Non-flat Surfaces Research Articles

Microstructured Liquid Metal-Based Embedded-Type Sensor Array for Curved Pressure Mapping.

Human hands can envelop the surface of an object and recognize its shape through touch. However, existing stretchable haptic sensors exhibit limited flexibility and stability to detect pressure during deformation, while also solely achieving recognition of planar objects. Inspired by the structure of skin tissue, an embedded construction-enabled liquid metal-based e-skin composed of a liquid metal microstructured electrode (LM-ME) array is fabricated for curved pressure mapping. The embedded LM-ME-based sensor elements are fabricated by using femtosecond laser-induced micro/nanostructures and water/hydrogel assisted patterning method, which enables high sensitivity (7.42kPa-1 in the range of 0-0.1kPa) and high stability through an interlinked support isolation structure for the sensor units. The sensor array with a high interfacial toughness of 1328Jm-2 can maintain pressure sensation under bending and stretching conditions. Additionally, the embedded construction and laser-induced bumps effectively reduce crosstalk from 58 to 7.8% compared to conventional flexible sensors with shared surfaces. The stretchable and mechanically stable sensor arrays possess shape-adaptability that enables pressure mapping on non-flat surfaces, which has great potential for object recognition in robotic skins and human-computer interaction.

In vitro photoprotective efficacy and photostability of synthesized star-shaped ZnO nanoaggregates associated with ethylhexyl methoxycinnamate and butyl methoxydibenzoylmethane

The heightened susceptibility to skin cancer correlates with exposure to ultraviolet (UV) radiation, which can induce various cutaneous injuries. Inorganic UV filters, like zinc oxide (ZnO), are extensively utilized in sunscreens owing to their capacity to scatter and reflect UV radiation. The efficacy of inorganic UV filters can be augmented across a wider spectrum through synergistic combinations with other active compounds, such as organic UV filters. In this study, we synthesized and evaluated the in vitro effectiveness of star-shaped ZnO nanoaggregates. The samples were obtained employing a simple and greener precipitation method in an aqueous solution. The synthesized ZnO nanoaggregates were characterized through X-ray diffraction, UV/Vis spectroscopy, and transmission electron microscopy. The characterization suggests the aggregation of nanocrystals, with hexagonal wurtzite geometry, enabling the formation of star-shaped particles. The irregular (non-flat) surface and high surface area combined with light absorption in the UVA region make the material susceptible to the application of sun protection. Sunscreens formulated with the synthesized ZnOng in conjunction with ethylhexyl p-methoxycinnamate (EHMC) and/or butyl methoxydibenzoylmethane (BMDBM) were evaluated for in vitro sun protection factor (SPF) and critical wavelength (cλ) using diffuse reflectance spectrophotometry with an integrated sphere. Photostability assessments were also conducted using artificial UV radiation. Sunscreen formulations containing ZnOng in combination with EHMC and BMDBM exhibited a substantial increase in in vitro SPF, approximately 990 % (from SPF 26 to 285). Furthermore, the synthesized ZnOng demonstrated higher in vitro efficacy compared to commercial ZnO active ingredients. Although all samples experienced reductions in SPF values during the photostability assay, ZnOng + EHMC + BMDBM retained a broad-spectrum profile (SPF > 15 and cλ > 370 nm). Based on the distinctive properties and in vitro performance of star-shaped ZnOng, we propose that this synthesized inorganic UV filter could serve as an alternative for enhancing the SPF of sunscreen systems while reducing the concentrations of organic UV filters.

Cognitive Maps for a Non-Euclidean Environment: Path Integration and Spatial Memory on a Sphere

Humans build mental models of the world and utilize them for various cognitive tasks. The exact form of cognitive maps is not fully understood, especially for novel and complex environments beyond the flat Euclidean environment. To address this gap, we investigated path integration—a critical process underlying cognitive mapping—and spatial-memory capacity on the spherical (non-Euclidean) and planar (Euclidean) environments in young healthy adults (N = 20) using immersive virtual reality. We observed a strong Euclidean bias during the path-integration task on the spherical surface, even among participants who possessed knowledge of non-Euclidean geometry. Notably, despite this bias, participants demonstrated reasonable navigation ability on the sphere. This observation and simulation suggest that humans navigate nonflat surfaces by constructing locally confined Euclidean maps and flexibly combining them. This insight sheds light on potential neural mechanisms and behavioral strategies for solving complex cognitive tasks.

