Contact Formulation Research Articles

Digital twin models of replicative ground stones: insight into simulating usage of Upper Paleolithic tools

This work presents the first attempt to create a physics-based digital twin model for predictive analysis of damage evolution during the use of ground stone tools (GSTs) in transformative tasks, encompassing the processing of raw resources for nutritional and non-alimentary purposes. The proposed methodology introduces a digital twin of the GSTs developed from 3D models generated using a photogrammetric technique based on Structure-from-Motion and Multi-View Stereo reconstruction. These models serve as the foundation for the development of the finite element (FE)-based digital twin model of the GSTs that exploits a contact formulation and the phase-field approach to simulate tool damage during pounding and grinding tasks. Defining the initial relative positions of the stones, their mechanical behaviour, and controlling the movement of the active stone in a way as close as possible to the real one, the digital twin model has been devised to evaluate how the surface damage is affected by perturbations in the loading conditions. The simulated damage is compared with the surface traces observed from experiments. The developed digital twin model aims at demonstrating its potentials for the GSTs investigations, as a supporting tool for experiments and for simulated tests on the archaeological records.

An adaptive model order reduction technique for parameter-dependent modular structures

AbstractThis work is concerned with an adaptive reduced order model of modular structures assembled from parameter-dependent substructures. The substructures are reduced by proper orthogonal decomposition (POD) and connected by means of a tied contact formulation. We present a method to adapt the matrices of the substructures to parameter changes. We employ interpolation on Grassmann manifolds for the parametric adaption of the projection matrices. For the adaptation of the stiffness matrices, we use the direct empirical interpolation method (DEIM). Manifold interpolation of the reduced stiffness matrices, cannot be applied here since it would require semi-positive definiteness, which is here not fulfilled because of necessary rigid body motion modes. The novelty of this work is the application of these interpolation methods to the special problem class of POD-based tied contact model order reduction. Furthermore, we show a methodology to compute significant snapshots on the substructure level to compute a POD basis that can be used in different global structures.

Separating fluid and solid contact constraints for hydro-mechanically coupled finite elements discretising fluid displacement

In the simulation of multi-phase porous media in contact with a structure, the contact constraints to be enforced depend on the spatially discretised variables and additional physical considerations. Typically, fluids in porous media behave differently at the contact interface than the solid phase through which they flow. Aspects of numerical modelling and considerations in defining constraints to model such phenomena are discussed in this work. To this end, a hydro-mechanically coupled finite element formulation discretising fluid displacement is supplemented by a mortar contact discretisation scheme enforcing the contact constraints separately for the different phases. Using the proposed multi-phase mortar contact formulation, it is demonstrated for which type of problems such a formulation offers advantages over formulations not distinguishing contact constraints of multiple phases.

Computational design of metamaterials with self contact

Inverse homogenization in combination with contact modeling, topology optimization and shape optimization is used to design metamaterials with optimized macroscopic response. The homogenization assumes length scale separation which allows the non-linear macroscopic behavior to be obtained by analyzing a single unit cell in a lattice structure. Self contact in the unit cell, which is modeled using a third medium contact method, is leveraged to obtain a complex homogenized response. The inverse homogenization problem is initially formulated as a topology optimization problem, where the macroscopic stress–strain behavior is tuned to our liking. However, it is well known that boundary phenomena are difficult to model in topology optimization and that interface modeling is crucial to accurately analyze contact. For that reason, the boundary representation of the topology optimized design is extracted and used as initial design in a subsequent shape optimization. The behaviors of our designs are verified by performing rigorous post-processing analyzes using conforming meshes and conventional contact formulations.

