Reference Solution Research Articles

Heuristic based physics informed neural network (H-PINN) approach to analyze nanotribology for viscous flow of ethylene glycol and water under magnetic effects among parallel sheets

In this article, we have conducted the study for the flow and thermal transfer of magneto-hydrodynamic squeezing nanofluid in the middle of two collateral plates extending to infinity using artificial neural network (ANN). The fluid employed in this research is a combination of Ethylene Glycol and water, and we delve into the utilization of a hybrid nanoparticle consisting of Fe3O4 and MoS2 particles. To solve the governing differential equations, we used unsupervised heuristic based physics informed neural network (H-PINN) based fitness function. In this research, the weights and biases of neural network were optimized using a hybridization of heuristic algorithms to achieve high accuracy. The fitness values obtained from proposed approach ranging from10−05 to10−08. The optimal results were then compared with numerical solutions obtained by using Runge-Kutta order-4 method through BVP4c tool as a reference solution, demonstrating the effectiveness of the unsupervised ANN method. The absolute error between the reference solution and proposed heuristic based physics informed neural networks approaches are ranging from2.36×10−04to3.46×10−06, 2.77×10−05to1.20×10−05 and1.10×10−06to6.53×10−07. Our findings demonstrate a strong agreement with the numerical approach, with the maximum discrepancy in the profiles of flow speed and energy profiles. Notably, we observed that an increase in the squeeze number and the Hartman number resulted in a reduction in the velocity profile.

Benchmarking numerical simulation of induced fault slip with semi-analytical solutions

AbstractPore pressure fluctuation in subsurface reservoirs and its resulting mechanical response can cause fault reactivation. Numerical simulation of such induced seismicity is important to develop reliable seismic hazard and risk assessments. However, modeling of fault reactivation is quite challenging, especially in the case of displaced faults, i.e., faults with non-zero offset. In this paper, we perform a systematic benchmarking study to validate two recently developed numerical methods for fault slip simulation. Reference solutions are based on a semi-analytical approach that makes use of inclusion theory and Cauchy-type singular integral equations. The two numerical methods both use finite volume discretizations, but they employ different approaches to represent faults. One of them uses a conformal discrete fault model (DFM) while the other employs an embedded (non-conformal) fault model. The semi-analytical test cases cover a vertical frictionless fault, and inclined displaced faults with constant friction and slip-weakening friction. It was found that both numerical methods accurately represent pre-slip stress fields caused by pore pressure changes. Moreover, they also successfully cope with a vertical frictionless fault. However, for the case with an inclined displaced fault with a constant friction coefficient, the embedded method can not converge for the post-slip phase, whereas the DFM successfully coped with both constant and slip-weakening friction coefficients. In its current implementation, the DFM is therefore the model of choice when accurate simulation of local faulted systems is required.

Modeling and Solving the Knapsack Problem with a Multi-Objective Equilibrium Optimizer Algorithm Based on Weighted Congestion Distance

The knapsack problem is a typical bi-objective combinatorial optimization issue, wherein maximizing the value of the packed items is achieved concurrently with minimizing the weight of the load. Due to the conflicting objectives of the knapsack problem and the typical discrete property of the items involved, swarm intelligence algorithms are commonly employed. The diversity of optimal combinations in the knapsack problem has become a focal point, which involves finding multiple packing solutions at the same value and weight. For this purpose, this paper proposes a Multi-Objective Equilibrium Optimizer Algorithm based on Weighted Congestion Distance (MOEO_WCD). The algorithm employs a non-dominated sorting method to find a set of Pareto front solutions rather than a single optimal solution, offering multiple decision-making options based on the varying needs of the decision-makers. Additionally, MOEO_WCD improves the balance pool generation mechanism and incorporates a weighted congestion incentive, emphasizing the diversity of packing combination solutions under the objectives of value and weight to explore more Pareto front solutions. Considering the discrete characteristics of the knapsack combination optimization problem, our algorithm also incorporates appropriate discrete constraint handling. This paper designs multiple sets of multi-objective knapsack combinatorial optimization problems based on the number of knapsacks, the number of items, and the weights and values of the items. This article compares five algorithms suitable for solving multi-objective problems: MODE, MO-PSO-MM, MO-Ring-PSO-SCD, NSGA-II, and DN-NSGAII. In order to evaluate the performance of the algorithm, this paper proposes a new solution set coverage index for evaluation. We also used the hypervolume indicator to evaluate the diversity of algorithms. The results show that our MOEO-WCD algorithm achieves optimal coverage of the reference composite Pareto front in the decision space of four knapsack problems. The experimental results indicate that our MOEO_WCD algorithm achieves the optimal coverage of the reference composite Pareto front in the decision space for four sets of knapsack problems. Although our MOEO_WCD algorithm covers less of the composite front in the objective space compared with the MODE algorithm for knapsack problem 1, its coverage of the integrated reference solutions in the decision space is greater than that of the MODE algorithm. The experiments demonstrate the superior performance of the MOEO_WCD algorithm on bi-objective knapsack combinatorial optimization problem instances, which provides an important solution to the search for diversity in multi-objective combinatorial optimization solutions.