Determination of the acoustic characteristics of a gabion noise barrier

In recent road construction projects in NL more and more stone gabions are used as noise reducing measure. First measurements on noise characteristics on gabions using EN 1793-5 showed peculiar results for sound absorption. This was thought to be an effect of the thickness of the gabion and due to scattering of the sound on the non-flat surface. A new investigation was done on stone gabion NRD's and on a regular reflective and absorptive NRD. Focus was on the applicability of EN 1793-5 for determination of the sound reflection characteristics of gabion NRD's. This paper shows the results of measurements on gabion and "regular" NRD's, and of model simulation of these measurements to understand the results, and give guidance on modeling a gabion NRD in a general TNM.

Visualization of Atomic Structures on Faceted and Nonflat Surfaces by the Difference-of-Gaussians Approach

Visualization of Atomic Structures on Faceted and Nonflat Surfaces by the Difference-of-Gaussians Approach

Determination of Parameters of Radio Frequency Identification Transponder Antennas Dedicated to IoTT Systems Located on Non-Planar Objects

Integration of Radio Frequency Identification (RFID) technology with conductive textiles has greatly expanded the possibilities for creating smart devices that fit perfectly into the concept of the Internet of Things. The use of e-textiles for antenna manufacturing has enabled the development of a textronic RFID tag. Integration of such tags into products with often non-flat surfaces may result in exposure to changes in antenna geometry caused by bending. As a result, the antenna parameters may change, resulting in disruption of the entire tag operation. The authors, through simulation and experimental studies, analyzed the effects of bending the antennas of RFID tags operating in the HF (High Frequency) band.

The characterization of cell traction force on nonflat surfaces with different curvature by elastic hydrogel microspheres.

It is of great importance to study the detachment/attachment behaviors of cells (cancer cell, immune cell, and epithelial cell), as they are closely related with tumor metastasis, immunoreaction, and tissue development at variety scales. To characterize the detachment/attachment during the interaction between cells and substrate, some researchers proposed using cell traction force (CTF) as the indicator. To date, various strategies have been developed to measure the CTF. However, these methods only realize the measurements of cell passive forces on flat cases. To quantify the active CTF on nonflat surfaces, which can better mimic the in vivo case, we employed elastic hydrogel microspheres as a force sensor. The microspheres were fabricated by microfluidic chips with controllable size and mechanical properties to mimic substrate. Cells were cultured on microsphere and the CTF led to the deformation of microsphere. By detecting the morphology information, the CTF exerted by attached cells can be calculated by the in-house numerical code. Using these microspheres, the CTF of various cells (including tumor cell, immunological cell, and epithelium cell) were successfully obtained on nonflat surfaces with different curvature radii. The proposed method provides a versatile platform to measure the CTF with high precision and to understand the detachment/attachment behaviors during physiology processes.

Highly Adaptive Kirigami-Metastructure Adhesive with Vertically Self-Aligning Octopus-like 3D Suction Cups for Efficient Wet Adhesion to Complexly Curved Surfaces.

An essential requirement for biomedical devices is the capability of conformal adaptability on diverse irregular 3D (three-dimensional) nonflat surfaces in the human body that may be covered with liquids such as mucus or sweat. However, the development of reversible adhesive interface materials for biodevices that function on complex biological surfaces is challenging due to the wet, slippery, smooth, and curved surface properties. Herein, we present an ultra-adaptive bioadhesive for irregular 3D oral cavities covered with saliva by integrating a kirigami-metastructure and vertically self-aligning suction cups. The flared suction cup, inspired by octopus tentacles, allows adhesion to moist surfaces. Additionally, the kirigami-based auxetic metastructure with a negative Poisson's ratio relieves the stress caused by tensile strain, thereby mitigating the stress caused by curved surfaces and enabling conformal contact with the surface. As a result, the adhesive strength of the proposed auxetic adhesive is twice that of adhesives with a flat backbone on highly curved porcine palates. For potential application, the proposed auxetic adhesive is mounted on a denture and performs successfully in human subject feasibility evaluations. An integrated design of these two structures may provide functionality and potential for biomedical applications.

