Nonlinear Material Response Research Articles

The stiffness adjustable wheel mechanism based on compliant spoke deformation

This study proposes a variable-stiffness mechanism for non-pneumatic tires such that can actively adapt to various environments. Non-pneumatic tire is a compliant wheel structure that offers superior robustness and adaptability compared to pneumatic tires. However, the tire designed for certain terrain exhibits relatively high rolling resistance and inadequate suspension. To address these problems, a stiffness-adjustable wheel (SAW) that can modify the force applied to the contact surface is introduced in this study. In addition, the shape of SAW is optimized to maintain a desirable range of stiffness under different conditions. The optimization is conducted with experimental method, because nonlinear response of material and interference between components make it difficult to predict the characteristic of the wheel at large deformation. The SAW has potential for application in various mobile platforms to provide adequate stiffness for a variety of terrains and driving conditions.

Avaliação sísmica em um pórtico de concreto armado considerando a modelagem com plasticidade concentrada e distribuída

Abstract Researchers must decide on how they will model the non-linear material response in a Finite Element simulation to assess seismic vulnerability. This paper aims at giving an insight into these modelling decisions by comparing Fiber and Lumped Plasticity Finite Element Models in static and dynamic non-linear analysis in a RC frame. The methodology is based on the performance-based earthquake engineering to determine the expected damage on structures. The results indicate that both models are in good agreement with the static analysis, and when considering Extensive and Complete Damage Limit States on the dynamic analysis. The choice between them depends on the main goals of the research and resources available, since they have a significant difference in processing time.

A controllable humidity sensitivity measurement solution based on a pure FPI fiber tip and the harmonic Vernier effect

Hygroscopic films used to enhance the humidity sensitivity of fiber-optic sensors often experience material aging and nonlinear response issues. To address this issue, this study proposes a controllable humidity sensitivity measurement solution that offers a simple and cost-effective fabrication process without requiring humidity-sensitive material sensitization. The solution is based on a Fabry-Perot interferometer (FPI) fiber tip and the harmonic Vernier effect. By employing a cascade structure of single-mode fiber (SMF)-hollow core fiber (HCF)-no core fiber (NCF) with fiber grinding techniques, the FPI-based fiber sensing probe constructed a resonance cavity to detect small variations in air refractive index (RI) induced by humidity. A reference spectrum, which can flexibly control parameters, such as free spectral range (FSR), contrast, phase, and intensity, is superimposed onto the sensing spectrum acquired by the FPI fiber sensing tip. By extracting features from the internal envelope generated by the harmonic Vernier effect, the mapping relationship between the center wavelength of the inner envelope and the humidity is determined. The harmonic Vernier effect amplifies the humidity sensitivity of the fiber-optic FPI sensing tip, with the magnification factor determined by the optical path length (OPL) detuning of the created reference and sensing spectra. For the harmonic order j = 4, a humidity sensitivity of approximately 76.01 pm/% RH@ 24 ℃ was achieved without using hygroscopic material sensitization. The proposed solution offers numerous advantages and enables high-precision and high environmental reliability humidity monitoring.

The impact of the nonlinear concrete behaviour on the required liner thicknesses of spray-repaired concrete pipes

Buried reinforced concrete pipes (including sewers, stormwater pipes and other gravity flow structures) that experience unsafe levels of deterioration are commonly rehabilitated using trenchless solutions, such as the application of cementitious liners. Cementitious liners are centrifugally cast onto the inner surface of the damaged pipes with a spinning head that travels along the length of the pipe. Once cured, the liner increases the strength of the damaged pipe to resist applied earth and surface loads. A design method previously proposed by the authors provides guidance for selecting the required liner thickness to rehabilitate deteriorated concrete pipes situated at deep burials. However, this design method considers the linear elastic behaviour of the soil and pipe materials. Neglecting the nonlinear effects of crushing concrete within the host pipe may impact the predicted liner thicknesses for repair. Thus, the current study evaluates the impact of incorporating nonlinear compressive material behaviour on the required liner thicknesses to repair damaged concrete pipes. The required liner thicknesses obtained from the nonlinear version of the design method for rehabilitations of several pipes selected from the ASTM C76-11 Standard experiencing varying levels of deterioration are compared to thicknesses obtained using the authors' linear elastic solutions. The comparisons indicated that considering the nonlinear material response of the concrete generates slightly larger estimates of required liner thickness. The discrepancies between the estimated liner thicknesses were observed to be insignificant for pipes experiencing cracking and losses of concrete cover, demonstrating that the linear elastic model is suitable for design purposes. However, for damaged pipes situated at deep burials experiencing losses of tensile reinforcement, the discrepancies between the liner and nonlinear calculations become more significant. It is recommended that the results of the linear elastic model be checked with the nonlinear model for the repair of pipes experiencing loss of tensile reinforcement, or for deeply buried pipes.

