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At least 127 records · Page 7

Microscale mechanical modeling of deformable geomaterials with dynamic contacts based on the numerical manifold method

Abstract Micromechanical modeling of geomaterials is challenging because of the complex geometry of discontinuities and potentially large number of deformable material bodies that contact each other dynamically. In this study, we have developed a numerical approach for micromechanical analysis of deformable geomaterials with dynamic contacts. In our approach, we detect contacts among multiple blocks with arbitrary shapes, enforce different contact constraints for three different contact states of separated, bonded, and sliding, and iterate within each time step to ensure convergence of contact states. With these features, we are able to simulate the dynamic contact evolution at the microscale for realistic geomaterials having arbitrary shapes of grains and interfaces. We demonstrate the capability with several examples, including a rough fracture with different geometric surface asperity characteristics, settling of clay aggregates, compaction of a loosely packed sand, and failure of an intact marble sample. With our model, we are able to accurately analyze (1) large displacements and/or deformation, (2) the process of high stress accumulated at contact areas, (3) the failure of a mineral cemented rock samples under high stress, and (4) post-failure fragmentation. The analysis highlights the importance of accurately capturing (1) the sequential evolution of geomaterials responding to stress as motion, deformation, and high stress; (2) large geometric features outside the norms (such as large asperities and sharp corners) as such features can dominate the micromechanical behavior; and (3) different mechanical behavior between loosely packed and tightly packed granular systems.

58 GEOSCIENCES↗

>24% screen printed Cu contacted n-TOPCon solar cells with successful implementation of LECO process

In this paper, we report the successful fabrication of >24.0 % efficiency n-TOPCon Si solar cells with screen-printed, fire-through Cu contact to n-TOPCon on the rear side and Ag contacted boron emitter on the front side by implementing optimized firing and LECO conditions. The highest efficiency (24.3%) Cu contacted n-TOPCon cell in this study showed excellent cell performance parameters with V oc >730 mV, J sc of 41.1 mA/cm 2 and FF of 80.8%, resulting in an absolute efficiency gap of 0.2% between Cu-contacted and fully Ag contacted n-TOPCon cells (24.5%). The mini-module fabricated with the Cu contacted n-TOPCon cell showed excellent reliability and durability of open-circuit voltage (V oc ), pseudo fill factor (pFF) and efficiency after prolonged damp-heat tests. Such high efficiency screen printed Cu contacted n-TOPCon cells provide unique opportunity to replace very expensive Ag contact on n-TOPCon with cheaper screen printable Cu metal pastes.

14 SOLAR ENERGY↗

Sputtered p-Type Cu x Zn 1– x S Back Contact to CdTe Solar Cells

As thin-film cadmium telluride (CdTe) solar cells gain prominence, one particular challenge is optimizing contacts and their interfaces to transfer charge without losses in efficiency. Back contact recombination is still significant and will prevent CdTe solar technology from reaching its full potential in device efficiency, and transparent back contacts have not been developed for bifacial solar technology or multijunction solar cells. To address these challenges, here we investigate sputtered Cu x Zn 1– x S as a p-type semi-transparent back contact material to thin-film polycrystalline CdTe solar cells at Cu concentrations x = 0.30, 0.45, and 0.60. This material is selected for its high hole conductivity (160–2120 S cm –1 ), wide optical band gap (2.25–2.75 eV), and variable ionization potential (approximately 6–7 eV) that can be aligned to that of CdTe. We report that without device optimization, CdTe solar cells with these Cu x Zn 1– x S back contacts perform as well as control cells with standard ZnTe:Cu back contacts. We observe no reduction in external quantum efficiency, low contact barrier heights of approximately 0.3 eV, and carrier lifetimes on par with those of baseline CdTe. These cells are relatively stable over one year in air, with V OC and efficiency of the x = 0.30 cell decreasing by only 1 and 3%, respectively. Using scanning electron microscopy and scanning transmission electron microscopy to investigate the Cu x Zn 1– x S/CdTe interface, we demonstrate that the Cu x Zn 1– x S layer segregates into a bilayer of Cu-Te-S and Zn-Cd-S, and thermodynamic reaction calculations support these findings. Despite its bilayer formation, the back contact still functions well. This investigation explains some of the physical mechanisms governing the device stack, inspires future work to understand interfacial chemistry and charge transfer, and elicits optimization to achieve higher-efficiency CdTe cells.

