Master-master frictional contact and applications for beam-shell interaction
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ORIGINAL PAPER
Master‑master frictional contact and applications for beam‑shell interaction Alfredo Gay Neto1 · Peter Wriggers2 Received: 15 April 2020 / Accepted: 24 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The surface-to-surface master–master contact treatment is a technique that addresses pointwise contact between bodies with no prior election of slave points, as in master–slave case. For a given configuration of contact-candidate surfaces, one needs to find the material points associated with a pointwise contact interaction. This is the local contact problem (LCP). The methodology can be applied together with numerical models such as geometrically nonlinear finite elements, discrete elements and multibody dynamics. A previous publication has addressed the possibility of degenerating the local contact problem, which yields the derivation of point-surface, curve-surface and other simplifications on the geometric treatment in the same mathematical formulation, sharing a single numerical implementation. This has useful applications for singularities or non-uniqueness scenarios on the LCP. The present work provides a framework for the degenerated master–master contact formulation including friction. An enhanced friction model is proposed, accounting for a combination of elastic and dissipative effects at the interface. Details of derivations and numerical implementation are given as well as examples related to beam-shell interaction. Keywords Contact · Friction · Master–master · Master–slave · Beam · Shell · Finite element · Multibody
1 Introduction The detection and treatment of contact interactions in a numerical model is an important task in engineering and mechanical sciences. Frequently one has to consider contact in applications involving finite elements, multibody dynamics and discrete element models, such as other techniques employed to simulate the mechanical behavior of systems composed of rigid or flexible bodies. Numerous approaches are available in literature to handle contact in numerical models. According to convenience and desired accuracy level, one may choose among a sort of possibilities. A detailed view of numerical models for contact is found in [1, 2]. In the finite element context there exist many different models, starting with the simple “node-to-node” discretization (see e.g.: [3, 4]) up to mortar methods to handle contact
* Alfredo Gay Neto [email protected] 1
Polytechnic School at University of São Paulo, São Paulo, Brazil
Leibniz Universität-Hannover, Hannover, Germany
2
constraint in large deformations, see e.g. [5, 6]. When handling the actual geometry of contacting surfaces, differential geometry comes as a basic tool to describe contact kinematics. In this context the reader may refer to [7]. Physically, contact phenomena take place in a surface: the so-called “contact patch”. This surface is an idealization of the realistic contact interface, which typically presents multiple complex localized interactions, that actually take pl
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