Nonlinearity shaping in nanostructured glass-diamond hybrid materials for optical fiber preforms

Nanodiamond integration with optical fibers has proved a compelling methodology for magneto-optics. We reveal that the applicability of nanodiamonds in nonlinear optics goes beyond the previous demonstrations of frequency converters. Instead, we exploit the recently reported volumetric integration of nanodiamonds along the optical fiber core and show that the nonlinear response of glasses can be manipulated by nanodiamonds. By taking the mature z-scan approach we measure the nonlinear absorption and nonlinear refraction of three dielectric materials containing nanodiamonds in different concentrations and sizes. The work begins with nanodiamond-water suspensions, which offer the advantage of rapidly assessing the dependence of the nonlinear refractive index on the nano-particle concentration and size. Subsequently we investigate two fiber preforms based on silica and soft glass doped with nanodiamonds to evaluate the feasibility of nonlinearity shaping. We achieve a nearly 20% reduction of the nonlinear refractive index of fused silica containing trace amounts of nanodiamonds relative to a pristine reference. The demonstration of such a noticeable impact on the nonlinear response of the key optical material widely accepted by ultrafast optics practitioners provides a guideline for future work on the novel concept of negative nonlinearity fibers, which could disrupt the established chromatic dispersion-nonlinearity landscape.

Addressing geometric and material nonlinearities in fluid-structure interaction with the ALE-SSM framework

A novel methodology was introduced for integrating skeleton-based structural models (SSMs) with an Arbitrary Lagrangian-Eulerian (ALE) formulation to perform fluid–structure interaction (FSI) simulations (i.e., ALE-SSM). In ALE-SSM, the structural domain consists of force-based line elements, which are favored in modeling solid structures because of their computational efficiency. This paper enhances ALE-SSM to account for geometrically nonlinear and inelastic material responses of the structural domain. Geometric nonlinearity is introduced in two stages: (1) at the basic coordinate system of the force-based elements, where second-order effects stemming from the transverse element deformations are accounted for in the element flexibility matrix; and (2) at the global coordinate system, where a corotational formulation is used to perform the geometric transformation from the basic to the global coordinate system. The proposed approach for modeling geometric nonlinearity in ALE-SSM is evaluated with benchmark problems involving large deformations of beam structures positioned parallel and perpendicular to one-phase flows. Next, ALE-SSM is employed to define a new benchmark study that evaluates the effects of geometric and material nonlinearities in FSI simulations with force-based elements.

Monitoring variations of refractive index via Hilbert–Schmidt speed and applying this phenomenon to improve quantum metrology

In this paper, we investigate the role of the nonlinear response of a material to improve quantum metrology. We show that the collective optical behavior of an atomic ensemble can be applied to enhance frequency estimation through one of the atoms. In fact, the collective optical behavior of the atomic ensemble by analyzing the quantum information extracted from one of its elements. Moreover, we introduce Hilbert–Schmidt speed (HSS), an easily computable theoretical tool, to monitor the variations of linear as well as nonlinear refractive indices and evaluate the strength of the nonlinear response of optical materials. Furthermore, we illustrate that quantum Fisher information and HSS can efficiently detect negative permittivity and refractive index, which is of great importance from a practical point of view.

Impact of Indenter Size and Microrelief Anisotropy on the Tribological Behavior of Human Skin.

