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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Characterization of wind conditions and impact on wind loading at an operational parabolic trough concentrating solar power plant using LiDAR observations

Wind loading is a major factor influencing the structural design costs of Concentrating Solar Power (CSP) collector systems, including heliostats and parabolic troughs. Traditionally, these designs have been based on wind-tunnel data, which often fail to accurately represent the dynamic effects experienced at full scale. This study presents a first-of-its-kind experimental characterization of wind conditions within an operational parabolic-trough CSP power plant focusing specifically on using lidar observations. The lidar observations give a unique opportunity to provide insights into wind flow conditions deep within the trough arrays. Our results suggest that (1) after being blocked by the first few rows, the wind speed above the troughs recovers to 73% of its inflow magnitude as it flows further over the trough field due to enhanced turbulent mixing and (2) due to the wind speed recovery, troughs in the interior field will likely experience higher shear-induced turning moments compared those at the front. The conclusions from this work stress the importance of better understanding the wind patterns and interior wind loads when designing solar collectors and highlights the need for more interior load measurements in the future field campaigns.

17 WIND ENERGY↗
DOE OSTI2025

Secondary Organic Aerosol from OH Oxidation of Acyclic Terpenes Is More Viscous and Less Volatile than That of Their Cyclic Analogs

Biogenic volatile organic compounds (BVOCs), a dominant source of secondary organic aerosol (SOA) globally, exhibit emission rates and composition that are plant species-specific and vary with environmental stressors. A common outcome of plant stress is increased emissions of acyclic terpenes. The paucity of information about acyclic terpene SOA chemistry contributes to uncertainties in predictions of SOA global loadings and impacts on Earth’s radiative budget, particularly in a changing climate where acyclic terpene emissions could become more prominent. This study compared properties of SOA derived from OH oxidation of acyclic and cyclic monoterpenes (ß-ocimene, a-pinene) and sesquiterpenes (ß-farnesene, ß-caryophyllene). Single particle mass spectrometry was used for assessing shape, density, and evaporation kinetics of size-selected SOA particles, and nanospray desorption electrospray ionization high-resolution mass spectrometry (nano-DESI-HRMS) was used to measure molecular composition of SOA. Acyclic terpene SOA exhibited higher viscosity and lower volatility compared to cyclic terpene SOA, and had a greater volume fraction remaining (VFR) after ~24 hours of evaporation - approximately 1.3-1.6 times higher VFR than that of cyclic terpene SOA. Additionally, HRMS analysis revealed greater chemical diversity and higher fractions of extremely low volatility compounds (56-62% ELVOC/LVOC) in acyclic terpene SOA compared to cyclic counterparts (25-37% ELVOC/LVOC). Our findings highlight the potential importance of accounting for acyclic terpene aerosol chemistry under conditions of plant stress to improve predictions of SOA loadings and impacts.

SOA physical properties↗
DOE OSTI2025

Development of Predictive Model for Accurate Rupture Time from Multi-Axial Creep in Alloy 709 with Physics-Based Simulations

A physics-based model is developed to predict multiaxial creep behavior in Alloy 709 (A709), an advanced austenitic stainless steel intended for high-temperature applications such as Sodium Fast Reactors (SFRs). Compared to conventional stainless steels like 316H, A709 offers superior high-temperature performance; however, comprehensive data on its multiaxial creep response remain limited. To address this gap, a crystal plasticity finite element (CPFE) framework is used to simulate the deformation and failure mechanisms of A709 under multiaxial loading conditions. The model incorporates an extended Hu-Cocks dislocation creep formulation that accounts for precipitation effects, along with the Sham–Needleman model to capture grain boundary cavitation-driven failure. These advanced constitutive models enable a detailed understanding of the interplay between microstructural evolution and macroscopic creep response. Furthermore, the study evaluates the predictive accuracy of various effective stress measures in estimating creep rupture life, leveraging simulated multiaxial creep data. The findings provide critical insights into the applicability of different stress measures for engineering design and life prediction of A709 components operating under complex loading conditions. This work contributes to improving the reliability of high-temperature structural components by advancing predictive modeling capabilities for advanced austenitic steels.