Droplet asymmetry bouncing on structured surfaces: A simulation based on SPH method

The impact of a liquid droplet onto a macro-structured super-hydrophobic surface, results in an asymmetric spreading-retraction process and a significant decrease in contact time. The process involves large deformation of droplets and evolution of surface morphology, so it is difficult to efficiently simulate using traditional grid-based methods. In this study, a numerical model is established using the mesh-free smoothed particle hydrodynamics (SPH) method to simulate the interaction of liquid droplets with solid surfaces exhibiting complex macro-textures. Leveraging the Lagrange nature of SPH, liquid droplets can be model using free surface boundary condition. The weakly compressible SPH formulation is employed to discretize the governing equations of liquid. Surface tension is captured by introducing an additional negative pressure term, inducing attractive forces among fluid particles. Kernel functions are carefully chosen to mitigate stress instability resulting from droplet spreading and retraction. The model is then applied to simulate the dynamic processes of droplets impact on flat and non-flat super-hydrophobic surfaces. The bouncing dynamics of droplets are investigated under varying conditions, including Weber number, size, and morphology of macro-scale surface structures. Our simulation results for contact time, maximum diameter, and droplet morphology align closely with experimental observations. The contact time of the droplet exhibits a dependency on its size and surface geometry, with a transition towards planar geometry diminishing asymmetric spreading effects. The findings highlight the significance of Weber number and cylinder diameter in determining contact time, providing insights for the design of optimized surface structures for specific droplet impact parameters. In addition, the use of a free-surface condition for modeling proved computationally efficient for 3D simulations. The model effectively reproduces nonlinear behaviors such as droplet spreading, splashing, and bouncing, highlighting the significant advantage of SPH in simulating such problems.

Design, Manufacturing, and Analysis of Periodic Three-Dimensional Cellular Materials for Energy Absorption Applications: A Critical Review.

Cellular materials offer industries the ability to close gaps in the material selection design space with properties not otherwise achievable by bulk, monolithic counterparts. Their superior specific strength, stiffness, and energy absorption, as well as their multi-functionality, makes them desirable for a wide range of applications. The objective of this paper is to compile and present a review of the open literature focusing on the energy absorption of periodic three-dimensional cellular materials. The review begins with the methodical cataloging of qualitative and quantitative elements from 100 papers in the available literature and then provides readers with a thorough overview of the state of this research field, discussing areas such as parent material(s), manufacturing methods, cell topologies, cross-section shapes for truss topologies, analysis methods, loading types, and test strain rates. Based on these collected data, areas of great and limited research are identified and future avenues of interest are suggested for the continued maturation and growth of this field, such as the development of a consistent naming and classification system for topologies; the creation of test standards considering additive manufacturing processes; further investigation of non-uniform and non-cylindrical struts on the performance of truss lattices; and further investigation into the performance of lattice materials under the impact of non-flat surfaces and projectiles. Finally, the numerical energy absorption (by mass and by volume) data of 76 papers are presented across multiple property selection charts, highlighting various materials, manufacturing methods, and topology groups. While there are noticeable differences at certain densities, the graphs show that the categorical differences within those groups have large overlap in terms of energy absorption performance and can be referenced to identify areas for further investigation and to help in the preliminary design process by researchers and industry professionals alike.

Numerical analysis of rotating scans’ effect on surface roughness in laser-powder bed fusion

The rotating scanning strategy is a critical factor for top surface roughness in laser-powder bed fusion (L-PBF), yet the underlying mechanism remains elusive. This study introduces an integrated L-PBF model, encompassing powder packing and molten pool fluid dynamics analysis, to investigate how surface roughness accumulates across layers with non-rotating scans but is mitigated with rotating scans. To address computational complexity and prediction errors associated with multi-layer simulations, the model utilizes an experimentally built part as substrate and simulates single-layer depositions with varying scanning rotation angles. Additionally, an as-machined surface representing ideal flat substrate is included for comparative analysis. Results indicate that on as-built surfaces featuring alternating peak-valley patterns, both powder packing structure and fusion zone shape are location-dependent. To effectively characterize the packing structure on such non-flat surfaces, an effective packing density is proposed. Specifically, peak locations exhibit a thinner powder layer, a 14.5% increase in effective packing density, and a 7% decrease in penetration depth compared to valley locations. The circulation flow, driven by recoil pressure and Marangoni force, is responsible for the reduced surface roughness with rotating scans. Specifically, the circulation flow intersects with multiple peaks and valleys, effectively promoting material redistribution among these tracks and disrupting the peak-valley patterns. Conversely, the peak-valley patterns are preserved and may propagate to subsequent layers with non-rotating scans.