Everyday, we interact with screens, sensors, and many other devices through contact with the skin. Experimental efforts have increased our knowledge of skin tribology but are challenged by the fact that skin has a complex structure, undergoes finite deformations, has nonlinear material response, and has properties that vary with anatomical location, age, sex, and environmental conditions. Computational models are powerful tools to dissect the individual contribution of these variables to the overall frictional response. Here, we present a three-dimensional high-fidelity multilayer skin computational model including a detailed surface topography or skin microrelief. Four variables are explored: local coefficient of friction (COF), indenter size, mechanical properties of the stratum corneum, and displacement direction. The results indicate that the global COF depends nonlinearly on the local COF, implying a role for skin deformation on the friction response. The global COF is also influenced by the ratio of the indenter size to the microrelief features, with larger indenters smoothing out the role of skin topography. Changes in stiffness of the uppermost layer of skin associated with humidity have a substantial effect on both the contact area and the reaction forces, but the overall changes in the COF are small. Finally, for the microrelief tested, the response can be considered isotropic. We anticipate that this model and results will enable the design of materials and devices for a desired interaction against skin.

Modulational instability and nonlinear dynamics of femtosecond lasers in transparent materials with non-Kerr nonlinearities

Femtosecond laser inscription in transparent materials is a physical process that finds widespread applications in material engineering, particularly in laser micromachining technology. In this process, the nonlinear optical response of the transparent material can be either intrinsic or induced by multiphoton ionization processes. In this work, a generic model is considered to describe the dynamics of femtosecond laser filamentation in transparent materials characterized by non-Kerr nonlinearities, focusing on the influence of multiphoton ionization processes in the generation of an electron plasma of inhomogeneous density. The mathematical model consists of a complex Ginzburg–Landau equation with a generalized saturable nonlinearity, besides the residual nonlinearity related to multiphoton ionization processes. This generalized complex Ginzburg–Landau equation is coupled to a rate equation for time evolution of the electron plasma density, where multiphoton ionizations are assumed to be the sole processes controlling the generation of the electron plasma. Dynamical properties of the model are discussed starting from the continuous-wave regime, where a modulational-instability analysis enables us to determine the stability conditions of continuous-wave modes in the system. The analysis reveals a dominant tendency of continuous-wave stability for relatively large values of the multiphoton ionization order K, provided the femtosecond laser operates in the anomalous dispersion regime. Numerical simulations of the mathematical model feature a family of wavetrains composed of self-focused, well-separated, pulse-shaped optical filaments whose repetition rates are shortened but amplitudes are increased, with an increase in K. Simulations suggest that such nonlinear wavetrain structures do not need the transparent material to be intrinsically nonlinear and that they may also be favored solely by the nonlinearity induced by multiphoton ionization processes in a linear transparent material.

Nonlinear Photoluminescence in Gold Thin Films

Promising applications in photonics are driven by the ability to fabricate crystal-quality metal thin films of controlled thickness down to a few nanometers. In particular, these materials exhibit a highly nonlinear response to optical fields owing to the induced ultrafast electron dynamics, which is however poorly understood on such mesoscopic length scales. Here, we reveal a new mechanism that controls the nonlinear optical response of thin metallic films, dominated by ultrafast electronic heat transport when the thickness is sufficiently small. By experimentally and theoretically studying electronic transport in such materials, we explain the observed temporal evolution of photoluminescence in two-pulse correlation measurements that we report for crystalline gold flakes. Incorporating a first-principles description of the electronic band structure, we model electronic transport and find that ultrafast thermal dynamics plays a pivotal role in determining the strength and time-dependent characteristics of the nonlinear photoluminescence signal, which is largely influenced by the distribution of hot electrons and holes, subject to diffusion across the film as well as relaxation to lattice modes. Our findings introduce conceptually novel elements ruling the nonlinear optical response of nanoscale materials, while suggesting additional ways to control and leverage hot carrier distributions in metallic films.

A diffusion–deformation model with damage for polymer undergoing rapid decompression failure

