Penalty-based Contact Research Articles

Nonlinear vibrations analysis of a fuel rod in nuclear heating reactor

Nonlinear vibrations of a single fuel rod in nuclear heating reactor with fixed-fixed ends and subjected to various excitation levels are comprehensively analyzed using explicit dynamics. The responses of empty, pellet-filled, and water-submerged rod are investigated. Pellet-cladding and pellet-pellet interactions are addressed by a penalty-based contact treatment, meanwhile the fluid-structure interactions (FSI) between the vibrating fuel rod and surrounding coolants are simulated by the Arbitrary Lagrangian-Eulerian (ALE) method, wherein the water is modeled as Eulerian elements. The results reveal that both empty and pellet-filled rods exhibit frequency hardening phenomena, where eigenfrequencies increase with vibration amplitude due to geometric nonlinearity. The damping decay resulting from fuel pellet motions is found to be positively correlated with vibration amplitude, thereby enhancing the reactor safety. For submerged rod, the frequency decreases due to added mass effects, and the overall system damping increases despite structural damping from dry friction and impacts is reduced.

Simulation of homogenization behavior of compacted bentonite containing technological voids using modified penalty-based contact model

Low-density zones generated during the bentonite blocks/voids homogenization process in the repository may serve as potentially preferential paths for radionuclide leakage. More importantly, void closure during homogenization process involves complex contact problems, where the stiffness at the contact interface typically undergoes significant fluctuations. In this work, with contact interface stiffness addressed through a step function approach, a modified penal.ty-based contact model was proposed to simulate the contact behavior involved at the gap closure stage of the bentonite/gap assemblage homogenization process. Then, unsaturated infiltration swelling tests on bentonite block (1.7 Mg/m3)/gap (width: 2 mm) assemblages were performed, and the variation of dry density at different hydrated times (0, 24, 72, 168, and 720 h) in specific areas were measured. Based on the results, time-dependent swelling pressure profiles of the assemblage were acquired, while the homogenization process was evaluated. Results reveal that after approximately 40 h of hydration, the gap is completely closed, and the radial stress condition of the compacted bentonite transits progressively from the initial free swelling into a constant volume expansion state. The swelling pressure correspondingly develops quickly to a peak value at 1.8 MPa once the hydration starts, then decreases to a valley value of 1.4 MPa at the complete gap closure, and subsequently begins to increase to the final stable value of 1.8 MPa. Further examination reveals that as hydration advances, dry density of the assemblage converges to the expected final dry density with a maximum residual inhomogeneity of about 2 %. Finally, validations demonstrate that the proposed model can accurately reproduce deformations of the assemblage during the free swelling stage, and the swelling pressure profiles. A comparative analysis was made with the previous approach of identifying gaps as highly deformable materials, revealing that the proposed model overcomes the traditional limitations associated with the separation or penetration behavior occurring between the compacted bentonite and contact boundaries during the gap closure.

Modeling of interfacial multi-cracks in dissimilar laminated structures using a nodal-based Lagrange multiplier/cohesive zone approach

Recent decades have witnessed a growing interest in simulating interfacial debonding in laminated structures using cohesive zone (CZ)-based algorithms. In the present work, we develop a nodal-based Lagrange multiplier/cohesive zone (LM/CZ) approach to achieve the end with a special focus on interfacial multi-cracks in dissimilar laminated structures. The main advantages of the developed approach are four-folded: (1) being flexible for the mesh discretization of dissimilar laminated structures and compatible with various element types; (2) being computationally more efficient for dissimilar laminated structures; (3) addressing the so-called artificial compliance issue arising in intrinsic CZ modeling; (4) providing smooth transitions from uncracked to cracking states, and from cracking to contact states. In the presented approach, nodal pairs are constructed with the aid of a searching algorithm capable of dealing with matching and non-matching meshes in a unified manner. For each nodal pair, the displacement continuity is accurately enforced using LMs that are calculated in a predictor–corrector manner with a limited number of iterations. The constraints for nodal pairs are switched from LMs to cohesive forces after a defined criterion is satisfied. The non-penetration condition between interfaces is fulfilled using penalty-based contact forces in the cracking and pure contact states, leading to a smooth transition from cracking to contact states. The accuracy and effectiveness of the presented approach are validated using three benchmark tests. Finally, the capacity of the approach to describe interfacial multi-crack behaviors of dissimilar laminated structures has been exploited and demonstrated.