Alloy 709↗
DOE OSTI2024

Dataset of simulated vibrational density of states and X-ray diffraction profiles of mechanically deformed and disordered atomic structures in Gold, Iron, Magnesium, and Silicon

This dataset is comprised of a library of atomistic structure files and corresponding X-ray diffraction (XRD) profiles and vibrational density of states (VDoS) profiles for bulk single crystal silicon (Si), gold (Au), magnesium (Mg), and iron (Fe) with and without disorder introduced into the atomic structure and with and without mechanical loading. Included with the atomistic structure files are descriptor files that measure the stress state, phase fractions, and dislocation content of the microstructures. All data was generated via molecular dynamics or molecular statics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. This dataset can inform the understanding of how local or global changes to a materials microstructure can alter their spectroscopic and diffraction behavior across a variety of initial structure types (cubic diamond, face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) for Si, Au, Mg, and Fe, respectively) and overlapping changes to the microstructure (i.e., both disorder insertion and mechanical loading).

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2024

Predicted Fracture Tendency of Naturally Occurring Aluminum Surface Coatings under Tensile Loading

Naturally occurring coatings on aluminum metal, such as its oxide or hydroxide, serve to protect the material from corrosion. Understanding the conditions under which these coatings mechanically fail is therefore expected to be an important aspect of predictive models for aluminum component lifetimes. To this end, we develop and apply a molecular dynamics (MD) modeling framework for conducting tension tests that is capable of isolating factors governing the mechanical strength as a function of coating chemistry, defect morphology, and variables associated with the loading path. We consider two representative materials, including γ-Al 2 O 3 and γ-Al(OH) 3 (i.e., oxide and hydroxide), both of which form readily as aluminum surface coatings. Our results indicate that defects have a significant bearing on the strength of aluminum oxide, with grain boundaries serving to reduce the strain at failure from ε zz = 0.300 to 0.219, relative to perfect single crystal. Our simulations also predict that porosity lowers the elastic stiffness and yield strength of the oxide. Relative to perfect crystal, we find porosity factors of 5%, 10% and 20% decrease the yield stress by 26%, 36% and 53%, respectively. MD predicts that perfect hydroxide and oxide single crystal have respective strains at failure of 0.08 and 0.31 under tensile uniaxial strain loading, and that the corresponding yield stresses are respectively 1.6 and 11.1 GPa. These data indicate that the hydroxide is substantially more susceptible to mechanical failure than the oxide. Our results, coupled with literature findings that indicate hot and humid conditions favor formation of hydroxide and defective oxide coatings, indicate the potential for a complicated dependence of aluminum corrosion susceptibility and stress corrosion cracking on aging history.

36 MATERIALS SCIENCE↗
DOE OSTI2026

ACT University Collaboration Proposal: Role of manufacturing defects on material failure under dynamic loading for developing enhanced failure models and theories (Final Report)

Research on the tensile behavior of additively manufactured 316L stainless steel coupon specimens at increasing strain rates was conducted over the past year at Penn State. Dynamic loading rates into the 1000 1/s loading rates were performed on specimens with nearly 1.32” gage lengths. Stress-strain plots show ductile and plastic behavior well beyond 12% strain with necked specimens, having smaller effective gage lengths showing up to 56% ultimate strain. Additional tests performed on compact tension specimens helped with simulation work to understand the deformation behavior. Using finite elements, it was possible to determine the feasibility of a comprehensive experimental validation study towards an improved model for AM material failure – specifically, the Bai-Wierzbicki approach which accounts for lode angle and triaxiality. A non-significant number of tests are projected for eight specific failure nodes, with additional replicates to provide strain-rate capabilities to the existing formulation. One such correction factor is explored for quasi-static, notched specimens. Finally, stress intensity factor was explored using a set of compact-tension specimens which would also provide useful validation data for any simulation work.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Unified Stress-Strain Model for Plasticity to the Structural Instability

A unified model for the work hardening Θσ Θ(σ) and stress-strain σε σ(ε) behavior is presented that accounts for deformation under tensile loading, from the onset of yielding at the proportional limit up to the ultimate strength as defined at the structural instability. The origin of this approach is based on a negative exponential formulation for an asymptotic-curvilinear work-hardening model that accounts for the rapid strengthening of metals as well as the continuation of steady-state deformation to the instability.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Uniform Mechanical Loading Can Test for Nonuniform Loading Durability