Green hydrogen is emerging as one of the most promising alternatives to replace fossil fuels. While hydrogen gas has a good energy density by weight, its poor energy density by volume requires it to be stored under high pressure for commercial use. The hydrogen infrastructure developed to handle this high pressure hydrogen contains multiple components made of polymers such as O-rings, pipes, hoses, and inner liners of storage tanks. Although polymers do not react chemically with hydrogen gas, they undergo a mechanical failure when high pressure hydrogen gas is suddenly depressurized. This phenomenon known as ‘rapid decompression failure’ (RDF) occurs due to the diffusion of hydrogen through polymer and getting trapped inside preexisting cavities or voids.In this paper, a continuum mechanics-based coupled diffusion–deformation-damage model was developed to predict the hydrogen distribution, stress distribution, and damage propagation inside the polymer while it undergoes rapid decompression failure. The polymer was modeled as a hyperelastic material because it represents the nonlinear material response observed in uniaxial tensile tests perfectly. The effect of hydrogen diffusivity, preexisting cavity size, cavity location, applied hydrogen pressure, and depressurization rate on damage initiation was studied. It was found that the coefficient of diffusion plays an important role in damage initiation and damage was mostly concentrated in the inside areas rather than near the surface. Experiments were conducted with ethylene propylene diene monomer (EPDM) which agreed well with the predicted trends using the given model. The effect of adding carbon black and silica filler particles and plasticizer to the pure EPDM polymer was also studied. It was found that damage during RDF decreases with the addition of fillers, but increases with the addition of the plasticizer. Finally, the damage evolution in the presence of two cavities was also studied, and was found that the interaction of stress fields around the cavities alters the damage occurring during RDF.

A Modified Bond-Associated Non-Ordinary State-Based Peridynamic Model for Impact Problems of Quasi-Brittle Materials.

In this work, we have developed a novel bond-associated non-ordinary state-based peridynamic (BA-NOSB PD) model for the numerical modeling and prediction of the impact response and fracture damage of quasi-brittle materials. First, the improved Johnson-Holmquist (JH2) constitutive relationship is implemented in the framework of BA-NOSB PD theory to describe the nonlinear material response, which also helps to eliminate the zero-energy mode. Afterwards, the volumetric strain in the equation of state is redefined by the introduction of the bond-associated deformation gradient, which can effectively improve the stability and accuracy of the material model. Then, a new general bond-breaking criterion is proposed in the BA-NOSB PD model, which is capable of covering various failure modes of quasi-brittle materials, including the tensile-shear failure that is not commonly considered in the literature. Subsequently, a practical bond-breaking strategy and its computational implementation are presented and discussed by means of energy convergence. Finally, the proposed model is verified by two benchmark numerical examples and demonstrated by the numerical simulation of edge-on impact and normal impact experiments on ceramics. The comparison between our results and references shows good capability and stability for impact problems of quasi-brittle materials. Numerical oscillations and unphysical deformation modes are effectively eliminated, showing strong robustness and bright prospects for relevant applications.

Predicting the non-linear response of composite materials using deep recurrent convolutional neural networks

This paper presents a novel framework to predict the full non-linear response of composite materials using Deep Recurrent Convolutional Neural (DCRN) Networks. The framework is based on a Representative Volume Element (RVE) database populated by sampling the composite design space in terms of layups, defects/variabilities and loading conditions. Several sources of material non-linearity are included in these models such as matrix damage, delamination, fibre failure and shear non-linearity. A DCRN Network architecture is proposed which combines convolutional layers, for spatial features detection, with Long/Short Term Memory layers, for material loading history dependencies. The models’ database consists of images of each RVE model, representing the layup and variables such as the presence of wrinkles, gaps or voids, and the homogenised 3D stress/strain curves. DCRN Networks are trained to predict the full 3D stress response of a laminated composite using the information from the RVE models database. Two formulations for the DCRN Network are studied, a pointwise prediction formulation and a time-marching prediction formulation. The two formulations are compared based on accuracy and robustness. The results show that both approaches can accurately predict the non-linear response of laminated composites.

Isotropic Gels of Cellulose Nanocrystals Grafted with Dialkyl Groups: Influence of Surface Group Topology from Nonlinear Oscillatory Shear

Attractive (non-self-assembling) aqueous cellulose nanocrystal (CNC) suspensions were topologically tailored into isotropic gels through the surface grafting of dialkyl groups. We thus focus on the influence of CNC concentration, including for pristine CNC, surface linker branching, branching degree, and the influence of side group size and branch-on-branch surface-grafted groups. The resulting mobility and strength of interaction in particle-particle interaction mediated by the surface groups was investigated from a rheological point of view. The emphasis is on nonlinear material parameters from Fourier-transform rheology and stress decomposition analysis. The results show that nonlinear material parameters are more sensitive than linear viscoelastic parameters to the onset of weakly interconnected networks in pristine CNC isotropic suspensions. All surface-modified CNC suspensions resulted in isotropic gels. The nonlinear material parameters were found to be broadly sensitive to CNC concentration, branching, degree of branching and surface-grafted linkers' length. However, the length of the grafted chains and the degree of branching were the primary factors influencing the nonlinear material response. Furthermore, the results showed evidence of two strain amplitude ranges with distinct nonlinear signatures that could be attributed to the disruption of weak network connection points and to distortions of more dense (aggregate) network regions, respectively.