14 SOLAR ENERGY↗

Accumulation-Type Ohmic van der Waals Contacts to Nearly Intrinsic WSe 2 Nanosheet-Based Channels: Implications for Field-Effect Transistors

We report the fabrication of ohmic van der Waals (vdW) contacts to nearly intrinsic WSe 2 nanosheet-based channels in field-effect transistors (FETs) using degenerately p-doped MoS2 (p + -MoS2) as a contact metal. We demonstrate that accumulation-type ohmic contacts and the high device performance are achievable without electrostatically gating the drain/source contact regions despite the nearly intrinsic nature of WSe 2 . Back-gated WSe 2 FETs with p + -MoS 2 bottom contacts (which screen the back-gate electric field in the drain/source regions) exhibit linear output characteristics, a high on/off ratio of 10 8 , and a high two-terminal field-effect mobility up to ~200 cm2 V –1 s –1 at room temperature. Our theoretical modeling reveals that the p + -MoS 2 /WSe 2 vdW junction behaves like a metal/semiconductor ohmic contact signified by a vanishingly thin space-charge region of ~1 nm on the p + -MoS 2 side and a substantial accumulation layer of free holes on the WSe 2 side, which is further verified by additional temperature-dependent and dual-gated measurements of WSe 2 FETs. We attribute the formation of accumulation-type ohmic contacts free of a Schottky barrier to the near absence of Fermi-level pinning at the vdW interface and the work function of p + -MoS 2 being larger than the ionization energy of WSe 2 . This study represents an important step toward achieving low-resistance ohmic contacts to two-dimensional (2D) semiconductors by eliminating the Fermi-level pinning effects, which is expected to have significant implications for next-generation 2D semiconductor-based nanoelectronics.

36 MATERIALS SCIENCE↗

Ultrathin stable Ohmic contacts for high-temperature operation of β -Ga2O3 devices

Beta gallium oxide (β-Ga2O3) shows significant promise in high-temperature, high-power, and sensing electronics applications. However, long-term stable metallization layers for Ohmic contacts at high temperatures present unique thermodynamic challenges. The current most common Ohmic contact design based on 20 nm of Ti has been repeatedly demonstrated to fail at even moderately elevated temperatures (300–400 °C) due to a combination of nonstoichiometric Ti/Ga2O3 interfacial reactions and kinetically favored Ti diffusion processes. Here, we demonstrate stable Ohmic contacts for Ga2O3 devices operating up to 500–600 °C using ultrathin Ti layers with a self-limiting interfacial reaction. The ultrathin Ti layer in the 5 nm Ti/100 nm Au contact stack is designed to fully oxidize while forming an Ohmic contact, thereby limiting both thermodynamic and kinetic instability. This novel contact design strategy results in an epitaxial conductive anatase titanium oxide interface layer that enables low-resistance Ohmic contacts that are stable both under long-term continuous operation (>500 h) at 600 °C in vacuum (≤10−4 Torr), as well as after repeated thermal cycling (15 times) between room temperature and 550 °C in flowing N2. This stable Ohmic contact design will accelerate the development of high-temperature devices by enabling research focus to shift toward rectifying interfaces and other interfacial layers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Li-Ion Battery Electrode Contact Resistance Estimation by Mechanical Peel Test

Li-ion battery electrode electronic properties, including bulk conductivity and contact resistance, are critical parameters affecting cell performance and fast-charge capability. Contact resistance between the coating and current collector is often the largest electronic resistance in an electrode and is affected by chemical, microstructural, and interfacial variations. Direct measurements of contact resistance and bulk conductivity have proven to be challenging. In their absence, a mechanical electrode peel test is often used to compare adhesion and electrical contact resistance. However, using a micro-flexible-surface probe, contact resistance can be directly determined. Here, this work compares contact resistance and mechanical peel strength of multiple commercial-grade HE5050 and NCM523 cathodes and graphite and silicon anodes. It was found that peel strength correlates well with contact resistance in a carefully curated data set (p < 0.05) and in some situations may be a good metric to estimate electrical properties. However, there were distinct outliers in the data set, indicating that peel strength may not accurately reflect electrical properties when there is significant variation in electrode composition. These results illustrate the value of the micro-flexible-surface probe in quantifying contact resistance and bulk conductivity to better understand how battery composition and processing steps affect microstructure and resulting cell performance.

