Contact Formulation Research Articles

Nonlinear Dynamics Research of Ground Undulatory Fin Robot with Flexible Deformation and Frictional Contact.

The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

Effects of interfacial debonding on the stability of finitely strained periodic microstructured elastic composites.

Predicting failure initiation in nonlinear composite materials, often referred to as metamaterials, is a fundamental challenge in nonlinear solid mechanics. Microstructural failure mechanisms encompass fracture, decohesion, cavitation, compression-induced contact and instabilities, affecting their unconventional static and dynamic performances. To fully take advantage of these materials, especially in extreme applications, it is imperative to predict their nonlinear behaviour using reliable, accurate and computationally efficient numerical methodologies. This study presents an innovative nonlinear homogenization-based theoretical framework for characterizing the failure behaviour of periodic reinforced hyperelastic composites induced by reinforcement/matrix decohesion and interaction between contact mechanisms and microscopic instabilities. Debonding and unilateral contact between different phases are incorporated by employing an enhanced cohesive/contact model, which features a special nonlinear interface constitutive law and an accurate contact formulation within the context of finite strain continuum mechanics. The theoretical formulation is demonstrated using periodically layered composites subjected to macroscopic compressive loading conditions along the lamination direction. Numerical results illustrate the ways in which debonding phenomena, in conjunction with fibre microbuckling, may influence the critical loads of the examined composite solid. The sensitivity of the results obtained through the proposed contact-cohesive model at finite strain with respect to its implementation is also explored. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Interlaminar fracture toughness of metal/composite bonded joints under high-speed mode I loading considering the elastic vibration

In the present work, the mode I fracture toughness at the initiation of a crack in a metal-composite bonded joint under high-speed loading is calculated, considering the effect of the elastic vibration of the specimen. A new hybrid analytical-experimental method is developed, which integrates kinematics from Digital Image Correlation (DIC) analysis to an analytical model to determine the fracture toughness and its individual components. The analytical model is based on Timoshenko beam theory and incorporates a Lagrangian contact formulation. The conditions under which the hybrid method can be applied are analysed. The experiments are conducted on a novel test set-up, featuring a wedge accelerated by a projectile from an air gun that is able to load the Double Cantilever Beam (DCB) specimen with an opening displacement rate up to 2m/s. The results reveal a correlation between the fracture toughness, the displacement rate, and the vibrational characteristics of the specimen.

Nano-scale modeling of energy dissipation in a single lamella reveals the significant contribution of collagen-mineral sliding to intrinsic bone toughness

Although collagen-mineral sliding is recognized as one of the intrinsic mechanisms that contribute to the bone toughness, its precise role in energy release at the nano-scale, as well as its relationship to other intrinsic toughness mechanisms, remains unclear. This lack of understanding stems from the challenges associated with quantifying the specific nature of contact at the mineral-collagen interface, and the energy dissipation capacity resulting from plastic deformation at this scale. To address this issue, we developed a three-dimensional model of mineralized collagen fibril using ABAQUS, incorporating hyperelastic isotropic collagen, elastic isotropic mineral, and a cohesive contact formulation to represent the collagen-mineral interface. Knowing the properties of collagen and mineral and using a parametric modeling approach, we estimated the properties of contact based on experimental measurements of the stress-strain behavior in a single bone lamella, considering the angle of the collagen fibril in relation to the loading axis. By comparing the experimental elastic modulus with the model predictions, we determined that the cohesive contact exhibited a maximum strength of 9 MPa and a fracture energy of 50 mJ/m2 within the bone. Further analysis indicated that fracture energy at the collagen-mineral interface is potentially closer to 5 mJ/m2. Using these findings, we concluded that the interfaces were responsible for 52% to 98% of the energy release in mineralized collagen fibrils, depending on collagen angle, both directly and indirectly by influencing stress and strain in adjacent collagen fibril. The results of this study demonstrated that plastic deformation at the collagen-mineral interface is the primary mechanism underlying bone toughness at the nano-scale. Importantly, we found that these conclusions held true regardless of the angle of the collagen fibril relative to the loading axis. The modeling framework presented in this study provides a valuable tool for investigating the elastic and post-yield behavior of bone across different mineral volume fractions at the nano-scale, and at the lamellar level.