Effects of Crosswind on Pantograph–Catenary Wear Using Nonlinear Multibody System Dynamic Algorithms

In this study, a multibody system (MBS) computational framework is developed to determine the exact location of the contact point and wear prediction resulting from the pantograph–catenary interaction. The railroad vehicle models in the MBS computational framework comprise rigid-body railroad vehicles, rigid-body pantograph systems, and flexible catenary systems. To avoid incremental rotation, the nonlinear finite element absolute nodal coordinate formulation is used to model a flexible catenary system in the MBS computational framework. To avoid co-simulation processes, the rigid-body railroad vehicle and the pantograph and flexible catenary systems were integrated into the MBS algorithms. The pantograph–catenary interaction is modeled using an elastic contact formulation developed to include the effect of pantograph–catenary separation and sliding contact. The proposed MBS approach evaluates the location of the contact point, contact force, and normal wear rate (NWR) from the mechanical and electrical contributions. This investigation considers the vibration caused by a crosswind scenario and determines the numerical result in the case of a steady crosswind scenario. The steady crosswind scenario contains the advantage of pantograph–catenary aerodynamic design, and the vibration of the catenary system remains significant after the excitation of a steady crosswind. In the case of a steady crosswind, the higher value of the steady crosswind effect significantly increases the mean contact force and the NWR from the mechanical contribution. After crosswind load disturbances, the mean contact force decreases, but the standard deviation of the contact force increases. Therefore, the NWR from the electrical contribution increases significantly. However, the total NWR increases with the crosswind velocity.

A variationally consistent contact formulation based on a mixed interpolation point method and isogeometric discretization

This work enhances the robustness of the standard displacement-based (penalty Gauss-point-to-segment) contact formulation by applying the so-called Mixed Interpolation Point method (MIP). We consider a smooth isogeometric discretization of the contact surface in order to avoid various artificial discontinuities of the normal contact gap function. Like any existing MIP-enhanced formulation in terms of implementation, the proposed MIP contact formulation only requires a minor modification from an existing implementation of the standard contact formulation. Nevertheless, the improvement in robustness is shown to be quite significant, which often enables the simulation of contact problems with a larger load step size for efficiency and/or a larger penalty parameter for accuracy in the contact constraint. The formalism of the proposed MIP contact method is based on the idea of relaxing the contact constitution at integration points. To this end, at first the contact pressure is considered as an additional unknown apart from the displacement field, and the perturbed Lagrange multiplier potential is used to enforce the contact constraint. The MIP method then eliminates the contact pressure unknown directly at integration points, instead of discretizing it as it is done in the standard mixed contact formulations. As a result, the residual vector is identical to the standard displacement-based contact formulation. However, the resulting tangent stiffness matrix is different, as the MIP tangent is now based on an extrapolation of the contact pressure iteratively over Newton iterations. Several challenging numerical examples are presented to illustrate the accuracy, robustness and efficiency of the proposed formulation.

A computational framework for crack propagation along contact interfaces and surfaces under load

We present the first implicit computational framework for simulating crack propagation along contact interfaces and surfaces under load in three-dimensional bodies, which is distinct from modelling the contact interaction associated with crack closure. We restrict ourselves to brittle fracture and frictionless contact and focus on numerical challenges associated with the coupling of unilateral constraints emerging from the Griffith’s criterion and the contact conditions. The formulation is based on the configurational mechanics framework and is solved using the finite element method. The approach utilises a monolithic Arbitrary Lagrangian–Eulerian formulation permitting simultaneous resolution of crack propagation and unilateral contact constraints. Contact is embedded in the model using the well-known mortar contact formulation. Evolving cracks are explicitly modelled as displacement discontinuities within the mesh. Heterogeneous approximation of arbitrary order is used to discretise spatial displacements, enabling hp-adaptive refinement around the crack front and the contact interfaces traversed by the crack. The result is a holistic approach which handles issues associated with thermodynamic consistency, numerical accuracy and robustness of the computational scheme. Several numerical examples are presented to verify the model formulation and implementation; they also highlight how contact pressure and load applied on surfaces traversed by cracks influence their propagation. The robustness of the approach is validated by comparison of our simulations with existing numerical results and an industrial experiment involving cracks of complex morphologies propagating along contact interfaces between multiple deformable bodies.