25 ENERGY STORAGE↗

Multiscale water drop contact angles at selected silica surfaces

In this paper, multiscale advancing contact angles for glycerol/water drops at silica surfaces are reported for millidrops, submicron-drops, and nanodrops. Selected silica surfaces were muscovite, silicon, and talc. The contact angles for millidrops (1–2 mm) were determined by the traditional sessile drop technique. For submicron-drops (0.1–1.0 μm), a hollow tip Atomic Force Microscope (AFM) procedure was used. The contact angles for nanodrops (~7 nm) were examined from Molecular Dynamics (MD) simulation. The results were compared to evaluate the effect of drop size on the contact angle. In the case of the hydrophobic talc surface, the 75° advancing contact angle did not vary significantly with drop size. For the hydrophilic muscovite surface, the water drop wet the surface and an advancing contact angle of about 10° was found for the millidrops and submicron-drops. However, for the MD simulated nanodrops, attachment and spreading of the ~7 nm drop created a 2D film of molecular dimensions, the contact angle of which was difficult to define and varied from 0° to 17°. Perhaps of equal interest from the MD simulation results was that the spreading of the glycerol/water nanodrop at the muscovite surface resulted in crystallographic directional transport of water molecules to the extremities of the 2D film. Such separation and segregation left the center of the film with an increased concentration of glycerol. Based on these results, the line tension, which has been found in other investigations to account for contact angle decrease with a decrease in drop size, does not seem to be a significant factor in this study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

Atomic force microscopy (AFM) is an important tool for measuring a variety of nanoscale surface properties, such as topography, viscoelasticity, electrical potential and conductivity. Some of these properties are measured using contact methods (static contact or intermittent contact), while others are measured using noncontact methods. Some properties can be measured using different approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip–sample force is applied. In this paper we discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip–sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method.

14 SOLAR ENERGY↗

Contact Multigraph Routing: Overview and Implementation

In Delay Tolerant Networking (DTN), the standard routing algorithm used to navigate time-varying networks has been Contact Graph Routing (CGR). In CGR, a globally distributed list of contacts, periods during which two DTN nodes may communicate, is used to construct a contact graph, in which contacts are vertices. A version of Dijkstra’s algorithm can then be used to find paths through this model of the timevarying network. However, since contact graphs may be large compared to the network, potentially growing with the square of the number of network nodes and linearly with the time interval represented, the resulting algorithm does not scale well with the size of the network or time. Any improvement to the routing algorithm will bring significant returns to scale. In a previous paper, we briefly introduced an alternative to the contact graph model for routing. This alternative model is based on a multigraph (a graph in which there may be multiple edges between a pair of vertices) where vertices represent network nodes instead of contacts. A version of Dijkstra’s algorithm in these multigraph models reduces the time needed to perform the same routing computations done in the existing CGR algorithm. Moreover, a modified version of Yen’s algorithm for multigraphs is included. Our variation of CGR, which we call Contact Multigraph Routing (CMR), provides an in-line replacement for the previously used pathfinding algorithms. This paper describes an implementation created based on the CMR approach, and experimental comparisons to traditional CGR are given. In addition, we explore some additional modifications to the routing pipeline traditionally assumed in CGR. These modifications range from the theoretical to the practical in terms of size and scope. We step forward our understanding of sheaftheoretic networking and describe how to model the routing pipeline using sheaves. We detail some enhanced route selection criteria that addresses some of the added complexity of DTNbased systems. We also include a future works section on future improvements and implementations that would be of service to the broader DTN community.

contact graph routing↗

Multigraph-based Routing in Delay Tolerant Networks: An Alternative to Contact Graph Routing

Satellites are leaving the realms of niche use, extending our day-to-day networked infrastructure to space – thereby forcing a generalization of network architectures. The Delay Tolerant Networking (DTN) protocol is being developed to give rise to this new Solar System Internet. Predominantly, DTNs in space use globally-distributed contact tables to compute routes. In this paper, we propose and analyze a novel optimized approach for route computations that improves upon traditional approaches. As the general DTN will always include some scheduled links, our new algorithm enables greater scalability and practicality of DTN routing. These contact tables include windows when two nodes can communicate and were classically organized into a contact graph, where the vertices represent contact opportunities. Because the complexity of a contact graph grows with the number of contacts, pathfinding on it does not scale. A new structure using multigraphs with the same data is proposed. We show that a multigraph-based approach, which we call contact multigraph routing, exhibits performance superior to routing based on contact graphs, allowing greater scaling to schedule-based routing. In this paper, the multigraph-based algorithm is detailed and a proof is included showing it outperforms the previous algorithm given the same input. Pseudocode is included, as are simulation results. We conclude with suggested future work.

