Large Deformation Frictional Contact Research Articles

Large deformation frictional contact formulations for isogeometric Kirchhoff–Love shell

The large deformation frictional contact between shell structures is commonplace in engineering applications like the sheet metal forming process. Due to the specific assumptions of shell structures, the numerical calculation of shell contact is more complicated than the computation of contact between normal two or three dimensional solids. In recent years, the Kirchhoff–Love shell has become one of the most popular mathematical shell models under the context of isogeometric analysis. In this paper, we detailedly formulate the frictional contact contributions for Kirchhoff–Love shell structures considering both stick and slide states. The variation and linearization of contact variables considered to be sophisticated are explicitly derived and plainly organized. The general nonlinear hyperelastic materials are utilized to describe the constitutive relations of shell structures undergoing large deformation. The normal and tangential contact constraints are enforced using the classical penalty method. Based on the precise representation of shell structures using NURBS functions, we developed an effective contact detection algorithm to accurately capture the contact areas between shells. A computation framework for solving Kirchhoff–Love shell frictional contact problems is established in the context of NURBS-based isogeometric analysis. Several shell contact examples are calculated, and the obtained results are compared with those of the classical finite element method. The convergence and accuracy of the presented method are verified in these examples.

A Surface-to-Surface Finite Element Algorithm for Large Deformation Frictional Contact in febio.

This study formulates a finite element algorithm for frictional contact of solid materials, accommodating finite deformation and sliding. The algorithm uses a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints in a nonmortar surface-to-surface approach. Use of a novel kinematical approach to contact detection and enforcement of frictional constraints allows solution of complex problems previously requiring mortar methods or contact smoothing algorithms. Patch tests are satisfied to a high degree of accuracy with a single-pass penalty method, ensuring formulation errors do not affect the solution. The accuracy of the implementation is verified with Hertzian contact, and illustrations demonstrating the ability to handle large deformations and sliding are presented and validated against prior literature. A biomechanically relevant example addressing finger friction during grasping demonstrates the utility of the proposed algorithm. The algorithm is implemented in the open source software febio, and the source code is made available to the general public.

Large deformation frictional contact analysis with immersed boundary method

This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.

An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact

In this paper we propose an extension of Nitsche’s method for frictional contact in large elastic deformations. In fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces, conversely to the master–slave strategy. This enables to take into account within the same formalism contact of two elastic bodies as well as self-contact. We provide a numerical study of the performance and robustness of the method.

A contact smoothing method for arbitrary surface meshes using Nagata patches

Abstract This paper presents a contact surface smoothing method combined with the node-to-segment discretization technique to solve large deformation frictional contact problems between deformable bodies. The Nagata patch interpolation is used to smooth the surface mesh, providing a master surface with quasi- G 1 continuity between patches. Moreover, the local support of the interpolation method allows to deal with surface meshes of arbitrary topology (regular and irregular finite element discretizations), as well as hybrid meshes. The non-physical oscillations in the contact force evolution, induced by the faceted contact surface representation, are reduced using the proposed smoothing method. Furthermore, the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces, while providing an important improvement in convergence behaviour. Four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method. The results show a significant improvement in the accuracy, robustness and performance of the numerical simulations using the smoothing approach, when compared with the piecewise faceted contact surface description.

3D finite element simulations of high velocity projectile impact

An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.

3D finite element simulations of high velocity projectile impact

An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.

An unbiased computational contact formulation for 3D friction

SUMMARYA new computational contact formulation is presented and analyzed for large deformation frictional contact. The new formulation uses an unbiased treatment of the two neighboring contact surfaces considering the two‐half‐pass contact algorithm, originally derived for frictionless contact. The presented work thus introduces several novelties to unbiased friction algorithms. The new algorithm does not enforce traction continuity at the contact interface explicitly but rather satisfies it intrinsically to high accuracy, as is shown. A new 3D friction formulation is also proposed, which is a direct extension of the 1D setup, expressing the friction variables in the parameter space used for the curvilinear surface description. The new formulation resorts to classical expressions in the continuum limit. The current approach usesC1‐smooth contact surface representations based on either Hermite or non‐uniform rational B‐spline interpolation. A penalty regularization is considered for the impenetrability and tangential sticking constraints. The new, unbiased friction formulation is illustrated by several 2D and 3D examples, which include an extensive analysis of the model parameters, a convergence study, and the comparison with a classical biased master/slave contact algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Applying Nagata patches to smooth discretized surfaces used in 3D frictional contact problems

The accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved. This paper presents a smoothing method applicable to 3D contact surfaces discretized with an arbitrary mesh topology. The quadratic Nagata patch interpolation is adopted to define the smooth surface. The resulting contact surface passes through all nodes of the mesh while providing a smooth description, with at least G1 continuity at the nodes and quasi-G1 continuity between the patches. Thus, the proposed method avoids the non-physical oscillations in the contact force, which are induced by the traditionally used faceted contact surfaces description, when slave nodes slide over several master segments. Moreover, it allows the accurate evaluation of kinematic variables, leading to important improvements in terms of convergence rate within the Newton–Raphson iteration loop. The developed global and local contact search algorithms, designed for contact surfaces described by Nagata patches, are described in detail. Three numerical examples were selected to illustrate the advantages of the proposed smoothing method, including a complex industrial example of sheet metal forming process. The results show the significant improvements attained with the proposed approach, in terms of efficiency, robustness and accuracy, when compared with the traditional faceted contact surfaces description.

A Finite Element Solution for Frictional Sliding Contact between Hyper-Elastic and Rigid Bodies

This paper is devoted to the analysis of frictional contact problems with large deformations and displacements between hyper-elastic body and rigid body. The material nonlinearity and contact nonlinearity are separated and, the geometrically nonlinear behavior is described by the total Lagrange formulation. The Coulomb friction law is employed to simulate the friction between rigid vessel and rubber by the use of augmented Lagrange approach with node-to-segment formulation. A formulation of finite element is taken in this paper to describe the frictional contact problem, which is solved by the Newton-Raphson iterative procedure. It is shown that the augmented Lagrange technique significantly avoids locking and over-constraining and provides optimal convergence rate. Finally, the numerical results show that the accuracy and efficiency of augmented Lagrange approach in modeling large deformation frictional contact problem.

The Nonlinear Contact Simulation for Manufacturing Process by Using ANSYS Program as Case study with Cylindrical rolling contact

Numerical simulation plays an indispensable role in the modern manufacturing process, especially in production operation and metal forming by using different of forming Dies Because it give perfect product design to improving quality and performance and reduce the time and cost .Because of the most of forming operation include contact option between the product surface (contact surface) and Die surface (Target surface) then the determination of the contact surface nature and material behavior ( uniform linear ) or ( not uniform nonlinear) that very effect on the carryout of forming process with required product .To improving simulation accuracy, approximations of linear behavior have become less acceptable, while it is possible to perform nonlinear analysis and design more often while minimizing approximations, the nonlinear analysis capabilities in general-purpose programs such as ANSYS Mechanical.The significance of the research is into linear simulation analysis and its limitation and development to nonlinear simulation where interest with the development manufacturing processes that including change in the geometry , properties and material behavior through forming ,the search give an example of Case study with Cylindrical rolling contact that very important for wide application to manufacturing processes such as drawing ,Rolling ,Forging , Extrusion, Bending and other .The structural nonlinearities can be classified as geometric nonlinearity, material nonlinearity, and contact or boundary nonlinearity Numerical results indicate the success of ANSYS contact technologies in solving very large scale engineering problems especially large deformation frictional contact problems with the new surface based contact elements have many advantages over the node based contact elements .

An augmentation technique for large deformation frictional contact problems

SUMMARYThe present work deals with a new approach to frictional large deformation contact problems. In particular, a new formulation of the frictional kinematics is introduced that is based on a specific augmentation technique used for the introduction of additional variables. This augmentation technique substantially simplifies the formulation of the whole system. A size reduction of the resulting system of algebraic equations is proposed. Consequently, the augmentation technique does not lead to an increase in size of the algebraic system of equations to be ultimately solved. The size reduction retains the simplicity of the formulation and preserves important conservation laws such as conservation of angular momentum. Copyright © 2013 John Wiley & Sons, Ltd.

Dynamic modeling of powder compaction processes via a simple contact algorithm

In this paper, the dynamic modeling of powder compaction processes is presented based on a simple contact algorithm to evaluate the distribution of final density in dynamic powder die-pressing. The large deformation frictional contact is employed by imposing the contact constraints via the contact node-to-surface formulation and modifying the contact properties of frictional slip. The Coulomb friction law is used to simulate the friction between the rigid punch and the work-piece. The nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large FE deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.