In this work, we present a method to evaluate the equivalency between any module mechanical loading conditions. The method is developed to address the specific failure mode of glass fracture and is based on Weibull analysis and weakest link theory. It considers the varying stress profile across the module to calculate the probability of glass fracture, which is used as the metric of equivalency. An idealized nonuniform loading scheme is employed to demonstrate the method and introduce the concept of the equivalent uniform load factor: a factor applied to the maximum pressure of the nonuniform load to obtain the equivalent uniform load value. It is demonstrated that this factor is less than unity for all nonuniform load cases considered, including snow and various characters of wind loading. These significant results suggest that uniform loading may be reliably, and practically, employed to evaluate photovoltaic module glass for nonuniform loading durability.

14 SOLAR ENERGY↗
DOE OSTI2025

Bulk-scale stress–strain hysteresis in layered crystalline solids: A study of graphite and Ti 3 SiC 2

Polycrystalline graphite and the MAX phase Ti 3 SiC 2 are layered crystalline solids with similar deformation mechanisms, including basal slip, ripplocation boundaries (RBs), kink boundaries (KBs), and cracking. The interplay of these mechanisms, notably in energy dissipation, has been much discussed in the past twenty-five years. This study builds upon previous work, investigating deformation with a renewed emphasis on the bulk-scale and given recent findings concerning RBs. Our investigation compares the evolution of energy dissipation, nonlinear recoverable and irrecoverable strain, and damage upon increasing stress for graphite and Ti 3 SiC 2 . Benitez et al.’s (2016) methodology of compressive cyclic loading and post-mortem electron backscatter diffraction (EBSD) to assess the prevalence of kinking based on low-angle grain boundaries (LAGBs) was used. Strains were measured with digital image correlation and EBSD was conducted on Ti 3 SiC 2 leveraging dictionary indexing, which was necessary herein to identify LAGBs accurately. The stress–strain stages of Ti 3 SiC 2 agree with literature on Ti 2 AlC. Damage and energy dissipation were more accelerated in graphite. No significant difference was observed in the fraction of LAGBs between pristine and unloaded Ti 3 SiC 2 . Trends observed and EBSD evidence that KBs were not dominant suggest that RBs are the primary dissipator of energy in both materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Environmentally Assisted Fatigue in Light Water Reactor Environment

This report summarizes the Environmentally Assisted Fatigue (EAF) research conducted at ANL under the US DOE Light Water Reactor Sustainability (LWRS) program. Starting from a rich background in theoretical and experimental EAF, ANL previously developed an approach to evaluate fatigue performance of reactor materials in light water reactor environments with the correction factor F en . The approach was based on a large body of experimental work performed at ANL and elsewhere, and was consistent with American Society of Mechanical Engineers (ASME)’s methodology governing the design and construction of reactor components. In recent years, the program was focused on component fatigue prediction and made several major and fundamental contributions in this area. These accomplishments help meet the needs identified by the industry concerning component level fatigue predictions in complex, transient conditions. The main contribution of the ANL program involved the development of a system-level model for estimating residual strain and life of nuclear reactor coolant system components under connected-system-thermal-mechanical boundary conditions. The goal was to predict the stress hotspots, strain residuals, strain amplitudes and the resulting fatigue lives. Thermal-mechanical stress analysis was performed considering thermal stratification and a design-basis reactor loading cycle. Based on the finite element (FE) model results, the strain residuals, strain amplitudes and resulting fatigue lives of reactor coolant system (RCS) components were predicted. The results show that some of the RCS components can have significantly different strain amplitudes, residual strain, and fatigue lives, despite having similar geometry and material. In addition, the simulated component-level strain profile can guide the selection of appropriate test inputs for conducting laboratory-scale EAF tests. Building upon the system-level model, ANL developed a digital twin (DT) framework to predict the structural states and associated fatigue life of components in real-time. This framework is a comprehensive system designed to predict the structural states and fatigue lives of reactor components. It includes multiple models and integrates artificial intelligence (AI), machine learning (ML), and FE based modeling tools to evaluate the structural states and fatigue lives.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