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.

Influence of coil contact on static behavior of helical compression springs

Large deformations of helical springs are affected by coil contact, but most available spring modelling techniques only account for nonlinear vertical motion, and Finite Elements (FE) nonlinear analysis that considers contact between coils can be very expensive. A 2D model based on equivalent beam and penalty-based contact algorithm is developed for efficient yet realistic prediction of non-uniform spring deflection. The proposed model is tested versus FE, where the helical wire is modelled using beam elements. Two scenarios are taken into account: a cylindrical spring in compression/bending and a progressive conical spring under simple compression. It is shown that the proposed model matches FE at a very low computational cost.

Experimental and numerical studies on the braiding of carbon fibres over structured end-fittings for the design and manufacture of high performance hybrid shafts

Braiding is an attractive manufacturing method for tubular elements such as hollow shafts and struts. One of the main challenges however is the integration of suitably performing end-fittings. Recent advances in additive layer manufacture have enabled the fabrication of end-fittings which can be ‘co-impregnated’ or ‘co-cured’ with the fibre preform in a single step, i.e. without the need for secondary adhesive bonding. This requires the introduction of protrusions onto the surface of the end-fitting to promote mechanical interlocking with the fibres. However, the lack of accurate modelling tools for the simulation of this manufacturing process means that much empiricism is currently used in the design of such structures. A novel numerical framework is presented here for the full-scale simulation of the braiding process over structured end-fittings. Nonlinear finite element analysis is applied at the meso-scale, with strands of beam elements representing individual yarns and meshed surfaces modelling the mandrel and tooling. Penalty-based contact formulations are then used to simulate all inter-yarn and yarn-metal interactions, enabling detailed predictions of fibre paths around surface protrusions. In order to verify and validate this numerical framework, a series of full-scale braiding experiments was conducted using additively-manufactured thermoplastic mandrels. Final braid patterns as well as the occurrence of braid imperfections were investigated and compared to model predictions. It is shown that the proposed modelling strategy reproduces well the trends observed experimentally in terms of final braid quality. A parametric study was then conducted on the effects of initial end-fitting alignment with respect to oncoming yarns, suggesting that better control over this parameter could reduce considerably the occurrence of braid imperfections.

Modelling and simulation methodology for unidirectional composite laminates in a Virtual Test Lab framework

A reliable virtual testing framework for unidirectionally laminated composites is presented that allows the prediction of failure loads and modes of general in-plane coupons with great realism. This is a toolset based on finite element analysis that relies on a cohesive-frictional constitutive formulation coupled with the kinematics of penalty-based contact surfaces, on sophisticated three-dimensional continuum damage models, and overall on a modelling approach based on mesh structuring and crack-band erosion to capture the appropriate crack paths in unidirectional fibre reinforced plies. An extensive and rigorous validation of the overall approach is presented, demonstrating that the virtual testing laboratory is robust and can be reliably used in for composite materials screening, design and certification.

6-DoF Haptic Rendering of Static Coulomb Friction Using Linear Programming.

Simulating frictional contact between objects with complex geometry is important for 6-DoF haptic rendering applications. For example, friction determines whether components can be navigated past narrow clearances in virtual assembly. State-of-the-art haptic rendering of frictional contact either augments penalty contact with frictional penalty springs, which do not prevent sliding and cannot render correct static friction, or uses constraint-based methods that are difficult to meet the stringent haptic loop computation time requirements for complex geometry. We give a 6-DoF Coulomb friction haptic rendering algorithm for distributed contact between rigid objects with complex geometry. Our algorithm is compatible with the fast point vs implicit function penalty-based contact method such as the Voxmap-PointShell method. Our algorithm incorporates the maximal dissipation principle and produces correct static friction, all the while inheriting the speed of penalty-based methods. We demonstrate our algorithm on several challenging 6-DoF haptic rendering examples.

Impact Dynamics Simulation for Multilayer Fabrics of Various Weaves

The high strength, light weight, and flexibility of fabric protection systems makes them an effective impact mitigation solution in some important engineering applications. Examples include body armor, fan blade containment systems, and orbital debris shielding. Most soft armor protection systems employ a plain weave fabric, suitable for use in flat or slightly curved geometries. However, future fabric protection system designs may employ nonplain weaves to protect highly curved surfaces (such as personnel extremities) or to optimize the performance of protection systems composed of a nonhomogeneous fabric stack. In recent research, the authors developed an improved hybrid particle-element method to simulate the ballistic impact performance of fabric protection systems. The new formulation is the first to address the full range of modeling issues (including penalty-based contact–impact, excessive yarn bending stiffness, and mass or energy discard) that have limited the effectiveness of legacy finite element-based fabric modeling methods for over two decades. Validation simulations modeled three-dimensional perforation dynamics in multilayer fabric stacks, and showed good agreement with new ballistic experiments conducted at three different target-layer counts for two different projectile types and four different weaves.