On Practical Aspects of Variational Consistency in Contact Dynamics

Abstract Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

An isogeometric frictionless beam‐to‐beam contact formulation for hyperelastic Cosserat rods with unconstrained directors

AbstractWe present an isogeometric finite element formulation of frictionless beam‐to‐beam contact, using a Cosserat beam formulation with unconstrained directors. The beam's cross‐sectional deformation can be efficiently represented by director vectors. For the first order beam kinematics, Poisson locking due to the inability to represent linear in‐plane strain field in the cross‐section is alleviated by an enhanced assumed strain (EAS) method [1]. We employ a Gauss point‐to‐surface contact formulation combined with an active set iteration and a penalty method. The beam's cross‐sectional boundary as well as the axis is parameterized by a NURBS (non‐uniform rational B‐spline) curve, so that the lateral boundary surface has at least C2‐continuity, which yields a continuous surface metric and curvature in the closest point projection [2]. Since we do not employ zero stress conditions, a three‐dimensional nonlinear constitutive law can be straightforwardly utilized. We present several numerical examples, where a compressible Neo‐Hookean material is particularly considered.

A discrete element analysis of the mechanical behaviour of a lithium-ion battery electrode active layer

Lithium-ion batteries experience charge capacity loss during their lifecycle caused by mechanical phenomena. In this study, a discrete element method (DEM) simulation model, to link the local mechanical behaviour in the positive electrode active layer to its global mechanical properties, was developed. DEM is a suitable method to use as the electrode active layer has a granular structure and the model includes contact formulations for the active particles and the binder domain. Simulations of the calendering process and the measurement of the active layer's global mechanical properties is possible with the framework. The model developed can capture the pressure sensitivity of the active layer, which has been observed in experiments.

Remediation of Surfactants Used by VUV/O3 Techniques: Degradation Efficiency, Pathway and Toxicological Analysis.

Surfactants are increasingly used in systems that come into contact with the human body, such as food, pharmaceuticals, cosmetics and personal hygiene products. Increasing attention is being devoted to the toxic effects of surfactants in various human contact formulations, as well as the removal of residual surfactants. In the presence of ozone (O3), anion surfactants-a characteristic micro-pollutant-such as sodium dodecylbenzene sulfonate (SDBS) in greywater, can be removed using radical advanced oxidation. Herein, we report a systematic study of the SDBS degradation effect of O3 activated by vacuum ultraviolet (VUV) irradiation and the influence of water composition on VUV/O3, and determined the contribution of radical species. We show a synergistic effect of VUV and O3, while VUV/O3 reached a higher mineralization (50.37%) than that of VUV (10.63%) and O3 (29.60%) alone. The main reactive radicals of VUV/O3 were HO•. VUV/O3 had an optimal pH of 9. The addition of SO42- had almost no effect on the degradation of SDBS by VUV/O3, Cl- and HCO3- slightly reduced the reaction rate, and NO3- had a significant inhibition on the degradation. In total, SDBS had three isomers, with which the three degradation pathways were very comparable. Compared with SDBS, the toxicity and harmfulness of the degradation by-products of the VUV/O3 process decreased. Additionally, VUV/O3 could degrade synthetic anion surfactants from laundry greywater effectively. Overall, the results show the potential of VUV/O3 in safeguarding humans from residual surfactant hazards.

Stress-adaptive design of 2D contact interfaces with uniform pressure: A bio-inspired approach

In this article, a bio-mimetic approach to the generative design of contact interfaces with uniform pressure distribution is explored. During the morphogenesis process, biological joints grow depending on the states of stress generating a shape adapted to the mechanical loads. This adaptation is driven by two main rules: shear stress inhibits growth, whereas cyclic hydrostatic compressive stress promotes it. In this work, we demonstrate that the stress-dependent growth rules of synovial joint morphogenesis can be applied to generate contact interfaces with uniform pressure in engineering applications. For that, we present a mathematical model that comprises a contact formulation and a bio-inspired growth function; the model is solved numerically using finite element methods. We analyse the impact of the growth rules of synovial joint development on the contact pressure distribution of two-dimensional contact interfaces. We study the parameter space of the bio-inspired growth function to fine-tune the model parameters. The model is tested in several cases with different boundary conditions and material properties. The results show that the proposed generative design process leads to contact interfaces that provide uniform contact pressure. A quantitative metric of the uniformity of the contact pressure is also defined. This metric indicates that the bio-inspired process generates geometries as good as those obtained with other methods present in the literature without the need of an initial shape close to the final one. Thus, this work demonstrates that synovial joint morphogenesis can be adapted for generative design in engineering.

