This workflow combines DFT simulations, kinetic Monte Carlo (kMC) and FEM. At the macroscale, FEM models the evolution of Li surface contact against a rigid solid electrolyte under mechanical compression, incorporating creep deformation governed by experimentally derived constitutive laws and assuming a self-affine surface roughness. Concurrently, a DFT-informed KMC model simulates nanoscale Li striping, vacancy hopping, and accumulation proximal to the Li/SSE interface. In particular, plane-wave DFT calculations are employed to determine the Li vacancy formation energy landscape and corresponding Li hopping barriers in both the bulk and interfacial regions. These barriers, in conjunction with transition state theory, yield the Li hopping rates utilized in the kMC simulations [482].

The simulations reveal that the steady-state contact area fraction and the effective overpotential required to sustain a given current density depend strongly on the specific interface (Li vs Li₂O, LLZO, or LiF) and the operating conditions, such as stack pressure and stripping current density. In particular, the Li/Li₂O interface exhibits exceptionally rapid Li diffusion near the Li/SSE interface, in quantitative agreement with recent experiments, validating the hybrid modeling approach.

A key challenge for the effective application of PFMs in electrochemical simulations, despite their capacity to elucidate thermodynamically driven microstructure evolution at electrode/SSE interfaces, lies in the prerequisite of a robust free energy functional capable of capturing kinetic phenomena. However, this requirement is frequently unmet, as many current phase-field simulations for battery materials simplify their electrolyte as ideal [483]. In a recent study [484], a realistic chemo-electro-mechanical PFM is described and adopted to elucidate how Li penetrates SSE in the co-presence of grain boundaries (GB) and interfacial nanovoids. Temporal evolution of the interfacial free energy (Allen–Cahn equation), the electrochemical reaction kinetics (Butler–Volmer), the Cahn–Hilliard equation for species transport, and the equations of electric and mechanical equilibrium are taken into account. To simulate lithium dendrite formation in the vicinity of these nanoscale GBs and interfacial nanovoids, the simulation domain —measuring 200 nm × 300–400 nm— was populated with multiple GBs, encompassing the lithium-metal anode and an SSE featuring a rough surface with triangular protrusions. The simulation sequence involved initial continuous plastic deformation at the Li/SSE interface, subsequently followed by phase-field modeling of lithium dendrite growth. This investigation reveals a strong correlation between grain-boundary-anisotropy-dependent lithium-ion transport and the presence of interfacial nanovoids.

The development of quality interface evolution models is also particular important for the investigation of novel electrode/SSE physics, such as for interfacial morphogenesis applied to Li metal solid state batteries [485], or for anode-free solid-state batteries [486] (here the ‘anode free’ terminology refers to the lack of lithium present at the negative electrode *upon cell assembly*).

## 6. Conclusions

This review highlighted recent progress in modeling tribological phenomena across a spectrum of research areas — from traditional theory-driven topics, where increasingly precise comparisons between theory, simulations, and experiments have been made, to emerging fields where modeling is still in its early stages. While AI is revolutionizing tribology — as it is across all scientific and engineering fields — by transforming how phenomena are modeled and systems optimized, progress continues and important advances have been made in conventional modeling approaches. This includes, but is not limited to, recent systematic rather than phenomenological extensions of boundary-element methods beyond the linear-response regime, or the adaptation of valid, modern approaches, such as Persson’s theory of (rubber) friction and contact mechanics, to an ever increasing number of applications.

A common trend in modern research is that phenomena are no longer studied primarily in isolation, such as the friction between two idealized flat surfaces separated by a lubricant. Such a simple setup can significantly underestimate friction coefficients by failing to capture instabilities that only arise in the presence of sufficiently large, roughness induced spatio-temporal stress fluctuations. In recent years, there has been growing emphasis on coupling different aspects of tribological systems, which are key to capture the inherent complexity of interactions depicted in Figure 1, like the one just alluded to. This includes non-trivial effects arising from the interplay between out-of-plane and in-plane elastic deformations in mechanical contacts, the combined influence of surface roughness and lubricants, triboelectricity, tribofilm formation and
evolution, or the synergistic role of (multi-scale) roughness, adhesion and viscoelasticity. Beyond coupling
physical phenomena, researchers are also actively developing and integrating diverse modeling strategies —
both sequential and concurrent — to better capture these complex interactions in the specific tribological
context, where capturing mechanochemical interactions is as important as successfully modeling fluid flow
and deformations.