A Tuneable and Easy-to-Prepare SERS Substrate Based on Ag Nanorods: A Versatile Tool for Solution and Dry-State Analyses

Surface-enhanced Raman spectroscopy is a powerful technique for the ultra-sensitive detection of organic analytes. In this paper, the preparation of SERS substrates based on silver nanorods (AgNRs) is proposed, exploiting a simple protocol which does not require complex procedures and/or sophisticated and expensive instrumentation. For this purpose, various syntheses of AgNRs were tested, and the best one for preparing the SERS active substrate proved to be the one which does not involve surfactants as nanoparticle stabilizers. The plasmonic properties of the selected substrate can be modified based on the concentration of the deposited nanoparticles, allowing for the experimentation of different excitation wavelengths. Positive results were obtained on reference solutions of three natural dyes of historical interest using both green exciting radiation (532 nm) and two near-infrared ones (785 and 850 nm; the latter is combined with the SSE™ technology for further fluorescence quenching). Furthermore, the substrates of AgNRs were found to be suitable for SERS measurements even in dry-state conditions, i.e., only exploiting the electromagnetic interaction between the nanostructured substrate and the dye molecules absorbed onto a wool fibre.

Fourth-order phase field modelling of brittle fracture with strong form meshless method

This study aims to find a solution for crack propagation in 2D brittle elastic material using the local radial basis function collocation method. The staggered solution of the fourth-order phase field and mechanical model is structured with polyharmonic spline shape functions augmented with polynomials. Two benchmark tests are carried out to assess the performance of the method. First, a non-cracked square plate problem is solved under tensile loading to validate the implementation by comparing the numerical and analytical solutions. The analysis shows that the iterative process converges even with a large loading step, whereas the non-iterative process requires smaller steps for convergence to the analytical solution. In the second case, a single-edge cracked square plate subjected to tensile loading is solved, and the results show a good agreement with the reference solution. The effects of the incremental loading, length scale parameter, and mesh convergence for regular and scattered nodes are demonstrated. This study presents a pioneering attempt to solve the phase field crack propagation using a strong-form meshless method. The results underline the essential role of the represented method for an accurate and efficient solution to crack propagation. It also provides valuable insights for future research towards more sophisticated material models.

Small-sample Bayesian error estimation for ergodic, chaotic systems of ordinary differential equations

The discretization of chaotic systems introduces statistical errors in addition to discretization errors into the estimation of quantities of interest. In order to efficiently arrive at estimates of quantities of interest, these two forms of error should be balanced; however, simulations are run without knowledge of the true/asymptotic outputs of interest or their error behaviors. In this work, we develop a framework for error modeling and identification using small-sample Bayesian inference that allows approximation of the optimal balance between sampling time and discretization precision without the computation of high-cost libraries of reference solutions. The result enables the possibility of running chaotic and turbulent simulations in a way that minimizes the total error between sampling and discretization without prior knowledge of the error behavior of the system.

Population Distribution Forecasting Based on the Fusion of Spatiotemporal Basic and External Features: A Case Study of Lujiazui Financial District