SEM/EBSD Characterization of Baffle-Former Bolts Designated for High Energy X-ray Microscopy Studies at the Advanced Photon Source

This report documents the microstructural and surface characterization of two high-fluence baffle-former bolts (BFBs) harvested from a commercial pressurized water reactor (PWR) after nearly four decades of service. These bolts experienced extreme conditions including high neutron fluence, elevated temperatures, corrosive primary water, and sustained mechanical loads, all of which contribute to degradation mechanisms such as irradiation-assisted stress corrosion cracking (IASCC). Using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD), the study assessed bulk and near-surface microstructures, grain boundary characteristics, and in-service oxide layers. The results revealed significant differences between bolts exposed to 41 dpa and 29 dpa, including differences in recrystallization extent, deformation structures, and oxidation morphology. These findings establish critical baseline data for integration with advanced synchrotron-based high-energy X-ray microscopy (HEXM) and computational crystal plasticity models. Ultimately, the work supports improved mechanistic understanding and predictive capability regarding the long-term performance of reactor core internal components.

Lach, Tim [Oak Ridge National Laboratory (ORNL), O↗
DOE OSTI2024

Design by analysis rules for ASME Section III, Division 5, Class B components

The current rules for elevated temperature ASME Section III, Division 5, Class B components, other than piping, were basically adapted from the Design-by-Rule approach for Section VIII, Division 1 vessels. A goal of the proposed new rules is to explicitly account for the design life and cyclic service while recognizing the less-rigorous requirements commensurate with lesser safety consideration. Further goals are to maximize the use of modern computational technology, for example finite element analysis in conjunction with reference stress concepts, and to avoid the need for stress classification. This paper summarizes the work done to address these issues. A summary of the design-by-analysis for primary loads, strain limit evaluation, and creep-fatigue damage assessment is presented. The proposed design-by-analysis creep-fatigue damage calculation approach uses a new elastic follow-up-based Isochronous Stress Strain Curve stress relaxation procedure. A set of sample problems are selected to validate the proposed design-by-analysis rules for creep-fatigue damage assessment. The proposed Class B rules are evaluated against the Class A elastic design rules and the experimental data obtained from a family of a simplified model test-based key-feature test results. The proposed Class B creep-fatigue damage assessment methodology yields conservative design cycles estimates compared to the experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Sustained strain applied at high rates drives dynamic tensioning in epithelial cells

Epithelial cells experience long lasting loads of different magnitudes and rates. How they adapt to these loads strongly impacts tissue health. Yet, much remains unknown about the evolution of cellular stress in response to sustained strain. Here, by subjecting cell pairs to sustained strain, we report a bimodal stress response, where in addition to the typically observed stress relaxation, a subset of cells exhibits a dynamic tensioning process with significant elevation in stress within 100 s, resembling active pulling-back in muscle fibers. Strikingly, the fraction of cells exhibiting tensioning increases with increasing strain rate. The tensioning response is accompanied by actin remodeling, and perturbation to actin abrogates it, supporting cell contractility’s role in the response. Collectively, our data show that epithelial cells adjust their tensional states over short timescales in a strain-rate dependent manner to adapt to sustained strains, demonstrating that the active pulling-back behavior could be a common protective mechanism against environmental stress.

bioinformatics↗
DOE OSTI2024

THERMAL STRUCTURAL AND SHOCK EVENT EVALUATIONS OF THE FUELING PELLET INJECTION SYSTEM FOR ITER

The US is among seven partner nations in a collaborative effort to design, build, and demonstrate fusion’s ability to be a large-scale carbon free energy source. Each country has its own Domestic Agencies (DA) that contribute directly to the ITER project. US ITER, which is a DOE Office of Science project managed by Oak Ridge National Laboratory, is developing world class engineering solutions to the design, construction, and assembly of the burning plasma experiment that can demonstrate the scientific and technological feasibility of fusion. US ITER’s scope includes completing the preliminary and final design, qualifying materials and processes for manufacture and testing, executing manufacturing, and delivering the Fueling Pellet Injection System (FPIS) to the ITER site for assembly. The US-ITER FPIS system is designed to inject cryogenically frozen pellets of deuterium-tritium (D-T) into the plasma. The FPIS has two main functions: 1. Provide a steady supply of deuterium and tritium fuel, 2. Mitigating the impact of edge localized modes on the plasma facing components. The FPIS will have the capability to reside in three port cells within a tritium second barrier containment cask. Each pellet cask contains three flight tubes linking with penetrations on the torus cryopump housing and vacuum vessel (VV): two for the magnetic high field side (HFS) pellet injection and one for the magnetic low field side (LFS) pellet injection. This paper presents results of the thermal-structural analyses of the FPIS flight tube structural components when subjected to various loads such as electromagnetic (EM) loads, nuclear heating, seismic, and operational, and dynamic shock events. The resulting temperatures and stresses under combined conditions have been found to satisfy the design criteria to ensure safe and reliable operation of the FPIS flight tubes within the vacuum vessel.

