This study explores fatigue crack propagation in face-centered cubic metals using an adaptive concurrent multiscale framework that couples coarse-grained molecular dynamics with the finite element method. The approach dynamically refines the mesh and activates atomistic regions as the crack advances, enabling high-resolution modeling near the crack tip while preserving computational efficiency in less critical regions. A crack-free surface identification method is used to track the evolving crack tip. Coarse-graining of dislocation plasticity mitigates large deformations, ensuring stable crack growth during fatigue cycles. A refinement scheme activates virtual atoms when the crack tip approaches the FEM domain, with the continuum model imposing displacements. The framework is applied to simulate fatigue failure in single-crystal aluminum. The results demonstrate agreement with fully atomistic and non-adaptive multiscale models in terms of crack trajectory, stress intensity versus crack growth rate, and the Paris law exponent, while achieving up to a 46

In this paper, multiscale simulations at macroscale and microscale are presented for microstructure directional evolution during directed energy deposition (DED) process of IN718. Macroscale simulations consist of heat conduction equation where a progressive function controls the thermal properties of materials in the front of and behind the laser beam. Microscale simulations are performed for a microcell considered within the solid-melt interface and are based on a mechanics-based phase field model for microstructure directional evolution which consists of Allen-Cahn equation for phase order parameter, Cahn-Hilliard equation for composition and elasticity equations. Incorporating elastic energy allows for accounting volumetric inelastic strains arising during melting/solidification. This approach also ensures the accurate representation of thermodynamically consistent stress at the interface between the solid and melt, allowing for the capture of residual stresses during microscale solidification and resulting deformation. To solve the coupled phase-field model, temperature is considered as a directional field to establish directional microstructure evolution in the computational microcell. The COMSOL finite element code is utilized to study the columnar growth. To do so, the distribution of transient laser in DED process is investigated. Also, the effect of the volumetric inelastic strain, thermal strain, inelastic surface stress, initial condition, temperature gradient and solidification rate on the solidification of IN718 are studied.

High speed machining generates severe thermomechanical loads that impact cutting tool performance and lifetime, yet systematic optimization of coated tool geometry considering coupled stress and temperature effects remains limited. To address this gap, this study develops a computational framework for multi-objective optimization of AlCrN coated carbide cutting tools by focusing on three key geometric parameters, namely coating thickness, edge radius, and rake angle, to simultaneously minimize maximum principal stress and temperature. The methodology combines Arbitrary Lagrangian Eulerian finite element simulations with Gaussian Process Regression, using distinct kernel combinations for each target, with both models attaining test R-2 > 0.90, while reducing computational cost through sampling. NSGA-II optimization identified Pareto optimal solutions spanning from 13.7 MPa at 566.0 K to 592.8 MPa at 475.6 K, with all optimal designs converging to 1 mu m coating thickness. Consequently, the trade-off between stress and temperature is controlled by rake angle and edge radius, with positive rake angles lowering stress and negative rake angles lowering temperature. The knee point solution balances competing objectives at 342.7 MPa and 494.3 K. While the framework is limited to computational analysis, the approach provides a quantitative basis for guiding tool geometry selection within the modeled machining conditions.

This study employs an advanced phase-field model, integrated with molecular dynamics simulations, to investigate edge dislocation dynamics in Σ5 Ni bicrystals under different temperatures (100–600 K) and applied shear (up to 18 GPa), focusing on their role in the crystalline-to-amorphous transition. While no direct MD simulations are performed, temperature-dependent parameters derived from prior MD studies are incorporated into the phase-field framework. The model, validated against existing theoretical and molecular dynamics data, accurately captures the dislocation parameters, such as slip system height and Burgers vector, using a stepwise crystalline energy barrier to prevent non-physical dislocation widening. The simulations reveal enhanced dislocation growth in the + 30° slip system due to favorable stress alignment at the grain boundary. Higher temperatures and shear stresses significantly increase dislocation density, with grain boundaries acting as dislocation sources, accelerating amorphization compared to single crystals, where dislocation motion delays structural disorder. Notably, bicrystals maintain stability up to 600 K, beyond which rapid defect activity causes instability within 2 ns. These findings underscore the crucial role of crystal structure, temperature, and stress in determining material stability, offering valuable insights for designing durable materials for high-stress applications in aerospace and energy systems. This work introduces a novel PF–MD coupling that implements a stepwise energy barrier at slip plane boundaries to prevent non-physical dislocation widening, enabling quantitative prediction of grain boundary-driven amorphization and revealing the + 30° slip system as a dominant dislocation growth pathway under shear. The focus remains on temperature-dependent dislocation slip behavior, with amorphization trends inferred from stress-induced disorder near grain boundaries rather than explicitly modeled.