Predicting the distribution of people in the time window approaching a disaster is crucial for post-disaster assistance activities and can be useful for evacuation route selection and shelter planning. However, two major limitations have not yet been addressed: (1) Most spatiotemporal prediction models incorporate spatiotemporal features either directly or indirectly, which results in high information redundancy in the parameters of the prediction model and low computational efficiency. (2) These models usually incorporate certain basic and external features, and they can neither change spatiotemporal addressed features according to spatiotemporal features nor change them in real-time according to spatiotemporal features. The spatiotemporal feature embedding methods for these models are inflexible and difficult to interpret. To overcome these problems, a lightweight population density distribution prediction framework that considers both basic and external spatiotemporal features is proposed. In the study, an autoencoder is used to extract spatiotemporal coded information to form a spatiotemporal attention mechanism, and basic and external spatiotemporal feature attention is fused by a fusion framework with learnable weights. The fused spatiotemporal attention is fused with Resnet as the prediction backbone network to predict the people distribution. Comparison and ablation experimental results show that the computational efficiency and interpretability of the prediction framework are improved by maximizing the scalability of the spatiotemporal features of the model by unleashing the scalability of the spatiotemporal features of the model while enhancing the interpretability of the spatiotemporal information as compared to the classical and popular spatiotemporal prediction frameworks. This study has a multiplier effect and provides a reference solution for predicting population distributions in similar regions around the globe.

Propagation of Hydraulic Fractures and Natural Fractures: The Bypassing Behavior in 3D Space

Summary The interaction between natural fractures (NFs) and hydraulic fractures (HFs) in 3D space poses significant challenges to numerical simulation. The interaction behaviors between HFs and NFs in 3D space include crossing, offset, stopping, and bypassing. Many existing numerical simulators are 2D, which inherently limits their ability to account for the vertical growth of fractures. Consequently, they are unable to model the bypassing behavior effectively. In this paper, a mathematical model for the propagation of HFs and NFs in a naturally fractured reservoir is established. The displacement discontinuity method (DDM) is used to solve the rock deformation, while the finite difference method (FDM) is utilized to solve the fluid flow within fractures. The undirected graph structure is used to represent the complex fracture network, and a dynamic adjustment of grid connectivity method is implemented to describe the process by which HFs bypass NFs. By integrating with graphics processing unit (GPU) computing, an efficient 3D simulator for HFs and NFs propagation is developed. The accuracy is verified against analytical solutions and reference solutions. Subsequently, a series of numerical studies on the bypassing behavior are conducted. The primary findings are as follows: (1) The simulator can accurately capture the interactions between HFs and NFs in 3D space, including crossing, arresting, and bypassing behaviors. (2) The bypassing behavior is characterized by three distinct processes—intersection, height growth of HF, and bypassing. (3) During the intersection stage, both the injection pressure and maximum NF width increase. During the height growth stage, the pressure is relatively stable, while the maximum NF width continues to increase. These two stages together result in the “storage” phenomenon. Once the bypassing behavior occurs, both the pressure and the maximum NF width decrease sharply, leading to a “release” phenomenon. Additionally, the “storage” and “release” phenomena may impact proppant transport. (4) Given the presence of bypassing behavior, it is essential to consider the NFs in 3D fracture simulators. The simulator and its findings can provide valuable insights for field design.

Dynamic inversion and optimal tracking control on the ball-plate system based on a linearized nonholonomic multibody model

This paper addresses the optimal control of the ball-plate system, a well-known nonholonomic system in the context of nonprehensile manipulation, using a multibody dynamics approach. The trajectory tracking control of a steady-state circular motion of the ball on the plate, for any radius and potentially off-centric with respect to the plate’s pivoting point, is achieved by designing a Linear-Quadratic Regulator. A spatial multibody model of the ball-plate system is considered. A key contribution is the analytical computation of the circular steady motion of the ball by dynamic inversion, including the control actions to achieve this reference solution. This enables the analytical computation of the linearized equations along this reference motion, resulting in a periodic linear time-varying (LTV) system, and the application of linear controllability criteria for LTV systems. A controllable linear system, involving the Cartesian coordinates of the contact point and the yaw angle of the sphere, is obtained using a convenient coordinate partition in the linearization. Compared to existing results on the same problem, closed-loop stability about the desired trajectory is achieved for any radius of the circular trajectory.

Particulate transport in porous media at pore-scale. Part 1: Unresolved-resolved four-way coupling CFD-DEM

Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) is a powerful approach to simulate particulate flow in porous media at the pore-scale, and hence decipher the complex interplay between particle transport and retention. Two separate CFD-DEM approaches are commonly used in the literature: the unresolved (particle smaller than the grid cell size) and the resolved (particle bigger than the grid cell size) approach. In this paper, we propose a novel CFD-DEM coupling approach that combines both unresolved and resolved coupling. Our new modeling technique allows for the simulation of particulate flows in complex pore morphology characteristic of porous materials. It relies on an efficient searching strategy to find grid cells covered by the particles and on an appropriate calculation of the fluid-solid momentum exchange term. The robustness and efficiency of the computational model are demonstrated using cases for which reference solutions – analytical or experimental – exist. The new unresolved-resolved four-way coupling CFD-DEM is used to investigate pore-clogging and permeability reduction due to the sieving and bridging of particles.