Robotized technologies for enhanced shipyard operations: challenges and solutions

Large component manufacturing relies heavily on manual operations and human workers. Human-centric solutions can preserve industry-specific knowledge, extend capabilities, and improve job performance. Three robotized technologies were developed for shipyard operations: ABB™ and KUKA™ robot hand-guiding systems (HGS), a lightweight collaborative system for plasma cutting, and a cost-effective 3D projection system for retrofitting. These technologies were developed at the open didactic factory, which served as platforms for rapid technological advancement. The HGS was integrated with ABB™ and KUKA™, and the 3D projection technology and lightweight collaborative system offered a cost-effective solution for small and medium shipyards. However, transitioning to non-flat surfaces presents challenges due to geometric variations and discrepancies between the computer-aided design model and the actual component.

A hybrid wave and finite element/boundary element method for predicting the vibroacoustic characteristics of finite-width complex structures

This paper presents a hybrid wave and finite element/boundary element method for predicting the vibroacoustic characteristics of complex panels characterised by an irregular cross-sectional shape with a non-flat upper surface. In this approach, the panels are treated as waveguides and only a small segment of the panel is modelled using finite elements. The mass and stiffness matrices of the segment are then post-processed to project the motion onto its cross-sectional boundaries interfacing with the surrounding fluids. The acoustic pressures in the fluids are modelled by applying Fourier transforms to the Helmholtz boundary integral equations in the wavenumber domain. For each wavenumber component, the pressures acting on the segment are transformed into external nodal forces by evaluating the virtual work performed by the surface pressure on the segment. The wave and finite element formulations are subsequently coupled to the discretised boundary integral equations to determine the response of the panel to acoustic wave excitation. The hybrid method for predicting dispersion curves and sound transmission is validated through comparisons with predictions obtained from both an analytical model and a wave-based method found in the literature. To demonstrate the practical utility of the approach, the hybrid method is employed to predict sound transmission through a corrugated sandwich panel, where developing an analytical model is difficult. The method provides accurate predictions at a low computational cost.

Free boundary problems of the incompressible Navier–Stokes equations with non-flat initial surface in the critical Besov space

Global well-posedness of the Navier–Stokes equations with a free boundary condition is considered in the scaling critical homogeneous Besov spaces B˙p,1-1+n/p(R+n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{B}}_{p,1}^{-1+n/p}({\\mathbb {R}}^n_+)$$\\end{document} with n-1<p<2n-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n-1< p< 2n-1$$\\end{document}. To show the global well-posedness, we establish end-point maximal L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document}-regularity for the initial-boundary value problem of the Stokes equations. Such an estimate is obtained via related estimate for the initial-boundary value problem of the heat equation with the inhomogeneous Neumann data as well as the pressure estimate in the critical Besov space framework. The proof heavily depends on the explicit expression of the fundamental integral kernel of the Lagrange transformed linearized Stokes equations and the almost orthogonal estimates with the space-time Littlewood–Paley dyadic decompositions. Our result here improves the initial space and boundary state than previous results by Danchin–Hieber–Mucha–Tolksdorf (Free boundary problems via Da Prato–Grisvard theory. arXiv:2011.07918v2) and ourselves (Ogawa and Shimizu in J Evol Equ 22(30):67, 2022; Ogawa and Shimizu in J Math Soc Jpn. arXiv:2211.06952v3).

ZMP — Where Are We After Fifty-Five Years?

