A contact smoothing method for arbitrary surface meshes using Nagata patches

Abstract

Highlights • A new 3D contact surface smoothing approach for large deformation contact problems between deformable bodies is proposed. • The local Nagata patch interpolation is used to smooth arbitrary surface meshes. • The original curvature of the master surface is recovered using a relatively coarse mesh. • The non-physical contact force oscillations usual in the faceted surface representation are eliminated. • The accuracy, robustness and performance of the numerical simulations is improved adopting the surface smoothing method.

A concise frictional contact formulation based on surface potentials and isogeometric discretization

“…Consequently, as the numerical examples show, the proposed formulation exhibits lower sensitivity to the load step size than previous formulations. (2015); Neto et al (2016)) and the moving friction cone formulation (Wriggers and Haraldsson, 2003). In comparison with the standard formulation, the implementation of the proposed formulation is much easier, since its theory is more concise even though it is still consistent with the surface potential-based contact theory of Sauer and De Lorenzis (2013).…”

Large deformation frictional contact analysis with immersed boundary method

“…p N + κ E h g N − ≤ 0, otherwise the problem equation would remain as the second equation in (31). We can again substitute the value at the quadrature points of λ N obtained in (30), so that the Coulomb friction limit is written as µ p N + κ E h g N − .Itisalsopossible to condense element-wise the Lagrange multipliers using the second equation in (28). In order to do that, we will distinguish between the different states during frictional contact, the sticking case and the sliding case.…”

“…In this case the normal field is discontinuous between elements, which is an issue to consider when it comes to solving contact problems, as the measures of the gap between contact bodies are strongly influenced by the accuracy of the definition of the surfaces [28,43]. Some studies have tried to improve the quality of the contact kinematics description using various approaches, such as an averaged normal field [34,46] construction of smooth surfaces to evaluate the contact gap [28,43], and the application of the isogeometric analysis [22] to solve contact problems (see e.g. [10,11,39]).…”

On the effect of the contact surface definition in the Cartesian grid finite element method

“…Several attempts to enhance the definition of the contact boundaries have been developed in the framework of body-fitted meshes, usually known as surface smoothing, using diverse techniques such as Hermite, Bezier spline and NURBS interpolations [15][16][17][18], Gregory patches [19] or Nagata patches [20]. It is proven in these works that the enhancement of the contact surfaces results in more accurate solutions and increased robustness of the contact algorithm.…”