An Unconstrained Convex Formulation of Compliant Contact

In this article, we present a convex formulation of compliant frictional contact and a robust performant method to solve it in practice. By analytically eliminating contact constraints, we obtain an unconstrained convex problem. Our solver has proven global convergence and warm-starts effectively, enabling simulation at interactive rates. We develop compact analytical expressions of contact forces allowing us to describe our model in clear physical terms and to rigorously characterize our approximations. Moreover, this enables us not only to model point contact but also to incorporate sophisticated models of compliant contact patches. Our time stepping scheme includes the midpoint rule, which we demonstrate achieves second order accuracy even with frictional contact. We introduce a number of accuracy metrics and show that our method outperforms the existing commercial and open-source alternatives without sacrificing accuracy. Finally, we demonstrate the robust simulation of robotic manipulation tasks at interactive rates, with accurately resolved stiction and contact transitions, as required for meaningful sim-to-real transfer. Our method is implemented in the open-source robotics toolkit Drake.

Continuous gap contact formulation based on the screened Poisson equation

We introduce a PDE-based node-to-element contact formulation as an alternative to classical, purely geometrical formulations. It is challenging to devise solutions to nonsmooth contact problem with continuous gap using finite element discretizations. We herein achieve this objective by constructing an approximate distance function (ADF) to the boundaries of solid objects, and in doing so, also obtain universal uniqueness of contact detection. Unilateral constraints are implemented using a mixed model combining the screened Poisson equation and a force element, which has the topology of a continuum element containing an additional incident node. An ADF is obtained by solving the screened Poisson equation with constant essential boundary conditions and a variable transformation. The ADF does not explicitly depend on the number of objects and a single solution of the partial differential equation for this field uniquely defines the contact conditions for all incident points in the mesh. Having an ADF field to any obstacle circumvents the multiple target surfaces and avoids the specific data structures present in traditional contact-impact algorithms. We also relax the interpretation of the Lagrange multipliers as contact forces, and the Courant–Beltrami function is used with a mixed formulation producing the required differentiable result. We demonstrate the advantages of the new approach in two- and three-dimensional problems that are solved using Newton iterations. Simultaneous constraints for each incident point are considered.

Nonlinear and chaotic dynamics of a vibratory conveying system

In this work, a simulation model of a vibratory conveying system is presented. The simulation model is based on a continuous contact formulation in vertical direction which is extended by a friction force in horizontal direction to simulate a conveying process. In contrast with complex 3D simulation tools, it enables the understanding of previously unexplained phenomena such as multiple feeding velocities at the same excitation amplitude, which are observed in practical measurements. The parameters that have an influence on this effect are investigated, and a method for predicting and adjusting the occurrence of multiple solutions is developed. It is shown that the calibration of the system is very difficult in practice, as it depends significantly on the initial conditions which are difficult to reproduce and predict. It is also shown that the system can exhibit chaotic behavior in some configurations. These chaotic states are shown with the simulation model by means of parameter studies, and the point at which the system becomes chaotic is predicted with the method of Lyapunov exponents and fractal dimensions. Knowledge of the chaotic states can be used to calibrate the conveyor, as they depend only on the excitation and not on the initial conditions. The interdependencies of the initial conditions are also discussed in more detail. Therefore, this work provides a deeper understanding of complex conveying processes using a simple simulation model.