Atomic amorphization in bi-crystals, marked by a loss of long-range order, is typically induced by factors such as high-energy atom irradiation, mechanical deformation, or thermal processes. In this study, the amorphization process in nickel (Ni) bi-crystals subjected to the simultaneous application of external shear stress and temperature is investigated using advanced Molecular Dynamics (MD) simulations. The physical stability of the Ni-based bi-crystal is rigorously assessed by analyzing the convergence ofpotential and total energy metrics. Findings reveal a substantial increase in the extent of atomic amorphization with elevated temperatures and increased external shear stress, attributed to the significant reduction in atomic attraction forces within the computational box under these conditions. Notably, the amorphous region's area remains constant, unaffected by simulation box dimensions, due to the size-independent design of the simulation setup. Quantitatively, the amorphization area expands from 2619 to 2838 angstrom 2 under varying conditions. These results conclusively demonstrate that the amorphization process can be meticulously controlled through precise adjustments of both temperature and shear stress, thereby greatly enhancing the suitability of Ni bi-crystals for a range of advanced mechanical applications. The insights gained from this comprehensive study provide a robust framework for the development and optimization of cutting-edge materials with tailored properties for specific industrial uses.

The stress field of a nanostructure caused by structural defects is investigated using the nonlocal elasticity with different kernels. Nanovoids and inclusions along with their inelastic strain fields are included. Mesh study is performed to solve the mesh independent solutions and numerical verification is provided. COMSOL Multiphysics code is utilized to implement the local and nonlocal elasticity equations for plane strain problems. A phase field method is used to obtain desired distribution of nanovoids and inclusions. The stress analysis of such defects is compared for local elasticity and nonlocal elasticity with two-phase, modified and compensated two-phase kernels. The compensated nonlocal kernel shows superiority over the other kernels by improving the boundary effects, fully recovering the local state and satisfying the normalization condition. The results show that the theory of nonlocal elasticity is effective in problems related to structural defects with small inelastic strains. In addition, nonlocal elasticity shows a higher accuracy than the local elasticity at strong stress concentrations. Besides the phase and characteristic parameters, the nonlocal elastic theory performance depends on the size and defect distribution in nanoscale.

This study investigates the physical stability and atomic amorphization of silicon bi-crystals through Molecular Dynamics simulations. Initially, the equilibrium phase of silicon bi-crystals with ∑3, ∑9, and ∑19 structures was established. Subsequently, amorphization of the equilibrated samples was simulated by embedding external shear stresses. The findings indicate that elevated temperatures and increased external shear stresses lead to an effective atomic amorphization and an increase in the dislocation velocity, characterized by a decrease in attraction forces and alterations in atomic distribution. Among the three structures, the ∑19 structure exhibits the most significant atomic evolution, suggesting a higher propensity for the amorphization under identical conditions. The study finds that all the modeled samples maintain physical stability across the working temperatures ranging from 100 to 600 K. The study also explores the impact of varying shear stress values on the atomic amorphization. Increasing the applied shear stress increases both the maximum stress and dislocation stress, with the ∑19 structure being the most affected. At 600 K, the maximum atomic stress required to initiate the amorphization in the ∑19, ∑9, and ∑3 structures is found to be 9.41, 10.02, and 10.39 GPa, respectively, corresponding to the external shear stresses of 1.36, 160, and 1.55 GPa, respectively. The study concludes that both working temperature and applied external shear stress are critical factors in the amorphization of silicon bi-crystals.