Assessing the behavior of a hybrid model of the knee with contact surrogate under parameter uncertainties

Modeling the knee is an important factor in increasing the quality of life of both healthy individuals and patients. Nevertheless, the intricate nature of the knee makes this problem complicated. In this study, an extension to an established planar knee joint model with Hertzian contact pairs is proposed with contact mechanics based on polynomial chaos expansion surrogate. Firstly, the finite element (FE) model is made representing a contact pair of sphere-to-plane type with two layers on both bodies, corresponding to the cartilage and the bone. Five variables corresponding to both geometry and material parameters are used to parametrize this model. Then, 128 distinct variants of the FE model are created based on a quasi-Monte Carlo sequence. This dataset is used to train and validate the surrogate. The trained surrogate is proven to have predictive capabilities with an average nRMSE of 0.2% in randomized test/train splits. When included in a model of the knee and tested under parameter uncertainties in Monte Carlo simulations, it results in nRMSE of 58% for angular coordinate compared to the original model with Hertzian pair. This signifies the high influence of contact formulation on the model output and the need for more physically based models in knee contact modeling.

Contact formulations for analysis of micropolar media with finite continuum beam elements

Microscale beam-like structures are standard components of micromechanical systems in many devices. However, the small dimensionality affects their deformation characteristics and leads to misinterpretations of the results. Presenting such size dependency is possible with advanced continuum descriptions via introducing additional variables compared to the classical one. Hence, the problems where contact occurs require the readjustment of boundary conditions considering these extra parameters. That burdens the already challenging task of contact problem calculations and restricts most demonstration examples to two-dimensional problems and geometrical linearity. The resolution of the imposed restrictions within finite element modeling further emphasizes the usage of advanced media in design and facilitates its application to various problems, which is the aim of this paper. The delivery of that task is as follows. Firstly, we present the kinematics and material descriptions for the micropolar media. The authors propose to use a newly developed continuum-based micropolar beam formulation to avoid an overwhelming computational burden and, at the same time, deal with nonlinear stress–strain relations. Secondly, the work develops a contact approach within the micropolar theory from two-dimensional to three-dimensional elasticity, although the contact is considered frictionless. Finally, it compares two existing contact formulations, including the developed one, for the contact beam problems, using the examples of two collinear sliding beams’ bending.

Computational assessment of carbon fabric reinforced polymer made prosthetic knee: Mechanics, finite element simulations and experimental evaluation.

A prosthetic knee is designed to replace the functionality of an anatomical knee in transfemoral amputees. The purpose of a prosthetic knee is to restore mobility and compensate amputees for their impairment. In the present research numerical modelling and simulation of a carbon fabric reinforced polymer made polycentric prosthetic knee with four-bar mechanism was performed. Virtual prototyping with computer-aided design and computer-aided engineering software ensured geometric and structural stability of the knee design. The linkage mechanism, instantaneous centre's location and trajectory were investigated using multibody dynamics and analytical formulations. Computational simulations with a non-linear finite element model were employed with joints, contact formulations and an orthotropic material model to predict the displacement, stress formulated and life of the knee prosthesis under static and cyclic loading conditions. Finite element analysis assessed the strength and durability of knee in accordance to standards. Maximum Principal stress of 155 MPa and life expectancy of 3.1 × 106 cycles were determined for the composite knee through numerical simulations ensuring a safe design. Experimental testing was also conducted as per standards and the percentage error was estimated to be 2.52%, thereby establishing the validity of the finite element model deployed. This type of simulation-based approach can be implemented to efficiently and affordably design and prototype a prosthetic knee with desired functioning criteria.

Numerical modelling of contact adhesion in a random assembly of elastic–plastic particles