Delay Tolerant Networking↗

Structure and Electronic Properties of Mesopores in Si PV Devices with PLEO Contacts

All current state-of-the-art silicon photovoltaic (PV) devices employ some flavor of passivating contact structure to minimize detrimental recombination while providing good conductivity. These properties are most often provided by a dielectric layer (SiNx, Al2O3, or SiOx) that is in contact with the crystalline silicon (c-Si) substrate. The effectiveness of these layers is heavily dependent on the nanoscale structure of both the dielectric layers and the crystalline silicon interface. As an example, the tunneling probability for charge carriers across thin SiOx layers, a process that is critical to maintain high conductivity, is extremely sensitive to the SiOx thickness. SiOx with a thickness below 2 nm readily allows charge carrier tunneling, whereas it is impeded for greater thicknesses. In the latter case it has been shown that modifications to the thermal processing schedule can induce disruptions, or pinholes, in thick SiOx layers that allow transport of charge carriers while maintaining excellent passivation. However, this requires higher temperatures processes that may inhibit widespread adoption by industry. Recently, another option has been presented that may circumvent the necessity for high temperature processing, namely metal assisted chemical etching (MACE). MACE relies on deposition of Ag nanoparticles onto the SiOx layers with subsequent electroless etching to form mesopores in the SiOx layers that are analogous to the pinholes created with high temperature processing. The size and density can be controlled based on the Ag nanoparticle deposition conditions. The resulting contact structure is known as polysilicon on locally etched oxide (PLEO) contacts. The nanoscale structure of the mesopores in PLEO contacts define the device level observables such as recombination current (Jo) and junction resistance. In this work we present atomic resolution transmission electron microscopy (TEM) analysis of mesopores in PLEO contacts formed with a different processing conditions to connect provide insight into how the nanoscale structure of the SiOx layer influences PV device properties. Additionally, we have previously used electron beam induced current (EBIC) to probe local transport properties in Si PV devices with a SiOx layer containing pinholes due to high temperature processing. Using EBIC we were able to directly show the enhance charge carrier transport through the pinholes. Here we also employ EBIC to study non-uniformities in charge carrier recombination and transport associated with mesopores in PLEO contacts and compare these results with our previous work on devices with pinholes in the SiOx formed through high temperature processes. The products of this work provide critical information that is required to both further optimize performance of Si PV devices with PLEO contact and to drive future adoption of this technology by industry.

ENGINEERING,SOLAR ENERGY↗

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗

Crystalline Organic Compounds as Effective Nuclei in Contact Efflorescence of Ammonium Sulfate

Contact nucleation is believed to play a role in liquid-to-solid phase transitions in the atmosphere including ice nucleation and salt efflorescence. Here, for this work, contact efflorescence of optically levitated ammonium sulfate droplets by collisions with organic particles is probed using a long working-distance optical trap. Two highly viscous water-soluble organic compounds (d-(+)-raffinose and citric acid), and two insoluble highly surface-active organic compounds (stearic acid and cis-pinonic acid) were probed for their ability to induce efflorescence upon contact. While three of the organics showed minimal effectiveness as contact nuclei, cis-pinonic acid showed a remarkable ability to initiate contact efflorescence of ammonium sulfate, occurring near ammonium sulfate’s deliquescence relative humidity. Further analysis of cis-pinonic acid using bright-field microscopy in an electrodynamic balance provided evidence that the cis-pinonic acid particles are crystalline under the laboratory conditions. We suggest that the close lattice match between crystalline ammonium sulfate and crystalline cis-pinonic acid may account for the observed effectiveness in initiating contact efflorescence of ammonium sulfate. In contrast, tests of contact nucleation between cis-pinonic acid and sodium chloride, a pair with a poor lattice match, did not result in efflorescence. These findings suggest that crystalline organic compounds in the atmosphere could act as effective nuclei for contact efflorescence of atmospherically relevant salts, provided they share a compatible lattice structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Identifying impacts of contact tracing on HIV epidemiological inference from phylogenetic data