Fatigue is one of the most destructive processes leading to the failure of mechanical components under cyclic loading. Traditionally, continuum methods have been used to predict and simulate fatigue, but they struggle to simultaneously capture crack nucleation and propagation under large deformations, as well as the physics of crack closure under compression. Recently, Molecular Dynamics (MD) has shown promising results in fracture mechanics; however, its application is limited by the scale of the models, making it more suitable for studying crack nucleation rather than full crack propagation. In this work, we used a coarse-grained molecular dynamics approach to model crack nucleation, propagation, and closure under cyclic loading in FCC metals. By coarse-graining the dislocation plasticity, this approach enables the simulation of crack nucleation and propagation within an atomistic framework while significantly reducing computational costs. A crack-free surface identification method was also implemented to trace crack surfaces and prevent crack closure during unloading. The method is applied to simulate fatigue crack processes in single-crystal aluminum, as well as cases with pre-existing grain boundary and bi-crystal. It is also extended to large-scale polycrystalline aluminum samples. The crack trajectory and the Paris law exponent were examined, demonstrating good agreement with experimental data. Overall, the proposed method, combined with the crack-free surface identification technique, provides a robust numerical approach for simulating fatigue behavior in metallic materials with reasonable computational efficiency.

A516 Gr.70 steel is widely used in industries such as petroleum refining, oil and gas, chemical, and power, especially in hydrogen atmospheres. Hydrogen can cause hydrogen embrittlement, negatively affecting the reliability of steels in these industries by reducing their static and fatigue lifespans. This research investigates the static fracture tendencies of A516 Gr.70 steel in the presence of hydrogen through experimental testing and finite element analysis. Using appropriate experimental tests, the stress–strain curve of the steel was first calculated based on the hydrogen content in the specimen. The J-integral was then calculated for specimens without hydrogen and with 7 PPM of hydrogen using a compact tension (CT) specimen fracture toughness test. Hydrogenation of the experimental specimens was performed using an electrochemical cell in conjunction with cathodic charging. The LECO RH400 instrument, with a precision of 0.1 PPM, was utilized to measure the amount of penetrated hydrogen in the specimens. Two finite element models were introduced and designed to simulate hydrogen embrittlement phenomena. First model was introduced to evaluate the J-integral as a measure of fracture toughness and second model is a traction separation law (TSL) to predict crack propagation in presence of hydrogen using cohesive element. TSL damage model parameters were determined through experimental data and the first model results. To ascertain models credibility, their results were compared against established literature and experimental findings. These verified models offer a robust tool for probing and analyzing the J-integral values and crack propagation in specimens with different hydrogen concentrations, highlighting its potential to be used for practical design and assessment.

Wear of tillage tools by hard soil particles is a serious concern in the industry since wear is the primary factor that defines an engaging tool's lifespan, stability, and reliability. Many studies have primarily focused on experimental methods to better understand the impact of various parameters on tool wear during tilling operations. Hence, this project focuses on both continuum damage mechanics (CDM) modesl based on thermodynamics for predicting the wear coefficient in tillage tools and experimental validation. The wear process is modeled as sand particle scratching at a prescribed speed and load on the surface of a tillage tool with different hardness, such as heat treated, chromium coated, heat-treated chromium coated, and samples without any treatment. Tillage tool wear is taken as the response (output) variable measured during contact, while operation parameters speed, load, and hardness are taken as input parameters. For C45E4 samples, tests are carried out with a dry sand/rubber wheel abrasion tester, and material loss from the tool surface during scratching is evaluated using the weight loss concept. The design of experiments technique is developed for three factors at four levels. The comparison shows an acceptable agreement in the experimental data and predicted results, which states an error of <20 %. The results also show that heat-treated samples with chromium coating have more abrasive resistance with respect to other samples.

This study investigates the effects of alumina nanoparticles on the amorphization process of silicon bi-crystals using molecular dynamics simulations. The simulations, conducted with the LAMMPS package, model a bi-crystal system containing 1620 atoms within a 129x180x7.5 & Aring;3 box, employing the TERSOFF potential for silicon and the Lennard-Jones potential for interactions between silicon and alumina nanoparticles. The simulation process consists of two stages: an equilibrium phase at temperatures ranging from 200 to 600 K for 1 ns, followed by an amorphization phase under external shear stresses from 1.55 to 2.50 GPa for another 1 ns. Key findings include the achievement of equilibrium after 1 ns at 300 K, with potential energy and mean atomic stress converging to-2.89 eV and 47.83 MPa, respectively. Amorphization is induced by shear stress, with the amorphization length increasing from 5.26 & Aring; at 300 K and 1.55 GPa to 5.98 & Aring; at 600 K and 2.50 GPa. Alumina nanoparticles serve as nucleation sites, significantly promoting the amorphization process by enhancing dislocation density and structural disorder. These results indicate that nanoparticles provide a more effective means of controlling amorphization compared to adjustments in temperature and shear stress, with potential applications in semiconductor device fabrication and solar cell manufacturing. The presence of nano-alumina slows the progression of the amorphization process. Consequently, under identical conditions including temperature, applied external shear stress, and time the rate of dislocation formation decreases, resulting in approximately 20% fewer dislocations overall. Additionally, the yielding stress threshold of a single crystal has increased from 8.2 to 12.8 GPa, indicating a significant enhancement in the material's resistance to deformation under applied stress.