The prediction of tensile strength properties of powder compacts remains an important industrial issue. In particular, one of the main problems of the powder compaction process is the failure of compacts. Indeed, some powder compacts exhibit cracks which appear during compaction. Such defects occur due to localised tensile or shear stresses, for example close to geometrical singularities. They are also related to the ability of a powder to create enough adhesion at contacts between particles to withstand tensile stresses. Therefore, cracks are a consequence of phenomena occurring at the particle scale and below, down to the molecular scale. To help understanding this mechanism, a particle-scale, numerical method called the multi-particle finite-element method was developed using the finite-element software suite Abaqus (Abaqus 6.14 Documentation, 2016). Such a method allowed to explicitly model the microstructure of a granular media idealised as an assembly of elastic–plastic spheres. The particles were meshed such that their deformations were fully taken into account, using a continuum-mechanics-based material model. The interactions between particles were managed using finite-element contact formulations. A multi-scale, adhesive contact model was developed based on the literature and implemented into the multi-particle finite-element code. The contact model was based on a surface energy formulation weighted by the roughness model developed by Pullen and Williamson (1972). It introduced a novel aspect, the development of adhesion under the effect of external mechanical loads, which is consistent with the cold compaction process. This model was then applied to predict the mesoscopic properties of a packing of spheres, i.e. its response to mechanical stresses of any type, in particular strongly deviatoric stress paths. Such a method intends to be a help toward the development of an efficient continuum model for the modelling of the powder compaction process.

Simulating the rheology of dense suspensions using pairwise formulation of contact, lubrication and Brownian forces

Dense suspensions of solid particles in viscous liquid are ubiquitous in both industry and nature, and there is a clear need for efficient numerical routines to simulate their rheology and microstructure. Particles of micron size present a particular challenge: at low shear rates, colloidal interactions control their dynamics while at high rates, granular-like contacts dominate. While there are established particle-based simulation schemes for large-scale non-Brownian suspensions using only pairwise lubrication and contact forces, common schemes for colloidal suspensions generally are more computationally costly and thus restricted to relatively small system sizes. Here, we present a minimal particle-based numerical model for dense colloidal suspensions that incorporates Brownian forces in pairwise form alongside contact and lubrication forces. We show that this scheme reproduces key features of dense suspension rheology near the colloidal-to-granular transition, including both shear thinning due to entropic forces at low rates and shear thickening at high rates due to contact formation. This scheme is implemented in LAMMPS, a widely used open source code for parallelised particle-based simulations, with a runtime that scales linearly with the number of particles, making it amenable for large-scale simulations.

Effect of forward kinematics on the motion-trajectory oscillations and inertia forces

In vehicle-motion scenarios, non-negligible centrifugal-force component that cannot be balanced by the gravity force may develop, leading to increase in wheel-contact forces. This inertia-force component, which depends on vehicle forward velocity and oscillation amplitude, can arise when the vehicle negotiates straight road or railroad track. An approach based on the Frenet geometry and recorded motion trajectory (RMT) is introduced in this investigation to examine forward-kinematics effect on the motion geometry and inertia forces and to obtain general expression of the ratio between the amplitudes of the centrifugal and gravity forces. While the two three-dimensional vectors of applied and constraint forces define Frenet osculating plane of mass-center trajectories; for non-centroidal points, the osculating plane is defined by two vectors; the resultant of the applied and constraint forces and an inertia-force vector that depends on the angular velocity and angular acceleration. The concepts of instantaneous motion plane (IMP) and instantaneous zero-force axis (IZFA) are used to convert three-dimensional Cartesian forces into two-dimensional Frenet forces, based on the Frenet-Newton equations. Because contact forces can be formulated using two fundamentally different approaches; constraint contact formulation (CCF) and elastic contact formulation (ECF), the effect of the contact formulation on the IMP and IZFA orientation is examined. The results obtained, using railroad suspended wheelset example, demonstrate the following: (1) limitations of roller rigs that do not properly account for forward-velocity effect on the inertia forces; (2) difference between IMP and intermediate wheelset plane defined by wheelset lateral axis and global vertical axis; (3) non-negligible inertia centrifugal-force component in the absence of physical curvature; and (4) need to distinguish between physical and motion geometries; the latter is one that directly enters into the definition of the inertia forces. Trajectories with oscillation frequency independent of the oscillation amplitude for a given forward velocity are also identified.

Frictional contact multi-point constraint in two dimensions

Node-to-Segment slideline frictional contact formulation as one of the simplest penalty-based contact algorithms could be further simplified to a general Multi-Point Constraint formulation. This effective MPC formulation is proposed in this paper.Two case specific and a general MPC formulations are proposed which uses the distance vector of the master boundaries with respect to a unique point for the calculation of the contact interaction. Accordingly, the general master surface is reduced to a control node and its MPC distance vector and MPC normal matrix. As a result, the numerous expressions for the contact stiffness matrix will be reduced to its first simple expression, exclusively.Static and dynamic examples are solved to illustrate that the MPC algorithm proposed maintains the same accuracy of Node-to-Segment algorithms while presents the efficiency and user-friendly properties of the multiple-point constraint algorithms used in advanced finite element programs.