Abstract Robust sampling methods are foundational to inferences using phylogenies. Yet the impact of using contact tracing, a type of non-uniform sampling used in public health applications such as infectious disease outbreak investigations, has not been investigated in the molecular epidemiology field. To understand how contact tracing influences a recovered phylogeny, we developed a new simulation tool called SEEPS (Sequence Evolution and Epidemiological Process Simulator) that allows for the simulation of contact tracing and the resulting transmission tree, pathogen phylogeny, and corresponding virus genetic sequences. Importantly, SEEPS takes within-host evolution into account when generating pathogen phylogenies and sequences from transmission histories. Using SEEPS, we demonstrate that contact tracing can significantly impact the structure of the resulting tree, as described by popular tree statistics. Contact tracing generates phylogenies that are less balanced than the underlying transmission process, less representative of the larger epidemiological process, and affects the internal/external branch length ratios that characterize specific epidemiological scenarios. We also examined real data from a 2007–2008 Swedish HIV-1 outbreak and the broader 1998–2010 European HIV-1 epidemic to highlight the differences in contact tracing and expected phylogenies. Aided by SEEPS, we show that the data collection of the Swedish outbreak was strongly influenced by contact tracing even after downsampling, while the broader European Union epidemic showed little evidence of universal contact tracing, agreeing with the known epidemiological information about sampling and spread. Overall, our results highlight the importance of including possible non-uniform sampling schemes when examining phylogenetic trees. For that, SEEPS serves as a useful tool to evaluate such impacts, thereby facilitating better phylogenetic inferences of the characteristics of a disease outbreak. SEEPS is available at https://github.com/MolEvolEpid/SEEPS.

Virology↗

Photometric Study and Absolute Parameter Estimation of Six Totally Eclipsing Contact Binaries

High precision CCD observations of six totally eclipsing contact binaries were presented and analyzed. It is found that only one target is an A-type contact binary (V429 Cam), while the others are W-type contact ones. By analyzing the times of light minima, we discovered that two of them exhibit secular period increase while three manifest long-term period decrease. For V1033 Her, a cyclic variation superimposed on the long-term increase was discovered. By comparing the Gaia distances with those calculated by the absolute parameters of 173 contact binaries, we found that the Gaia distance can be applied to estimate the absolute parameters for most contact binaries. The absolute parameters of our six targets were estimated using their Gaia distances. The evolutionary status of contact binaries was studied, and we found that the A- and W-subtype contact binaries may have different formation channels. The relationship between the spectroscopic and photometric mass ratios for 101 contact binaries was presented. It was discovered that the photometric mass ratios are in good agreement with the spectroscopic ones for almost all of the totally eclipsing systems, which is corresponding to the results derived by Pribulla et al. and Terrell & Wilson.

47 OTHER INSTRUMENTATION↗

Dynamics of solid dispersions in oil during the lubrication of point contacts. Part 1: Graphite

A Hertzian contact was lubricated with dispersed graphite in mineral oils under boundary lubrication conditions. The contact was optically observed under pure rolling, combined rolling and sliding, and pure sliding conditions. The contact was formed with a steel ball on the flat surface of a glass disk. Photomicrographs are presented which show the distribution of the graphite in and around the contact. Friction and surface damage are also shown for conditions when the base oils are used alone and when graphite is added to the base oils. Under pure rolling and combined rolling and sliding conditions, it is found that, for low speeds, a graphite film can form which will separate the contacting surfaces. Under pure sliding conditions, graphite accumulates at the inlet and sweeps around the contact, but very little of the graphite passes through the contact. The accumulated graphite appears to act as a barrier which reduces the supply of oil available to the contact for boundary lubrication. Friction data show no clear short term beneficial or detrimental effect caused by addition of graphite to the base oil. However, during pure sliding, more abrasion occurs on the polished balls lubricated with the dispersion than on those lubricated with the base oil alone. All observations were for the special case of a highly-polished ball on a glass surface and may not be applicable to other geometries and materials, or to rougher surfaces.

Cusano, C.↗

Influence of linear profile modification and loading conditions on the dynamic tooth load and stress of high contact ratio gears

A computer simulation for the dynamic response of high-contact-ratio spur gear transmissions is presented. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. It is shown that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.

Lee, Chinwai↗

Sensitivity analysis of frictional contact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the static frictional contact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of nodal displacements, and Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for the frictional contact of a composite spherical cap pressed against a rigid plate.

Karaoglan, I.↗