Research on the Progress of Modulation Technology and Data Transmission Technology in Underwater Wireless Optical Communication

Recently, as an efficient data transmission method, underwater wireless optical communication has become one of the key research topics in the fields of military communication and underwater surveillance. Modulation technology and technology in the transmission process play a key role in the UWOC system, which directly affects the performance, accuracy and safety of the system. The advanced modulation techniques from Intensity Modulation (IM), Pulse Modulation, Quadrature Amplitude Modulation (QAM), and Quadrature Phase Shift Keying (QPSK) to the combination of multiple modulation techniques, as well as the development process of modulation technology in optical encryption, are summarized in this paper. In terms of data transmission technology, the technological progress process from simplex to full-duplex communication is summarized. Finally, a reference solution is proposed to solve the challenges in realizing the underwater communication goals of long-distance, high-speed, low-bit error rate, and large-capacity underwater communication at the same time, and future development is prospected.

A DATA DRIVEN METHOD FOR THE DERIVATION OF EXPLICIT ALGEBRAIC REYNOLDS STRESS MODELS APPLIED TO THE WAKE LOSSES OF LOW-PRESSURE TURBINE CASCADES

Abstract This paper introduces and validates a data-driven approach to improve the prediction of linear eddy viscosity models (LEVMs). The general approach is adopted in order to improve the wake mixing of low-pressure turbine (LPT) cascades. The approach follows the rationale applied in the derivation of explicit algebraic Reynolds stress models (EARSMs) by including additional second-order tensors in the Boussinesq assumption. The unknown scalar functions that determine the contributions of each second-order tensor to the Reynolds stresses are approximated as polynomials. A metamodel-assisted multi-objective optimization determines the value of each of the polynomial coefficients by minimizing the difference between the result of the EARSM simulation and reference data provided by a high fidelity large eddy simulation (LES). In this study, tailor made EARSMs are calibrated to improve the prediction of the kinetic energy loss distribution in the wake of the T106C LPT cascade. We investigated the influence of each polynomial coefficient of the EARSM on the results. The models generated by the approach reduced the deviations in total kinetic energy loss between the LES reference solution and the baseline model by approximately 70%. The turbulent quantities are analyzed to identify the physical correlations between the model inputs and the improvement. The transferability of the models to unseen test cases was assessed using the MTU-T161 LPT cascade. In summary, the suggested approach was able to generate tailor made EARSM models that reduce the deviations between RANS and LES for the mixing of turbulent wake flows.

Jade Identification Using Ultraviolet Spectroscopy Based on the SpectraViT Model Incorporating CNN and Transformer

Jade is a highly valuable and diverse gemstone, and its spectral characteristics can be used to identify its quality and type. We propose a jade ultraviolet (UV) spectrum recognition model based on deep learning, called SpectraViT, aiming to improve the accuracy and efficiency of jade identification. The algorithm combines residual modules to extract local features and transformers to capture global dependencies of jade’s UV spectrum, and finally classifying jade using fully connected layers. Experiments were conducted on a UV spectrum dataset containing four types of jade (natural diamond, cultivated diamond (CVD/HPHT), and moissanite). The results show that the algorithm can effectively identify different types of jade, achieving an accuracy of 99.24%, surpassing traditional algorithms based on Support Vector Machines (SVM) and Partial Least Squares Discriminant Analysis (PLS_DA), as well as other deep learning methods. This paper also provides a reference solution for other spectral analysis problems.