Ghost material in geotechnical applications of the CEL method

The Coupled-Eulerian-Lagrangian (CEL) method is an established numerical approach for the simulation of geotechnical boundary value problems involving soil–structure interaction and large deformations. A consequence of this approach is the existence of two overlapping numerical meshes, one Lagrangian and one Eulerian. The structure is usually modeled by the Lagrangian part while the soil is represented by the Eulerian part. The material within the Eulerian part of the mesh overlap may be considered a kind of ’virtual’ or ’ghost’ material, as it only exists due to the numerical approach and has no counterpart in reality. Up to now it has never been evaluated how much this ghost material influences the simulation results. In this study, two geotechnical applications of CEL are analyzed which contain ghost material in a zone of soil–structure-interaction. Each example implements several model variants by applying different material combinations and contact formulations. Additional simulations with a pure Arbitrary-Lagrangian-Eulerian (ALE) approach, in which no ghost material exists, are presented to give further insights.

A Computational Model for All-Solid-State Batteries Coupling Electrochemistry and Solid Mechanics on Resolved Microstructures Enabling Optimization of Battery Electrode Design

All-Solid-State Batteries (ASSB) are a promising technology to replace conventional Lithium-Ion Batteries (LIB) since the energy density and fast charging capability of LIBs are projected to reach a physical limit soon. In this regard, the ASSB technology is considered superior, especially if the incorporation of the lithium metal anode, or other high-capacity anode materials like silicon is achieved. However, these systems still require intensive research as many physical effects, especially those concerning the interaction of electrochemistry and solid mechanics, are to date not well understood [1]. Most experimental investigations on ASSB cells are performed on laboratory scale and are usually operated at elevated mechanical pre-stress to obtain satisfactory system performance. The delamination of active materials and solid electrolyte during cycling is expected to be one of the key effects for the required mechanical pre-stress. Furthermore, a lot of experimental research focuses on the development of new material classes and their stability in the cell compound, while a systematic optimization of the cell setup is missing.Comprehensive computational models can help to generate insights in these regards as they allow for detailed investigations of local effects, which is often not possible in experimental setups. Another advantage of computational models compared to experiments is the ability to change input parameters in a fast and systematic way to quantify their influence on the battery cell performance and thereby help to speed up the optimization of battery designs. Since the multitude of physical effects that are relevant in ASSB are computationally challenging, a lot of modeling approaches rely on numerous simplifications like spatial homogenization or neglect of mechanical effects to name just two. However, such assumptions can significantly limit the validity of the model.We propose a novel computational model for ASSB [2] to thoroughly investigate the interdependence of electrochemistry and solid mechanics on resolved microstructures that vastly influence the behavior and the performance of an ASSB cell. It is based on nonlinear continuum mechanics and accounts for large deformations due to lithiation dependent volume changes of the active materials. The mass and charge conservations are consistently formulated to also ensure the conservation property in large deformation scenarios. Furthermore, the model is extended by interaction effects of electrochemistry and solid mechanics like a nonlinear contact formulation at the electrode-electrolyte interfaces to account for delamination phenomena and the subsequent absence of charge transfer reaction (see Fig. 1). We thereby show how delamination phenomena drastically change available percolation paths in the microstructure. The efficient parallel implementation of the computational model allows to investigate realistic three-dimensionally resolved microstructures of ASSB cells while accounting for the coupling effects of electrochemistry and solid mechanics. A combination of elaborate physical models and probabilistic methods enables to gain further understanding and to quantify main influencing factors on the cell performance. To showcase these capabilities and how they can be exploited to increase system understanding, we analyze how statistical values like the porosity, or the composition of the electrode microstructure influence the capacity of an ASSB cell and thereby contribute to find optimal electrode designs.