Experimental characterization and phenomenological modeling of nonlinear viscoelasticity, plasticity and damage of continuous carbon fiber-reinforced thermoplastics

The presented work addresses the experimental characterization and phenomenological modeling of the complex rate dependent mechanical response of continuous fiber-reinforced thermoplastics (cFRTP). The theoretical basis is given by the concept of an equilibrium curve of the material which provides a comprehensive framework for separating the mechanical response into a rate dependent overstress and a rate independent equilibrium stress. In long-term creep and relaxation tests, it is shown that relaxation tests provide several advantages over creep tests when determining the equilibrium response. A stepwise loading–unloading relaxation (SR) test is proposed which makes it possible to extract nonlinear viscoelasticity, damage and plasticity present in the material from a single test. The application to cFRTP is exemplified by using the proposed method for the experimental characterization of a continuous carbon fiber-reinforced polycarbonate (CF-PC). Based on the obtained experimental data, a phenomenological material model is developed which describes the mechanical response of a unidirectional ply. The model consists of an overstress branch addressing the nonlinear viscoelastic material response and an equilibrium branch that utilizes a coupled damage-plasticity approach. After calibrating the model using the experimental data, it is shown that the proposed model is able to accurately reproduce the mechanical response of cFRTP.

Electronic-Based Model of the Optical Nonlinearity of Low-Electron-Density Drude Materials

Low-electron-density Drude (LEDD) materials such as indium tin oxide (ITO) are receiving considerable attention for their combination of CMOS compatibility, unique epsilon-near-zero (ENZ) behavior, and giant ultrafast nonlinear thermo-optic response. However, current understanding of the electronic and optical response of LEDD materials is limited due to the simplistic modeling that extends only the known models of noble metals without considering the interplay among the lower electron density, relatively high Debye energy, and the nonparabolic band structure. We bridge this knowledge gap and provide a complete understanding of the nonlinear electronic-thermal-optical response of LEDD materials. In particular, we rely on state-of-the-art electron dynamics modeling, as well as a time-dependent permittivity model for LEDD materials under optical pumping within the adiabatic approximation. We find the electron temperature may reach values much higher than realized before, even exceeding the Fermi temperature, in which case the effective chemical potential dramatically decreases and even becomes negative, thus, transient giving the material some characteristics of a semiconductor. We further show that the nonlinear optical response of LEDD materials originating from the changes to the real part of the permittivity is associated with changes of the population. This resolves the argument about the rise time of the permittivity, showing that it is instantaneous. In this vein, we show that referring to the LEDD permittivity as having a Kerr or ``saturable'' nonlinearity is unsuitable since its permittivity dynamics is absorptive rather than nonresonant and does not originate from population inversion. Finally, we analyze the probe-pulse dynamics and unlike previous work, we obtain a quantitative agreement with the results of recent experiments.

Selection of geometry for nonlinear rheology using large amplitude oscillatory shear: Poly (vinyl alcohol) based complex network systems

AbstractOscillatory rheology is a common technique to characterize the linear and nonlinear mechanical response of complex materials. The present work studies two crosslinked systems of poly(vinyl alcohol) (PVA): physically crosslinked PVA‐Borax, and glutaraldehyde (GA) based chemically crosslinked PVA‐hyaluronic acid (HA) gel. Both exhibit nonlinear viscoelasticity with characteristic intracycle mechanisms during large amplitude oscillatory shear (LAOS), owing to H‐bonding (physical) and covalent (chemical) interactions respectively, unlike PVA solutions/vinyl polymer melts. Parallel plate (PP) geometry is commonly utilized for rheology of crosslinked systems due to flexible gaps, and ease to retain exact material shapes. Unlike the widely employed cone and plate (CP) geometry for LAOS analysis, the inherent deformation and flow fields are not uniform in PP, which manifests as qualitative difference in the response of the material within the two geometries. A quantitative dissimilarity in the response of PVA based crosslinked systems is demonstrated in this work. Three approaches for PP correction from literature are explored to obtain a geometry independent response of the systems. Therein, the true stresses are computed from the apparent stresses via torque balance, their harmonics, and harmonic ratios based single‐point correction. The first two are shown to have limited application, owing to their implicit assumption of geometry independence in the linear regime. The third approach is found to be effective upto medium strain amplitudes. We outline these shortcomings, and present guidelines to analyze PP LAOS results for the two PVA systems. The analysis can be generalized for the broader class of complex network systems' nonlinear rheology.