Multi-Batch Carrier-Based UAV Formation Rendezvous Method Based on Improved Sequential Convex Programming

The limitations of the existing catapults necessitate multiple batches of take-offs for carrier-based unmanned aerial vehicles (UAVs) to form a formation. Because of the differences in takeoff time and location of each batch of UAVs, ensuring the temporal and spatial consistency and rendezvous efficiency of the formation becomes crucial. Concerning the challenges mentioned above, a multi-batch formation rendezvous method based on improved sequential convex programming (SCP) is proposed. A reverse solution approach based on the multi-batch rendezvous process is developed. On this basis, a non-convex optimization problem is formulated considering the following constraints: UAV dynamics, collision avoidance, obstacle avoidance, and formation consistency. An SCP method that makes use of the trust region strategy is introduced to solve the problem efficiently. Due to the spatiotemporal coupling characteristics of the rendezvous process, an inappropriate initial solution for SCP will inevitably reduce the rendezvous efficiency. Thus, an initial solution tolerance mechanism is introduced to improve the SCP. This mechanism follows the idea of simulated annealing, allowing the SCP to search for better reference solutions in a wider space. By utilizing the initial solution tolerance SCP (IST-SCP), the multi-batch formation rendezvous algorithm is developed correspondingly. Simulation results are obtained to verify the effectiveness and adaptability of the proposed method. IST-SCP reduces the rendezvous time from poor initial solutions without significantly increasing the computing time.

Effect of Natural Inhibitors on the Corrosion Properties of Grade 2 Titanium Alloy.

This study investigates the effects of natural inhibitors (pomegranate, algae, and tomato extracts) on the corrosion resistance of titanium (grade 2). To deepen understanding the inhibition mechanism, Molecular Dynamic (MD) and Monte Carlo (MC) simulations were employed to analyze adsorption behaviors and identify optimal adsorption sites on titanium oxide (TiO2) surfaces for compounds within the inhibitors. Results indicate non-flat adsorption orientations, with pomegranate peel extract components showing superior inhibition capabilities, attributed to the formation of strong O-H chemical bonds with the TiO2 surface. In the experimental part of the study Electrochemical Impedance Spectroscopy (EIS) and Potentiodynamic Polarization (PDP) were conducted. Two electrolytes were tested: a solution 3.5% NaCl and a solution 0.5 M NaOH. All the tests were performed with 5% of inhibitor and with the reference solution. Also, inhibition efficiency was calculated on the base of PDP tests. The study found that pomegranate extract can act as a good corrosion inhibitor for titanium alloy in aqueous solutions 0.5 M NaOH. This was demonstrated by the increase in the corrosion potential and impedance modulus and decrease in the corrosion current density after the addition of pomegranate extract to the solution. However, in a 3.5% NaCl solution, the efficacy of pomegranate extract was less pronounced, probably due to the high aggressivity of the electrolyte. Tomato and algae extract have instead shown very low inhibition effects in all the tested conditions.

Closed-Boundary Reflections of Shallow Water Waves as an Open Challenge for Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving partial differential equations (PDEs) in fluid dynamics. By using PDE-derived loss functions and auto-differentiation, PINNs can recover solutions without requiring costly simulation data, spatial gridding, or time discretization. However, PINNs often exhibit slow or incomplete convergence, depending on the architecture, optimization algorithms, and complexity of the PDEs. To address these difficulties, a variety of novel and repurposed techniques have been introduced to improve convergence. Despite these efforts, their effectiveness is difficult to assess due to the wide range of problems and network architectures. As a novel test case for PINNs, we propose one-dimensional shallow water equations with closed boundaries, where the solutions exhibit repeated boundary wave reflections. After carefully constructing a reference solution, we evaluate the performance of PINNs across different architectures, optimizers, and special training techniques. Despite the simplicity of the problem for classical methods, PINNs only achieve accurate results after prohibitively long training times. While some techniques provide modest improvements in stability and accuracy, this problem remains an open challenge for PINNs, suggesting that it could serve as a valuable testbed for future research on PINN training techniques and optimization strategies.

Three-dimensional anisotropic unified continuum model for simulating the healing of damaged soft biological tissues.

The soft biological tissues have the ability to heal and self-repair after damage or injury. During the healing process, damaged tissues are replaced by newly produced undamaged tissue to restore homeostasis. Computational modeling serves as an effective tool for simulating the healing process and understanding the underlying mechanisms. In previous work, we developed the first unified continuum damage model for the healing of soft biological tissues. However, the initial theory lacked generalizability to more realistic scenarios and applicability to biomechanical problems due to the simplicity of the isotropic constitutive model and two-dimensional simulations. Therefore, we further improve our approach by developing a three-dimensional anisotropic unified healing model to address more realistic challenges. By using the Holzapfel-Gasser-Ogden model as the hyperelastic term, the influence of the collagen fibers is considered and the reorientation of fibers in healing is simulated. Three numerical examples related to hypertension, aneurysm, and restenosis of the atherosclerotic artery after balloon angioplasty are presented to demonstrate the effectiveness of the proposed model. By comparing numerical solutions and reference solutions, we demonstrate the ability of the proposed model in simulating long-term tissue healing process and analyze the impact of anisotropic terms.