Dynamics of structures coupled to particle-chain impact dampers: A parametric numerical analysis

Particle impact dampers are dissipative devices that can easily be coupled to structures in order to reduce vibrations over a wide frequency range and in adverse environmental conditions. In this work, a multiple-sphere chain impact damper is coupled to a cantilever beam in order to attenuate its flexural motions. This simple configuration was chosen to better understand the energy dissipation phenomena by the device when the beam is subjected to random excitations. In addition, a parametric study of the coupled system is conducted in order to assert optimal working conditions of the damper. This study is mostly based on a numerical model of the vibro-impacting system, which was calibrated based on an experimental rig. Firstly, the computational modal basis of the bare beam was experimentally identified, and then theoretically modified taking into account the mass of the container. Secondly, calibration of the impact model was achieved by fitting the parameters of the contact formulation with respect to sphere-dropping experiments. Finally, extensive parametric computations are presented and discussed. The vibratory responses are computed using a frequency banded Gaussian random excitation, for several values of the excitation amplitude, for an increasing number of spheres and for several values of the damper clearance. The numerical results concern the r.m.s. motion of the spheres and the beam, the r.m.s. spheres/beam contact forces, the average mechanical and dissipated energies by the beam modes and the damper, as well as the effective beam modal parameters when fitted with the damper, which are essential results for understanding these damping devices. Finally, the numerical results are reduced into relevant dimensionless parameters, which prove reasonably effective in collapsing the dynamical data from such a highly nonlinear system. The present study thus highlights interesting essential features on the dynamics of structures coupled to multiple particle vibro-impact dampers under random excitation.

Dynamic modeling and simulation for pneumatic landing airbag system with frictional contact

The landing airbag system, a mechanism composed of thin-walled structures, is designed to ensure the safe landing of a lander. To investigate the dynamic behavior of the landing airbag with large deformations, a novel modeling approach incorporating gas exchange and frictional contact is proposed. The Absolute Nodal Coordinate Formulation (ANCF) is introduced to model the flexible airbag. Subsequently, the gas parameters inside the airbag are calculated by integrating the Control Volume (CV) Method and the energy conservation equation. Additionally, based on master–slave techniques, a frictional contact formulation for the thin-walled structure and the rigid plane is presented, in which the normal contact force is estimated using the penalty method, and the velocity-based friction model accounting for the stick–slip transition characterizes the tangential friction. Furthermore, the bounding box technology is adopted to improve contact detection efficiency. A series of numerical examples are performed, which demonstrates the proposed model’s advantages in terms of precision and versatility. Finally, the landing dynamic characteristics of the airbag landing system for the small lunar lander are successfully revealed, and the parameter analysis for the airbag system is expected to aid the design optimization of the airbag cushioning system.

Modelling Friction-Induced Dynamic Instability Dedicated for Isogeometric Formulation

Flutter-type dynamic instability induced by friction is a highly nonlinear phenomenon and computationally expensive to model through transient analysis. An efficient way to make inference of such instabilities in a dynamical system is through analyzing the first-order effect of a perturbation at one of its equilibrium with eigenvalue analysis. The contact characteristics of such dynamical systems are typically modelled through the normal compliance approach with inference from experiments. In this case, the dynamical response of the system is implied to be sensitive to the contact stiffness modelled through the normal compliance approach. Typically, with the normal compliance approach, the continuum of the contact interface is approximated through a set of nonlinear springs which can be interpreted as a collocation method. Such approximations or the numerical implication of contact formulations in general for such problems is not largely studied. We focus on a variational formulation-based contact formulation without domain decomposition which is computationally efficient with small sacrifice in accuracy, where we imply that the dynamical response can be robustly modelled with the given accuracy. Further, we expose the inadequacy of the collocation method for such problems, where the dynamical system is observed to be sensitive to the extent of inaccuracy as a result of collocation for low values of contact stiffness. The inferences numerically imply the characteristics of the dynamical system for variation in contact stiffness.

Numerical strategy for solving general C1‐continuous beam‐to‐beam contact problems

AbstractIn the context of a multibody numerical environment, when aiming at representing the contact interaction between bodies one needs the inclusion of special mathematical formulations. They can be geometrically described as surface‐to‐surface or line‐to‐line contacts, for instance. The last one is usually the natural choice when addressing beam‐to‐beam contact. In the present work, a geometrically nonlinear structural formulation is combined with a beam‐to‐beam spline‐based contact formulation with a particular numerical strategy to address challenging contact problems. The numerical strategy consists of introducing criteria to evaluate, characterize and decide about the contact problem solutions. According to these criteria, a contact problem solution may be accepted, rejected, or proceed to a degeneration process (as a simplification of the original tentative for the geometric description). The main advantages of the proposed technique are the lack of special contact formulations for ill‐defined contact problems and the automatic switch between degenerated and nondegenerated scenarios. Therefore, one can naturally handle scenarios of pointwise or conformal contact, even in situations of transition between such categories along the model evolution. The adopted spline‐based formulation includes normal and tangential contact contributions. To test the proposed strategy, several pointwise and conformal contact examples are proposed.