Experimental and numerical study of structural damping in a beam with bolted splice connection

The objective of this research is to develop a numerical model of one widely used bolted beam splice connection that dissipates energy through structural damping. The reference experimental setup is carefully designed to obtain the highly nonlinear dynamic response due to the suddenly released load. The fact that the monolithic beam with welded connection has a linear response is utilized for the initial calibration of the numerical and experimental models. Then, the numerical model of bolted beam splice connection is verified and adopted through an iterative process. The influences of time and spatial integration, bolt load application, element type, contact formulation, bulk viscosity, and mass scaling are discussed. A special attention is given to the load application and load release functions. After the verification, the Abaqus/Explicit numerical model is validated through the comparison with experimental data, where an appropriate friction coefficient is adopted. It is demonstrated that the nonlinear structural damping occurs due to the complex micro slip behavior at the contact interface.

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.

Reduced order modeling of modular parameter dependent structures based on proper orthogonal decomposition and mesh tying

AbstractA model order reduction technique in combination with mesh tying is used to efficiently simulate many different structures that are assembled from a set of substructures. The stiffness matrices of the substructures are computed separately and assembled into a global stiffness matrix with tied contact formulation. Reducing the degrees of freedom of each substructure with a projection‐based model order reduction technique further decreases the computational time. The mode matrices that project the system into the low‐dimensional subspace are computed for each module separately with proper orthogonal decomposition and the method of snapshots. For the development and optimization of new construction strategies for fiber‐reinforced concrete, many different combinations of the modules have to be tested. The mechanical behavior of these modules depends on a set of parameters. Here the parameters are the fiber directions for transversely isotropic material behavior and parameters that describe the shape of the module. The sensitivity of the model order reduction technique to parameter changes requires a mode adaption technique to obtain reasonable results. Mode matrices for any parameters are computed by interpolating in a tangent space to the Grassmann manifold.

Dynamic modeling and analysis for inflatable mechanisms considering adhesion and rolling frictional contact

A new modeling approach is proposed for dynamic analysis of inflatable mechanisms with large deformations, involving frictional contact and adhesion. Firstly, the Absolute Nodal Coordinate Formulation (ANCF) shell element is employed to model the flexible appendage. Then, by combining the master-slave and master-master techniques, a frictional contact formulation for the thin shell and the rigid cylinder is presented, which can capture the stick–slip transition and address both large sliding and rolling scenarios. In addition, a modified contact detection approach is proposed by optimizing the contact detection region to effectively avoid mutual over-penetration and improve detection efficiency. Furthermore, an adhesion element with failure mechanism is developed. Finally, a series of numerical examples are carried out to validate the proposed modeling approach. Together with the successful simulation against the resistance controlled deployment of an inflatable mechanism, the advantages of the proposed approach are demonstrated. Moreover, the most appropriate parameters for adhesion constitutive relationship are obtained to serve the adhesion-based controller design.

Modeling the debonding process of osseointegrated implants due to coupled adhesion and friction

Cementless implants have become widely used for total hip replacement surgery. The long-term stability of these implants is achieved by bone growing around and into the rough surface of the implant, a process called osseointegration. However, debonding of the bone–implant interface can still occur due to aseptic implant loosening and insufficient osseointegration, which may have dramatic consequences. The aim of this work is to describe a new 3D finite element frictional contact formulation for the debonding of partially osseointegrated implants. The contact model is based on a modified Coulomb friction law by Immel et al. (2020), that takes into account the tangential debonding of the bone-implant interface. This model is extended in the direction normal to the bone-implant interface by considering a cohesive zone model, to account for adhesion phenomena in the normal direction and for adhesive friction of partially bonded interfaces. The model is applied to simulate the debonding of an acetabular cup implant. The influence of partial osseointegration and adhesive effects on the long-term stability of the implant is assessed. The influence of different patient- and implant-specific parameters such as the friction coefficient mu _text {b}, the trabecular Young’s modulus E_text {b}, and the interference fit I!F is also analyzed, in order to determine the optimal stability for different configurations. Furthermore, this work provides guidelines for future experimental and computational studies that are necessary for further parameter calibration.