Martinez, Oscar↗
DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Microstructure-sensitive mechanical behavior of an additively manufactured psuedoelastic shape memory alloy

The additive manufacturing of shape memory alloys into complex geometries enables fabrication of advanced functional systems across a variety of fields and domains. This work presents results focused on the mechanical behavior of additively manufactured shape memory pseudoelastic NiTi. The deformation induced solid state phase transformation from austenite to martensite allows this system to accommodate large recoverable strains. This deformation behavior is fundamentally driven by crystal-scale transformation physics. Laser powder bed fusion processing reveals that the resulting microstructure, both grain morphology and crystallographic texture, is strongly dependent on the manufacturing processing history. Exhaustive mechanical testing demonstrates that these microstructural factors strongly impact both tensile and cyclic stress–strain behavior. Cyclic dissipative behavior, however, is similar across all tested microstructures following an initial transient period. Remarkably, analysis of spatial strain fields during tensile loading reveals two distinctly different localization “modes”. The first is initiation of localized deformation bands which continuously propagate through the tensile bar during loading. In the second mode localization is observed but lacks propagation; instead additional localization cites nucleate during subsequent loading. The latter phenomena is suspected to be driven by grain-scale deformation physics as the localized band morphologies coincide with grain morphologies. These phenomena strongly impact the resulting aggregate stress–strain behavior. Hence, manufacturers and designers of psuedoelastic functional components must at the very least consider the potential variability in properties when considering additive manufacturing processing. More ideally the process–structure–property relations can be used to further tailor and optimize final functional performance.

Additive manufacturing↗
DOE OSTI2024

Methodology to determine printability criteria of highly concentrated pastes through rheological characterization

Material extrusion is an additive manufacturing technique that enables the creation of reproducible and complex hardware by depositing a viscous, shear-thinning ink onto a substrate in a custom-pattern via extrusion through a syringe. Here, the ability of an ink to be extruded onto a substrate in many layers, and maintain the desired shape is what defines the printability. Printability is often investigated by formulating, printing, and postmortem analysis of final parts in an iterative manner. Investigations of printability through rheological characterization have often been concerned with inks that straddle the line between printable and too thin, leaving out an entire class of inks that are highly-filled pastes, where extrudability is the limiting factor. Highly-filled pastes continue to pose issues for researchers as the effect of filler morphology, size, loading, and packing fraction on the ink rheology and corresponding printability is not understood. While traditional rheological characterizations may be useful for some inks, we show that protocols utilizing steady-shear, or large-amplitude oscillatory shear are difficult and unreliable for highly-filled pastes. Through transient rheology paired with real-time images we show that each traditional protocol produces inhomogeneous deformations that violate the assumptions that underly common rheological definitions. Instead, we demonstrate metrics measured with small-amplitude oscillatory shear that are correlated to the printability of various ink formulations ranging in loading. The rheological measures that accurately predict the printability of the inks are the axial stress measured at small amplitudes, and the critical stress amplitude above which rheological characterizations become impossible. In addition, we estimate the maximum packing fraction for each filler, based on the exponent common to hard sphere models, and show that the printability of each ink can be predicted by the ratio of the packing fraction to the theoretical maximum. We show how small-amplitude oscillatory shear allows users to develop printability criteria for any ink to enhance the workflow in the development of new inks, increase the performance of material extrusion printing, and improve the stability of printed parts, with less wasted time and materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Competition between roughness and strength for scale-dependent surfaces

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

elasticity↗