Twenty years ago in the first issue of IJHR, among others, there was a published paper [M. Vukobratović and B. Borovac, Zero-moment point — Thirty five years of its life, Int. J. Humanoid Robot. 1(1) (2004) 157–173], devoted to well-known zero-moment point (ZMP) concept. Its role in biped locomotion (in the preservation of dynamic balance during walking and gait synthesis) was (and still is) extremely significant. This paper is aimed to present, how far we have gone in the past 20 years in the realization of bipedal walking, what are remaining open challenges and what we can expect in the further development. At the beginning of the paper, we will briefly refer to some still existing misinterpretations of the ZMP notion, related to specific boundary cases, when the terms Center of Pressure (CoP) and ZMP are still being mixed. Then, we will point your attention to the discussion of two important issues: attempts of generalization of ZMP notion in case of motion in the presence of multiple, spatially distributed and non-planar contacts and walk realization in a non-laboratory environment (unstructured environment and on the non-flat ground surface). Of course, looking at “how humans do it” has always been an inspiration for the realization of complex tasks by humanoids. Learning to walk is a task where several successful realizations have appeared only recently, so we will look at this topic at the end of this paper.

Evaluating the Field Emission Properties of N-Type Black Silicon Cold Cathodes Based on a Three-Dimensional Model.

Black silicon (BS), a nanostructured silicon surface containing highly roughened surface morphology, has recently emerged as a promising candidate for field emission (FE) cathodes in novel electron sources due to its huge number of sharp tips with ease of large-scale fabrication and controllable geometrical shapes. However, evaluating the FE performance of BS-based nanostructures with high accuracy is still a challenge due to the increasing complexity in the surface morphology. Here, we demonstrate a 3D modeling methodology to fully characterize highly disordered BS-based field emitters randomly distributed on a roughened nonflat surface. We fabricated BS cathode samples with different morphological features to demonstrate the validity of this method. We utilize parametrized scanning electron microscopy images that provide high-precision morphology details, successfully describing the electric field distribution in field emitters and linking the theoretical analysis with the measured FE property of the complex nanostructures with high precision. The 3D model developed here reveals a relationship between the field emission performance and the density of the cones, successfully reproducing the classical relationship between current density J and electric field E (J-E curve). The proposed modeling approach is expected to offer a powerful tool to accurately describe the field emission properties of large-scale, disordered nano cold cathodes, thus serving as a guide for the design and application of BS as a field electron emission material.

Thermally and electrically tunable infrared perovskite devices for alternatively cooling and heat energy harvesting

Radiative energy harvesting from the sun and outer space is a feasible pathway to develop novel low-carbon energy technologies. However, most reported radiative energy harvesting is discontinuous during the alternation of day and night. Herein, a simple intelligent device is designed for all-weather radiative energy harvesting by depositing bendable mica substrate through oxide perovskite. Under thermal excitation, the intelligent device exhibits a comparable infrared emissivity as the emissivity at the phase transition temperature of 323 K. Below the phase transition temperature, it is first reported that the infrared emissivity shows a significant electrically adjustable characteristic, which increases with the increase of voltage. Outdoor experiments demonstrate that the intelligent device can achieve a sub-ambient temperature drop of 8 °C with a harvested cooling energy of 62W/m2 at nighttime and a temperature rise of 75 °C with a harvested heat energy of 627W/m2 at daytime. More importantly, the bendable mica substrate provides good flexibility for devices, making it easy to attach to any flat or non-flat surface. This intelligent design promotes the development of bendable perovskite devices with alternating cooling and heat acquisition.

Finite-difference method for modeling the surface wave propagation with surface topography in anisotropic-viscoelastic media

The growth of urbanization makes it increasingly important to accurately investigate underground spaces. Surface-wave-based inversion methods are becoming popular due to their cost-effectiveness and efficiency in reconstructing underground space. However, these methods may produce inaccurate results in the presence of media anisotropy or/and viscoelasticity. To investigate the influence of media anisotropy or viscoelasticity on surface waves, it is crucial to develop an efficient and accurate forward modeling method in anisotropic-viscoelastic (AV) media. The finite-difference (FD) method is a widely used forward modeling method in surface-wave-based inversion methods. However, implementing the free-surface boundary condition and representing non-flat topography can be challenging. Considering the challenges described above, this study proposes a simple and efficient FD method for modeling surface-wave propagation. The proposed method employs a parameter-modified strategy to implement the stress-free condition by modifying the model parameters near the (non-) flat free-surface boundary. A staircase discretization strategy is then used to represent the non-flat free surface. To suppress the staircase diffractions caused by the staircase discretization strategy, an independent wavefield superposition is adopted with modeling results of different parameter configurations. Compared with conventional FD methods, the proposed method can reduce computational costs while accurately simulating surface waves. Numerical experiments have demonstrated the accuracy and feasibility of the proposed method. The proposed method provides a theoretical basis for surface-wave-based inversion methods and contributes to the development of accurate underground space investigation.