Mesh d-refinement: A data-based computational framework to account for complex material response

Model-free data-driven computational mechanics (DDCM) is a new paradigm for simulations in solid mechanics. The modeling step associated to the definition of a material constitutive law is circumvented through the introduction of an abstract phase space in which, following a pre-defined rule, physically-admissible states are matched to observed material response data (coming from either experiments or lower-scale simulations). In terms of computational resources, the search procedure that performs these matches is the most onerous step in the algorithm. One of the main advantages of DDCM is the fact that it avoids regression-based, bias-prone constitutive modeling. However, many materials do display a simple linear response in the small-strain regime while also presenting complex behavior after a certain deformation threshold. Motivated by this fact, we present a novel refinement technique that turns regular elements (equipped with a linear-elastic constitutive law) into data-driven ones if they are expected to surpass the threshold known to trigger material non-linear response. We term this technique “data refinement”, “d-refinement” for short. It works both with data-driven elements based on either DDCM or strain–stress relations learned from data using neural networks. Starting from an initially regular FEM mesh, the proposed algorithm detects where the refinement is needed and iterates until all elements presumed to display non-linearity become data-driven ones. Insertion criteria are discussed. The scheme is well-suited for simulations that feature non-linear response in relatively small portions of the domain while the rest remains linear-elastic. The method is validated against a traditional incremental solver (i.e., Newton–Raphson method) and we show that the d-refinement framework can outperform it in terms of speed at no loss of accuracy. We provide an application that showcases the advantage of the new method: bridging scales in architected metamaterials. For this application, we also succinctly outline how d-refinement can be used in conjunction with a neural network trained on microscale data.

Thermomechanical response of nonlinear viscoelastic materials

In this article, the thermomechanical properties of the classical and nonclassical viscoelastic materials with particular emphasis on the entropy are studied in the framework of continuum thermodynamics. Specifically, considering the Clausius integral as “Part I” of the second law of thermodynamics in the classical formulation of continuum thermodynamics, the entropy function for various classes of nonclassical thermo-viscoelastic materials is shown to exist. This is achieved by employing the first law of thermodynamics and a scalar potential known as the Helmholtz free energy function. In addition, another function known as the internal rate of production of entropy defined for the classical and nonclassical thermo-viscoelastic materials is adopted to obtain a balance law for the entropy. Finally, upon linearizing the theory, a coupled system of differential equations is obtained for the nonclassical thermo-viscoelastic materials, which under some special circumstances, permits propagation of damped harmonic waves in the viscoelastic medium.

Numerical Investigation of Presliding in Viscoplastic Spherical Contacts

AbstractPresliding contacts play an important role in stiffness, damping, and thus dynamic response of assembled structures. Load-dependent nonlinearities in presliding contacts still hinder predictive modeling. Classical models apply only to smooth elastic contacts and a small subset of materials. Recently, the authors tested high density polyethylene (HDPE) inside a scanning electron microscope (SEM) and observed that nonlinearity trends in tangential stiffness and damping deviate from the predictions of the classical models. This discrepancy was attributed to HDPE’s nonlinear viscoplastic response. The aim of this study is to model aforementioned experiments numerically and investigate the influence of nonlinear material response on the presliding response of spherical contacts. A finite element model of a rigid spherical indenter pressed and sheared on a nonlinear viscoplastic half-space is constructed. The indenter geometry and boundary conditions are set in accordance with the experiments, and the constitutive model is tuned to the measured indentation responses. The tuned model delivers a shear response in agreement with the experiments. Accumulated plastic deformations are also found to correlate well with the wear profiles. The model further reveals that nonlinear viscoplasticity dominates tangential stiffness and dissipation at high normal preloads. Our results confirm further that nonlinear material response contributes significantly to the load-dependent nonlinearities in viscoplastic presliding contacts.