Efficient seismic fragility analysis considering uncertainties in structural systems and ground motions

AbstractFragility plays a pivotal role in performance‐based earthquake engineering, which represents the seismic performance of structural systems. To comprehensively understand the structural performance under seismic events, it is necessary to consider uncertainties in the structural model, i.e., epistemic uncertainties. However, considering such uncertainties is challenging due to computational complexity, leading most fragility analyses only to consider the chaotic behavior of ground motions on structural responses, i.e., aleatoric uncertainties. To address this challenge, this study proposes an adaptive algorithm that intertwines with the conventional fragility analysis procedures to consider both aleatoric and epistemic uncertainties. The algorithm introduces Gaussian process‐based metamodels to efficiently consider epistemic uncertainties with a small number of time history analyses. Steel moment‐resisting frame structures and a reinforced concrete building are used to demonstrate the improved efficiency and wide applicability of the proposed method. In each case, the proposed method yields fragility curves consistent with reference solutions but with substantially lower computational effort. Comprehensive discussions are provided regarding ground motion sets, structural types, and definitions of limit‐states to demonstrate the robustness of the proposed approach.

Semi-implicit schemes for modeling water flow and solute transport in unsaturated soils

The coupled model of water flow and solute transport in unsaturated soils is addressed in this study. Building upon previous research findings by Keita, Beljadid, and Bourgault, we investigate a class of second-order time-stepping techniques where two free parameters are introduced, to identify the most stable and accurate scheme. The spatial discretization of the Richards equation is accomplished using the mixed finite element method. The proposed approach involves formulating noniterative schemes using an extrapolation formula and Taylor approximation in time to linearize nonlinear terms. Additionally, a specialized regularization technique is applied to ensure the convergence of the proposed numerical methods. Numerical simulations are conducted to determine the optimal scheme for solving the Richards equation, which is subsequently extended to the transport equation.Numerical simulations of water flow reveal the good accuracy of three schemes—SBDF, MSBDF, and Richards-M2 for homogeneous and heterogeneous soils. Notably, the SBDF scheme stands out for its computational efficiency and stability, especially when gravity forces dominate over capillary forces. Through numerical analysis of the coupled semi-implicit schemes, our results affirm the SBDF scheme’s superior robustness, establishing it as the optimal choice among the proposed numerical methods. Therefore, the SBDF scheme is employed to solve the coupled model of water flow and solute transport. We conducted various numerical experiments to solve the coupled model, addressing scenarios including single and multispecies nitrogen transport, pore water electrical conductivity, and nitrate transport. The SBDF scheme’s accuracy was rigorously verified through comparisons with reference solutions and experimental data. This establishes the SBDF scheme as an efficient alternative to traditional implicit methods for modeling water flow and solute transport in unsaturated soils.

Adding friction to Third Medium Contact: A crystal plasticity inspired approach

This paper presents the first method to enable friction in the Third Medium Contact (TMC) method. TMC embeds a solid in a highly compliant medium, which becomes infinitely stiff under ultimate compression, thus allowing forces to be transferred between the solids when the medium between the solids is compressed. This approach is increasingly adopted for integrating internal contact in structural design processes, owing to its continuous, fully implicit characteristics, simplicity, and its stability when applying regularisation to the third medium regions. The lack of friction has previously restricted the use of the TMC method in simulating real-world contact conditions. Here, we address this issue by (1) integrating an anisotropic term into a Neo-Hookean material model to provide shear resistance, and (2) employing a framework inspired by crystal plasticity that includes a yield criterion specifically designed to replicate the effects of Coulomb friction.The effectiveness of the method is demonstrated through two examples: (1) a smooth sliding contact problem and (2) a non-smooth C-shaped structure. Results demonstrate a close agreement with reference solutions obtained by a conventional Lagrange multiplier approach. While the method, for now, requires user-defined slip directions, it represents a significant advancement by enabling the integration of friction into TMC, thereby broadening its applicability to problems involving realistic frictional contact. Future research should focus on restoring the fully implicit nature of TMC in the presence of friction, and on developing automated slip direction definitions to enhance usability and expand the method’s versatility.