Despite continued progress in traditional modeling approaches, the integration of AI with conventional
methods might currently represent the most promising research direction. This is evident in already maturing applications, such as the use of machine-learned potentials that strike an unrivaled balance between the
accuracy of density-functional-theory based modeling of tribochemical phenomena and the computational
efficiency of classical force fields. AI also shows great promise in overcoming human-imposed limitations in
constitutive model development. For instance, machine learning can effectively characterize slip-boundary
conditions between lubricants and solid surfaces as functions of temperature, pressure, and shear rate. As a
last example, generative AI can help design entirely new lubricant molecules or surface topographies. These
designs can then be ‘pre-tested’ in molecular or continuum simulations to screen for specific tribological
properties. However, significant opportunities for further effective combination of AI with traditional modeling remain. One example is the simulation of contact opening between nominally flat viscoelastic solids
with short-range adhesion. While this might appear as a relatively simple “single-physics” problem, it proves
exceptionally challenging due to its intrinsically multi-scale nature in both space and time, compounded by
painfully slow mesh-size convergence. Another addition to traditional modeling approaches is the integration
of experimental data in near real-time, exemplified by emerging digital twin frameworks. These frameworks
offer the potential for predictive, continuously updated tribological models, while simultaneously enabling
simulations to directly inform and optimize practical applications.

Despite all methodological progress, the aim of modeling extends beyond producing accurate numbers
or optimized surface geometries—it must also deepen our qualitative understanding. Such insights continue to emerge even from single-method approaches. Examples include the sensitivity of tribochemical
reaction products to multiple stress tensor elements, as well as advances in understanding traditional systems (e.g., zinc-phosphates) and the formation of protective carbonaceous films. Atomistic and microscale
modeling have also fundamentally reshaped our grasp of metallic friction and wear by linking tribological
behavior to microstructural evolution. Simulations reveal how deformation mechanisms—dislocation activity, grain boundary sliding—govern friction across scales, offering predictive insights beyond experimental
reach. These findings have identified strategies to control friction through grain refinement, surface engineering, and multilayered structures, enabling tailored materials for applications from aerospace to vacuum
lubrication.

Similar detailed insights are now targeted for emerging fields like haptic feedback, soft robotics, and
electroadhesion, as well as the broader role of friction in multifunctional systems. A key challenge remains
to reliably incorporate electrical effects, particularly in triboelectricity—one of the oldest and most debated
phenomena. While triboelectric nanogenerators already harness this effect to convert motion into stored
electric energy, even basic questions persist: What are the dominant charge carriers? The answer remains
unclear even for seemingly simple systems, like a raindrop moving past slushy ice in a thundercloud. While
understanding why the skies end up positively charged and the Earth negative may not be central to
tribology, cracking this ancient puzzle might just spark a few more answers—and perhaps even a lightning
bolt of inspiration within tribology and beyond.

## Acknowledgements

S.J.E. and H.J.E. acknowledge Project K2 InTribology2, no. 906860 of the Austrian Research Promotion Agency (FFG). D.D. acknowledges the support received from the Engineering and Physical Sciences Research Council, United Kingdom (EPSRC) via EP/V038044/1 and EP/N025954/1, as well as the support provided from the Royal Academy of Engineering (RAEng) Research Chair in Complex Engineering Interfaces (RCSRF2122-14-143). J.P.E. thanks the RAEng for support via their Research Fellowships scheme. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for
the US Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.
Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views
of the US Department of Energy or the USA Government. Open access funding was provided by TU Wien.

CRediT authorship contribution statement

**Lars Pastewka:** Conceptualization; Writing – original draft (Sect. 2, 3.3, 6) – review & editing (remaining sections). **Antonis I. Vakis:** Conceptualization; Writing – original draft (Sect. 5.1) – review & editing (remaining sections). **Ramin Aghababaei:** Writing – original draft (Sect. 4.1). **Andreas Almqvist:** Writing – original draft (Sect. 2). **Giuseppe Carbone:** Writing – original draft (Sect. 3.1). **Michael Chandross:** Writing – review & editing (Sect. 4.1). **Daniele Dini:** Conceptualization; Visualization; Writing – original draft (Sect. 1, 5, 6). **Stefan J. Eder:** Conceptualization; Data curation; Visualization; Writing – original draft (Sect. 4.1). **Hendrik J. Ehrich:** Visualization. **James P. Ewen:** Writing – original draft (Sect. 2, 4.2). **Nicola Menga:** Visualization; Writing – original draft (Sect. 3.1, 3.2). **Jean-François Molinari:** Conceptualization; Writing – review & editing (all sections). **Gianpietro Moras:** Visualization; Writing – original draft (Sect. 4.2). **Lucia Nicola:** Writing – original draft (Sect. 3.1). **Marco Paggi:** Writing – original draft (Sect. 2, 3.3). **Carmine Putignano:** Writing – original draft (3.3). **Michele Scaraggi:** Writing – original draft (3.3, 5.2,5.3). **Vladislav A. Yastrebov:** Visualization; Writing – original draft (5.1). **Martin H. Müser:** Conceptualization; Writing – original draft (1, 3.4.2,6) – review & editing (remaining sections).

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the authors used ChatGPT in order to improve grammar and
writing. After using this tool/service, the authors reviewed and edited the content as needed and take full
responsibility for the content of the publication.

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