Large deformation frictional contact formulation based on a velocity description (original) (raw)
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Large Deformation Frictional Contact Formulation for Low Order "Solid-Shell" Elements
2000
A special contact formulation which is compatible with the so-called 'Solid-Shell' is developed for applications involving large deformation and frictional contact. The contact conditions are considered in the covariant form from the surface geometry point of view, which is very similar to shell theory. The contact integral and the necessary kinematical values are considered on the tangent plane of the
Algorithmic aspects in large deformation contact analysis using ‘Solid-Shell’ elements
Computers & Structures, 2005
A special application for the so-called 'Solid-Shell' elements are sheet metal forming problems with high stretching and large local contact pressure where standard 2D-shells fail to converge resp. do not give reasonable results. To describe such kind of problems besides a full 3D continuum discretization appropriate contact formulations are necessary to introduce the contact condition of the metal sheets against the rigid tools. In this contribution a velocity description is taken for formulation of contact conditions. A penalty as well as an Augmented Lagrangian approach for frictionless contact is used as a first step in our developments. Special attention is paid to different numerical integration schemes of the contact integral and tangent matrices. As a result a series of different contact elements including various cases as "node-to-surface", "segment-to-segment" and "analytical rigid surface-to-segment" is considered under the unified description. For selected numerical examples the influence of the order of the quadrature formulae in a subdomain integration approach as well as the order of finite element interpolation used in the computations is discussed. The algorithms appear also to work well for friction type problems, which will be tested in a following paper.
A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis
Computer Methods in Applied Mechanics and Engineering, 2009
In the first part of this work, the theoretical basis of a frictional contact domain method for two-dimensional large deformation problems is presented. Most of the existing contact formulations impose the contact constraints on the boundary of one of the contacting bodies, which necessitates the projection of certain quantities from one contacting surface onto the other. In this work, the contact constraints are formulated on a so-called contact domain, which has the same dimension as the contacting bodies. This contact domain can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. The introduced contact domain is subdivided into a non-overlapping set of patches and is endowed with a displacement field, interpolated from the displacements at the contact surfaces. This leads to a contact formulation that is based on dimensionless, strain-like measures for the normal and tangential gaps and that exactly passes the contact patch test. In addition, the contact constraints are enforced using a stabilized Lagrange multiplier formulation based on an interior penalty method (Nitsche method). This allows the condensation of the introduced Lagrange multipliers and leads to a purely displacement driven problem. An active set strategy, based on the concept of effective gaps as entities suitable for smooth extrapolation, is used for determining the active normal stick and slip patches of the contact domain.
A large deformation frictional contact formulation using NURBS-based isogeometric analysis
International Journal for Numerical Methods in Engineering, 2011
This paper focuses on the application of NURBS-based isogeometric analysis to Coulomb frictional contact problems between deformable bodies, in the context of large deformations. A mortar-based approach is presented to treat the contact constraints, whereby the discretization of the continuum is performed with arbitrary order NURBS, as well as C 0-continuous Lagrange polynomial elements for comparison purposes. The numerical examples show that the proposed contact formulation in conjunction with the NURBS discretization delivers accurate and robust predictions. Results of lower quality are obtained from the Lagrange discretization, as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface.
Computational Mechanics, 2004
A velocity description, based on the consideration of contact from the surface geometry point of view, is used for a consistent formulation of contact conditions and for the derivation of the corresponding tangent matrix. Within this approach differential operations are treated as covariant derivatives in the local surface coordinate system. The main advantage is a more algorithmic and geometrical structure of the tangent matrix, which consists of a "main", a "rotational" and a pure "curvature" term. Each part of the tangent matrix contains the information either about the internal geometry of the contact surface or about the change of the geometry during incremental loading and can be estimated in a norm during the analysis. Representative examples with contact and bending of shells modelled with linear and quadratic elements over some classical second order geometrical figures serve to show situations where keeping all parts of the tangent matrix is not necessary.
Finite-deformation interface formulation for frictionless contact problems
Communications in Numerical Methods in Engineering, 1994
An interface finite element for non-linear analysis of frictionless contact problems is presented. A constitutive equation relates stresses in the interface layer to the deformation gradient with respect to an imaginary reference configuration where the layer thickness is constant and finite. The equation of equilibrium is written in the same configuration, while the boundary conditions involve stresses related to an actual reference configuration used in the formulation for the contacting bodies. Finite element discretization is introduced for the layer in order to calculate the unknown field of displacements. Computational examples demonstrate properties of the contact element and its range of applicability in the analysis of large deformation contact problems including relative sliding of curved surfaces.
2D or 3D frictional contact algorithms and applications in a large deformation context
Communications in Numerical Methods in Engineering, 1995
The paper is devoted to the analysis of two-or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviours with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability.
A C 1 -continuous formulation for 3D finite deformation frictional contact
Computational Mechanics, 2002
A new 3D smooth triangular frictional node to surface contact element is developed using an abstract symbolical programming approach. The C 1 -continuous smooth contact surface description is based on the six quartic Bézier surfaces. The weak formulation and the penalty method are formulated for the description of large deformation frictional contact problems. The presented approach, based on a non-associated frictional law and elastic-plastic tangential slip decomposition, results into quadratic rate of convergence within the Newton-Raphson iteration loop. The frictional sliding path for the smooth, as well as the simple frictional node to surface contact element presented herein, is defined by the mapping of the current in the last converged configuration. Examples demonstrate the performance of symbolically developed contact elements, as well as the stability and more realistic contact description for the smooth elements in comparison with the simple ones.
On the treatment of frictional contact in shell structures using variational inequalities
International Journal for Numerical Methods in Engineering, 1999
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