A contact formulation based on localized Lagrange multipliers: formulation and application to two‐dimensional problems

Abstract

SUMMARYThe non-penetration condition in contact problems is traditionally based on the classical Lagrange multiplier method. This method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non-matching. To deal with this problem we introduce a novel element in the Lagrange multiplier approach of contact modelling, namely, a contact frame placed in between contacting bodies. It acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models. Only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic. The contact frame has its own independent freedoms, which allows the formulation to pass contact patch tests by design.

Mixed finite element formulation in large deformation frictional contact problem

“…The solution to a contact problem is obtained using various methods such as the penalisation or the Lagrange multiplier methods 5,6,7,8,9,10 . Among these last methods one finds the gradient methods 11,12 , those of the increased Lagrangian or other mixed approaches 13,14,15 .…”

Concurrent Process-Product Design Optimization Using Coupled Nonlinear Finite-Element Simulations

“…While keeping the punch and dies fixed in their respective positions, the holding forces are increased linearly from zero to the specified value matching the corresponding manufacturing process control parameter. In this stage, the kinematic contact formulation is used because of the computational efficiency of the formulation (Rebel et al, 2002;Oden and Kikuchi, 1982;Oden and Pires, 1983;Bayram and Nied, 2000;Wriggers, 2006). Due to the simplicity of the geometry, die and holder surfaces are defined through standard analytical rigid surfaces.…”

Application of the Localised Lagrange Multiplier Method to a 3D Contact Patch Test

“…These discretisations are substituted into variational form (14). After carrying out the integrations and the linearisation about the reference configuration, we can add the governing equations of the discrete frame based contact formulation to the behaviour of the contacting bodies (given by equation (30) for the non-barred side) and obtain (see also [11] ) …”

“…By utilising the design freedom in the frame setup we demonstrated that the localised Lagrange multiplier method leads to perfect results in the 2D contact patch test problem [10,11] .…”