Constraining effect of load frames during full-scale rotor blade fatigue testing

In rotor blade fatigue tests used for the certification process, load frames are used to introduce the loads to the blade. These load frames have a constraining effect on the cross-sectional deformation. This work investigates these constraining effects using a finite element contact analysis on a current-generation commercial rotor blade. Two different load frame variants are considered: a conventional load frame covering most of the cross-section and a reduced load frame covering only the main spar caps. The interaction between blade and load frame is implemented via contact formulations, which allows pretensioning in combination with a flap and a lead-lag load case. Strains on the outer surface of the blade are evaluated and compared to an artificial reference loading. The area of influence of the load application through the load frame, in which the strains deviate significantly due to clamping effects, mostly corresponds to the 0.75 times the chord length assumed for the certification [1]. The strains in the trailing edge are significantly less affected by the reduced load frame variant than by the conventional one, thus potentially making it possible to consider the trailing edge at the position of the load frame as being properly tested for certification purposes.

Nonlinear data-driven zero-thickness joint element for concrete dam shear keys

Shear keys have been designed into the contraction joints of many concrete gravity dams to provide interlocking and shear transfer between adjacent monoliths. Their shear transferring capacity is usually estimated as the friction and cohesion that can be mobilized across a 2D plane located at the base of the keys. Once the shear stress in the contraction joint exceeds its estimated shear capacity, the shear keys are typically considered failed, and the joint may subsequently only transfer shear through concrete-concrete friction. This behaviour is often simulated in practice by placing tiebreak contact formulations along contraction joints. However, the nonlinear response and potential residual strength of the keys are usually ignored. In this paper, a novel nonlinear zero-thickness joint element named Macro Shear Key Joint Element (MSKJE) is proposed to simulate the response of a detailed shear key while capturing its nonlinear behaviour. A detailed geometrical numerical model of shear keys using a concrete Continuous Surface Cap Model (CSCM) is first validated against experimental data. Then, a parametric analysis of the number of keys in the joint, confinement pressure, initial opening and lateral boundary condition is performed using the validated detailed shear key numerical models. The stress-displacement responses obtained from the parametric analysis are used to calibrate the proposed MSKJE. At the local shear key scale, the MSKJE models present a very similar stress-displacement response compared to the detailed geometrical key models in terms of stiffness, maximum shear capacity, residual strength and nonlinear softening. At the global dam scale, the MSKJE presents a somewhat similar behaviour to the conventional tiebreak formulations. However, the advantages of the MSKJE over the tiebreak contact include its capability to simulate the nonlinear softening of shear keys, and residual sliding displacement, and, once calibrated, it is not necessary to estimate the shear keys capacity a priori.

A contact formulation using local frame of SE(3) group for corotational beam against rigid solid via moving signed distance field

In this paper, we present a contact formulation for corotational beam and rigid body based on body-attached signed distance field (SDF). All formulations are based on the unified SE(3) framework, whose prominent advantage lies in its frame invariance property. For solid body, the geometry surface can be implicitly described by a moving SDF. Consequently, the interaction between beams and rigid solids can be viewed as immersion in a field-described force. The contact force is formulated using SDF interpolation, and exact tangent matrices are provided to facilitate implicit iteration. Notably, this approach eliminates the need for contact detection during simulation, because the SDF database is constructed before the simulation. To enhance the spatial adaptivity of the SDF algorithm, we introduce an octree refinement strategy. Besides, we incorporate the concept of contact potential volume into the subdivided stopping criterion. Compared to the uniform SDF, this approach demonstrates higher generation speed and smaller errors. Several examples are used to verify the accuracy, convergence and efficiency of the proposed formulation. It is observed that the invariance property of SE(3) description leads to enhanced computational performance. Both frame invariance and SDF-based approach are expected to improve efficiency for large-scale problems. The presented method is easily applicable to other types of flexible bodies.