Implicit Multibody Penalty-BasedDistributed Contact.

The penalty method is a simple and popular approach to resolving contact in computer graphics and robotics. Penalty-based contact, however, suffers from stability problems due to the highly variable and unpredictable net stiffness, and this is particularly pronounced in simulations with time-varying distributed geometrically complex contact. We employ semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination and a SVD solver to simulate stable penalty-based frictional contact with large, time-varying contact areas, involving many rigid objects and articulated rigid objects in complex conforming contact and self-contact. We also derive implicit proportional-derivative control forces for real-time control of articulated structures with loops. We present challenging contact scenarios such as screwing a hexbolt into a hole, bowls stacked in perfectly conforming configurations, and manipulating many objects using actively controlled articulated mechanisms in real time.

Graphic Processing Units (GPUs)-Based Haptic Simulator for Dental Implant Surgery

This paper presents a haptics-based training simulator for dental implant surgery. Most of the previously developed dental simulators are targeted for exploring and drilling purpose only. The penalty-based contact force models with spherical-shaped dental tools are often adopted for simplicity and computational efficiency. In contrast, our simulator is equipped with a more precise force model adapted from the Voxmap-PointShell (VPS) method to capture the essential features of the drilling procedure, with no limitations on drill shape. In addition, a real-time torque model is proposed to simulate the torque resistance in the implant insertion procedure, based on patient-specific tissue properties and implant geometry. To achieve better anatomical accuracy, our oral model is reconstructed from cone beam computed tomography (CBCT) images with a voxel-based method. To enhance the real-time response, the parallel computing power of GPUs is exploited through extra efforts in data structure design, algorithms parallelization, and graphic memory utilization. Results show that the developed system can produce appropriate force feedback at different tissue layers during pilot drilling and can create proper resistance torque responses during implant insertion.

A penalty-based contact element for pipe and 3D rigid body interaction

In this paper a contact element tailor-made for global response prediction of pipelines subject to interaction with rigid 3-dimensional bodies is presented. A continuous representation of the contact geometry is applied. The contact contribution to virtual work and associated linearizations are presented on matrix format suitable for implementation into computer codes based on a co-rotated description of beam kinematics. Experimental tests of trawl gear and subsea pipeline interference are used to validate the performance of the element. The benefit of including a tangent stiffness matrix proportional to the normal contact force and the effect of performing artificial symmetrization of the linearized friction contribution are investigated in terms of numerical efficiency.

Efficient yarn-based cloth with adaptive contact linearization

Yarn-based cloth simulation can improve visual quality but at high computational costs due to the reliance on numerous persistent yarn-yarn contacts to generate material behavior. Finding so many contacts in densely interlinked geometry is a pathological case for traditional collision detection, and the sheer number of contact interactions makes contact processing the simulation bottleneck. In this paper, we propose a method for approximating penalty-based contact forces in yarn-yarn collisions by computing the exact contact response at one time step, then using a rotated linear force model to approximate forces in nearby deformed configurations. Because contacts internal to the cloth exhibit good temporal coherence, sufficient accuracy can be obtained with infrequent updates to the approximation, which are done adaptively in space and time. Furthermore, by tracking contact models we reduce the time to detect new contacts. The end result is a 7- to 9-fold speedup in contact processing and a 4- to 5-fold overall speedup, enabling simulation of character-scale garments.

Handling contact in multi-domain simulation of automobile crashes

This paper proposes a method to deal with unilateral contact in multi-domain, multi-time-scale calculations in explicit dynamics. The advantage of the approach chosen, which relies on a penalty-based contact model and a “master–slave” representation, is that it enables maximum uncoupling of each subdomain, which can evolve with its own stability time step. The algorithm involved guarantees kinematic continuity at the interfaces while exchanging minimal information among subdomains. Three examples of applications show the validity and the efficiency of the method compared to the classical, single-domain approach.