Examining polarizing and non-polarizing filters for road sports.

The use of sunglasses and polarized sunglasses is common in all aspects of life and is very popular in outdoor athletic activities. However, the choice of athletes regarding their sunglasses is often not dictated by the performance ensured by one model rather than another but by other factors such as look or wearability due also to the lack of technical data on cataloguess. A conscious choice of filters to use, also according to road and weather conditions, supported by quantitative data, would instead allow athletes to improve their visual comfort and sport experience. The transmission spectra of 10 pairs of sports sunglasses (five polarized and five not polarized) were measured and related to the road luminance for different sun positions in both horizontal and vertical polarizations. The luminous transmission factor was calculated, and the luminance quantities while wearing the glasses were defined and calculated for all cases. A survey was submitted to a group of athletes to collect their impressions and relate them to the measurement results. The pairs of polarized and non-polarized sports sunglasses showed similar transmission factors, so their ability to mitigate outdoor light is almost the same-the main difference lies in the polarized light transmitted. Outdoor measurements showed that the light reflected by the road has a substantial polarized horizontal component. Polarized sunglasses block much of the light reflected by the road, resulting in a darker appearance of the road and reducing the glare of the scene in bright sunlight. The decrease in road luminance increases the contrast discrimination of other objects in the scene, which reflect sunlight in a non-polarized way (e.g., non-flat surfaces). The survey demonstrates that interviewed athletes prefer polarized sunglasses for these aformentioned reasons. This study highlights the advantages of polarizing sunglasses for athletic activities on roads because the road surface often reflects polarized light depending on the position of the sun.

Modelling the cross-sectional profile of the kerf generated in overlapped pass erosion in abrasive waterjet milling of Al6061-T6 alloy

Machining complex surfaces on difficult-to-cut materials by conventional methods is challenging due to the issues that arise from both the ‘freeform surface generation’ and the ‘machining difficult-to-cut materials’. On the other hand, abrasive waterjets (AWJs) have proven their unique capabilities in machining a wide range of materials and 3D shapes by maneuvering the jet strategically. In realizing 3D shapes through AWJ milling, the cross-sectional profile (CP) of the kerf, i.e. (i) trench — formed in a single pass erosion and (ii) cavity — formed in an overlapped pass erosion, need to be predicted apriori. However, the stochastic and aggressive behaviour of the AWJ, and the lack of complete understanding of the kerf generation, make the accurate prediction of its CP a difficult task. Furthermore, the cavity generated (by overlapping two trenches) is not a simple linear combination of trenches generated in two single AWJ passes. Also, the modelling efforts that consider both the dynamic jet characteristics and the non-linearity in the kerf formation are very limited. In this work, analytical models are proposed to predict CP the kerf (trench and the cavity) milled by the AWJs by considering the experimental understanding gained on the kerf generation in single and overlapped pass erosion. The modelling strategy evaluates the local erosion volume and sweeps this over the CP along the top width of the kerf. This strategy enables the incorporation of region-wise physical phenomenon in the material removal. Furthermore, it considers the (i) aggressive and stochastic nature of the AWJ, and (ii) particle erosion theories applicable to ductile materials, which pose multiple challenges during conventional machining. The model developed for the trench considers the effective jet divergence, spatial abrasive mass- and velocity-distributions in the jet plume, as inputs. Towards capturing the non-linearity in the cavity generation, the non-flat surface from the previous pass and its effect on the variation of local particle impact angles, uneven jet deflection during subsequent passes around the jet axis, and the degree of overlap were considered. From the experimental validation, it was observed that in the single pass and overlapped passes at different degrees of overlaps (5 %–80 %), the proposed model predicts the kerf geometry with a maximum mean absolute error (MAE) of 36 μm and 49 μm, and the maximum depth of CP with a maximum error of 7 % and 11 %, respectively.