, as exemplified by the Coulomb frictional model. The overall algorithm has excellent momentum and energy conservation characteristics, as several numerical examples demonstrate.

Multisymplectic Variational Integrators for Nonsmooth Lagrangian Continuum Mechanics

“…We refer to Fetecau et al [41] for the application of this variational approach to several examples in nonsmooth continuum mechanics and for the physical interpretation of the jump conditions (17). In Section 3, we include impenetrability constraints in this geometric setting, in order to give a variational formulation of contact mechanics.…”

“…Impact of elastic bars. We illustrate the theory of Section 4.3, with configuration space C c (discontinuous with separation, see (8)), employing the standard benchmark example of elastic contacts between two bars which have been previously presented in Taylor and Papadopoulos [126]; see also Cirak and West [17] and Glocker [53]. The configuration bundle is π : Y = X × R × R → X , so the first jet bundle can be canonically identified with the vector bundle over Y = X × R × R (t, s 1 , s 2 , ϕ 1 (t, s 1 ), ϕ 2 (t, s 2 )), with fiber R 2 × R 2 (∂ t ϕ 1 (t, s 1 ), ∂ t ϕ 2 (t, s 2 ), ∂ s 1 ϕ 1 (t, s 1 ), ∂ s 2 ϕ 2 (t, s 2 )).…”

Cyclic steady states of nonlinear electro-mechanical devices excited at resonance

“…Energy conserving contact algorithms for the second-order schemes as used in this work are well established; see for example [42][43][44][45][46][47] and the more recent studies in [48][49][50]. We outline the main ideas for our context in Appendix A, please refer to [31] for a more detailed discussion.…”

“…The algorithmic enforcement of (A.3) and (A.4) simultaneously becomes non-trivial while preserving energy and momentum of the deformable bodies involved. For the various computational treatments of this issue, we refer to [42][43][44][45][46][47] and [48][49][50] .g n C g nC1 / ; otherwise : (A.6)…”

“…In order to ensure (A.3) and (A.4) in the explicit setting, we employ a similar approach to a recent method by [48], where the equations of motion are integrated in time with a predictor-corrector-type algorithm. The equations of motion are advanced for one step .t i 1 ; t i by a predictor-step without consideration of contact.…”