A phase-field method is utilized to investigate the progression of dislocations in silicon bi-crystals under shear stresses at different temperatures. The study main feature is that the primary parameters of the phase field model such as the Burgers vector, the slip system height, and the distance between the dislocation cores are derived from molecular dynamics simulations at different temperatures. These calculations exhibit close alignment with existing theoretical predictions and unlike previous models, lead to a more physical dislocation growth. Due to the generation of dislocation pileup at one grain and consequently, the high stress concentration at the grain boundary, two titled slip systems at +/- 30o appear in the adjacent grain, along with the amorphization near the grain boundary. Here, the number of dislocations for each slip system is calculated using both the molecular dynamics and phase field methods for different temperatures and under different applied shear stresses and a good agreement between their results is found. As result, the number of dislocations enhances as the temperature or the applied shear increases but not proportionally for all the slip systems. This is evidenced by a reduction in attraction forces and changes in atomic arrangement. The transformation work fields resolved by the phase field method are also compared among three silicon structures. Additionally, a parallel set of slip systems was analyzed, where different dislocations slide over each other, resulting in highly dense pileups along the grain boundary. Out of the three structures that were examined, the & sum;19 structure shows the most prominent changes in atomic structure, indicating a higher propensity for such changes in equivalent conditions. The survey also confirms that all the samples under study retain structural stability within the working temperature range of 100 K to 600 K. However, as the temperature exceeds 600 K, the system loses its stability. Also, increasing the applied shear stress shows a higher impact on the & sum;19 structure. Consequently, both embedded external shear stress, and working temperature are identified as critical factors influencing the dislocation evolution in silicon bicrystals.

In this paper, a mechanics-based phase-field model at the microscale is introduced for microstructure evolution during solidification. The couple phase-field model consists of Allen–Cahn equation for phase order parameter, Cahn–Hilliard equation for composition, heat conduction and elasticity equations. The introduced elastic energy allows for volumetric inelastic strains due to melting/solidification as well as a thermodynamically consistent solid-melt interface stress and consequently, residual stresses during solidification at the microscale and deformation can be captured. The computational microcell is considered at the melt-solid interface and the temperature as a time dependent function is used for its boundary conditions to solve the coupled phase-field model. Using COMSOL FE code, examples of columnar growth are studied. As result, the suppressive effect of elastic driving forces and the reduction in solidification rate, due to the volumetric inelastic strains, on solidification are revealed. The inelastic surface stress, concentrated inside the interface, can change the morphology of solidified structure but does not show a remarkable effect on the solidification rate. The thermal strain was included which reduced the effect of volumetric transformation strain and consequently, the internal stresses near constrained regions were decreased. The effect of undercooling was studied which showed that increasing the undercooling increased the temperature gradient in the vertical direction and near the interface and solidification rate and significantly changed the morphology of solidified structure, as a homogeneous growth was resolved for larger undercooling while a columnar growth was obtained for smaller undercooling. Solidification was studied under mechanical loading which showed external loading changes the stress distribution and magnitude and the morphology of solidified structure. Effect of an inclusion on solidification was also investigated. The inclusion represented a more homogeneous distribution of stress and temperature with different magnitudes compared to the rest of the sample, creating a directional solidification toward the inclusion.

In this study, melting of finite -length aluminum nanowires is investigated using a mechanics -based phase field (PF) model in which the deviatoric transformation strain provides a driving force for melting. The interface tension and variable surface energy boundary conditions (VSEBCs) are included. Evolution of the melt solution is obtained by solving the coupled system of Ginzburg-Landau equation for melting, elasticity equations and a kinetic equation for deviatoric transformation strain using COMSOL multiphysics software. Melting temperature is calculated for various nanowire lengths and radii which shows a good agreement with molecular dynamics (MD) and analytical data. Effect of the VSEBCs and insulation boundary conditions (IBCs) on melting temperature is investigated, which revealed that the variable surface energy (VSE) is the main factor in dependence of the melting temperature on the nanowire length. The deviatoric transformation strain also shows a length -dependent effect on the melting temperature. The obtained results help for a better understanding of melting mechanism of nanowires and their thermal applications.