3D dynamic modeling of powder forming processes via a simple and efficient node-to-surface contact algorithm

In this paper, a simple and efficient contact algorithm is presented for the evaluation of density distribution in three-dimensional dynamic modeling of powder compaction processes. The contact node-to-surface algorithm is employed to impose the contact constraints in large deformation frictional contact, and the contact frictional slip is modified by the Coulomb friction law to simulate the frictional behavior between the rigid punch and the work-piece. The 3D nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large finite element deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. The accuracy and robustness of contact algorithm is verified by the impact analysis of two elastic rods, which is compared with the analytical solution. Finally, the performance of computational schemes is illustrated in dynamic modeling of a set of powder components.

A large deformation frictional contact formulation using NURBS‐based isogeometric analysis

AbstractThis 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 C0‐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. Copyright © 2011 John Wiley & Sons, Ltd.

A new computational algorithm for 3D contact modeling of large plastic deformation in powder forming processes

In this paper, the three-dimensional large deformation frictional contact of powder forming process is modeled using a simple computational algorithm based on the augmented-Lagrange approach. The technique is applied by imposing the contact constraints and modifying the contact properties of frictional slip through the node-to-surface (NTS) contact algorithm. The Coulomb friction law is employed to simulate the friction between the rigid punch and the work-piece by the use of penalty and augmented-Lagrange approaches. It is shown that the augmented-Lagrange technique significantly improves imposing of the constraints on contact surfaces. The nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model for highly nonlinear behavior of powder within the framework of large FE deformation in order to predict the non-uniform relative density and stress distributions during the large deformation of powder die-pressing. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.

A contact domain method for large deformation frictional contact problems. Part 2: Numerical aspects

This second part of the work describes the numerical aspects of the developed contact domain method for large deformation frictional contact problems. The theoretical basis of this contact method is detailed in the first part of this work. Starting from this, the present contribution focuses on describing important algorithmic details that go along with the finite element implementation for two-dimensional problems. Important aspects are the construction of the contact domain mesh, via a constraint Delaunay triangulation, the linearization of the discretized contact contributions and some important technical aspects about the extrapolation procedure used for the predictive active set strategy. Finally a set of numerical examples is presented to demonstrate the performance of the developed contact strategy. Demanding static and dynamic contact problems in the context of large deformations, including frictional effects as well as self contact, show the wide applicability and the robustness of the proposed method.

A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis

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 new computational algorithm for contact friction modeling of large plastic deformation in powder compaction processes

In this paper, the large deformation frictional contact of powder forming process is modeled based on a new computational algorithm by imposing the contact constraints and modifying the contact properties of frictional slip. A simple and efficient numerical algorithm is presented for imposing the contact constraints and frictional contact properties based on the node-to-surface contact technique to simulate the large deformation contact problem in the compaction process of powder. The Coulomb friction law is used to simulate the friction between the rigid punch and the workpiece by the use of penalty approach. A double-surface cap plasticity model is employed together with the nonlinear contact friction algorithm within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die-pressing. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.

Mechanical models of fracture reactivation and slip on bedding surfaces during folding of the asymmetric anticline at Sheep Mountain, Wyoming

We use finite element methods to investigate the reactivation of fractures (opening and shearing) and the development of bedding-surface slip during the deformation of the asymmetric anticline at Sheep Mountain, Wyoming. A series of numerical simulations were run to show the effect of mechanical stratigraphy, layer thickness, slip on bedding surfaces, and tectonic shortening of the fold on the response of a representative three-layer (ductile, brittle, ductile) two-dimensional system. The model uses large deformation frictional contact mechanics to capture the response of existing fractures and slip along bedding surfaces, and considers both elastic and elastoplastic layer properties. The computational results demonstrate the relationships among overall configuration of the multilayer, slip on bedding surfaces, and the sequence and mode of deformation (opening versus shearing) of bed-perpendicular fractures. We show that fractures located in the hinge are mainly reactivated as joints and that those in the forelimb are predominantly reactivated as thrust faults. A flexural-slip mechanism develops during folding when the layers bounded by frictional bedding surfaces have similar stiffnesses. In contrast, when the difference in the layer stiffnesses is significant (softer outer layers) the deformation is accommodated within the softer units without exceeding the frictional strength of the bedding surfaces. A reduction of the middle layer thickness from 100 m to 10 m has a minor quantitative effect on the slip along the bedding surfaces. We compare the numerical results with fracture data collected at Sheep Mountain Anticline, and discuss the similarities and differences between the field observations and the model results.