To design a more efficient energy absorber, it is critical to evaluate how changing the design parameters affects its performance, and also determine each one's order of significance. In this paper, using a new approach, the behavior and response of straight, double-tapered, and triple-tapered thin-walled tubes with rectangular cross sections under axial and dynamic loading are investigated by performing a sensitivity analysis on a support vector machine (SVM) as a surrogate machine learning model. First, a finite element model of the energy absorber is constructed and validated with available experimental and theoretical studies. Next, a design of experiments was developed using the Sobol series sampling method and an appropriate dataset was created. This information is then used to develop an SVM model to predict the initial peak load and mean load of tubes. The accuracy of the machine learning created in this study is then assessed, and it is demonstrated that the developed model can precisely predict the performance of the absorber. The machine learning model is then subjected to a Sobol sensitivity analysis, and the outcomes are compared to those of the parametric study. The results suggest that the thickness of the tube has a stronger effect on the absorber performance than other geometric parameters. Comparing the effects of different material parameters on the behavior of tubes, the results show that yield strength has the greatest impact on the response of the energy absorber. It is also observed that the tapered tubes have a much lower initial peak load compared to straight ones.

One of the main parameters that affect the design of suction caisson--supported offshore structures is uplift behavior. Pull--out of suction caissons is profoundly utilized as the offshore wind turbine foundations accompany by a tensile resistance that is a function of a complex interaction between the caisson dimensions, geometry, wall roughness, soil type, load history, pull--out rate, and many other parameters. In this paper, a parametric study using a 3 --D finite element model (FEM) of a single offshore suction caisson (SOSC) surrounded by saturated soil is performed to examine the effect of some key factors on the tensile resistance of the suction bucket foundation. Among the aforementioned parameters, caisson geometry and uplift loading as well as the difference between the tensile resistance and suction pressure on the behavior of the soil--foundation system including tensile capacity are investigated. For this purpose, a full model including 3--D suction caisson, soil, and soil--structure interaction (SSI) is developed in Abaqus based on the.. -.. formulation accounting for soil displacement (..) and pore pressure, P.The dynamic responses of foundations are compared and validated with the known results from the literature. The paper has focused on the effect of geometry change of 3--D SOSC to present the soil--structure interaction and the tensile capacity. Different 3--D caisson models such as triangular, pentagonal, hexagonal, and octagonal are employed. It is observed that regardless of the caisson geometry, by increasing the uplift loading rate, the tensile resistance increases. More specifically, it is found that the resistance to pull--out of the cylinder is higher than the other geometries and this geometry is the optimum one for designing caissons.

This paper proposes a framework for physics-informed neural networks (PINNs) in the nonlinear bending of 3D functionally graded (FG) beams. Utilizing the underlying physical rules governing a 3D FG porous beam resting on a Winkler-Pasternak foundation and motivated by the advancements in the research area of machine learning, this paper develops a PINN framework to predict the nonlinear bending of the beam system. PINNs need much less training data and can achieve high accuracy using a more straightforward network. The powerful tool presented in this work is general enough to handle any class of PDEs. We also take advantage of the recently developed deep learning platform TensorFlow with the company of DeepXDE library to design our network. In this study, the PINN framework takes information from the governing equations and the data from boundary conditions. We developed a mathematical model using the Euler-Bernoulli beam theory and inhomogeneous beam model and validated the results with those extracted from the finite difference method. Furthermore, PINN is presented to accurately predict the nonlinear bending of the system up to 37 times faster than the numerical method.

This paper proposes a physics-informed neural network (PINN) framework to analyze the nonlinear buckling behavior of a three-dimensional (3D) FG porous, slender beam resting on a Winkler-Pasternak foundation. PINNs need much less training data to obtain high accuracy using a straightforward network. The powerful tool used in this work can handle any class of PDEs. We use the deep learning platform TensorFlow and DeepXDE library to design our network. In this study, the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load. The mathematical model is developed using Hamilton’s principle, considering geometry’s nonlinearity. The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors. Finally, the PINNs results are validated with those extracted from the generalized differential quadrature method (GDQM). It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous, slender beams with satisfactory accuracy. Furthermore, PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.