Classical Energy Release Rate (ERR) criteria, which rely on the singular & ell;-> 0 limit, are effective for many Mode-I and Mode-II fracture problems, although fundamentally fail to predict the experimentally observed off-bisector fracture initiation and segmented echelon morphology of Mode-III cracks in V-notched bodies and torsion-loaded shafts subjected to anti-plane shear loading. The present paper resolves this orientation paradox by developing a finite-volume shear-energy theory that retains the leading Williams anti-plane eigenfield while explicitly introducing a mesoscopic process-zone length & ell;> 0. This length represents the characteristic microstructural grain size or cohesive zone extent, the functional is derived by integrating the local shear energy density of the leading Williams eigenmode over a finite sectorial volume. It is mathematically demonstrated that the resulting angular sensitivity integral, I(alpha, beta), evaluated over a finite sectorial volume, is unconstrained by symmetry, allowing its energetic maximum to naturally predict off-bisector nucleation. In other words, the predicted orientation of a candidate daughter facet is controlled by the finite distribution of elastic energy rather than by a pointwise singular kernel.To account for the fact that fragmentation in Mode III is a nucleation problem and not solely an energy-balance problem, the finite-volume criterion is coupled to a local strength-violation gate. The resulting formulation provides a unified description of initiation angle, critical loading, and segmented crack morphology. Through rigorous validation and verification (V&V) against benchmark experimental datasets (e.g., PMMA and glass fractography) and numerical phase-field data, we establish that fracture orientation and topological fragmentation are explicitly governed by the material's shear-to-tensile strength ratio (Rs) and the geometric-to-process length ratio (Pi). The model accurately predicts the continuous transition from smooth, shallow-angled fracture in ductile materials to highly segmented, strength-dominated 45(degrees )echelon crack arrays in brittle solids, achieving excellent quantitative agreement with empirical metrics. This unified finite-volume framework successfully bridges linear elastic asymptotics with modern cohesive theories, providing a minimal, physically grounded analytical tool that perfectly subsumes classical ERR as its & ell; becomes zero limiting sharp cracks case, while illustrating the singular breakdown for V-notches. The theory reproduces the expected Mode-I/II limit in which the usual material parameters Gc and sigma c are sufficient, while also explaining why ModeIII requires an additional length scale and a stress-based nucleation condition. The paper distinguishes analytical and numerical verification through the accompanying Octave implementation, and validation against published benchmark experiments and peer-review numerical studies.

A semi-analytical triangular-cell surrogate model is presented for the rapid prediction of shock-system structure and intake-capture geometry in supersonic external-compression inlets. The method couples classical two-dimensional oblique-shock relations with a discrete triangular-cell discretization implemented in open-source Octave, and it is intended for rapid preliminary-design and system-level modeling and simulation of air-breathing defense systems. The inlet is idealized as a planar, piecewise-ramped compression system so that each station is solved sequentially for shock angle, static pressure rise, total pressure recovery, downstream Mach number, and cowl-tip placement with minimal computational cost. The model is benchmarked against a curated set of published planar and piecewise-planar inlet cases, while conical and axisymmetric references are retained for context because they exceed the strict assumptions of the present surrogate. For geometry-matched planar cases, the model reproduces the principal shock and performance trends with small errors, whereas the larger divergence observed for conical or strongly curved references is explicitly attributable to the planar idealization and incomplete geometric reporting in the source literature. The resulting implementation is orders of magnitude faster than Reynolds Averaged Navier-Stokes compressible fluid dynamics (RANS CFD) and is therefore suitable for rapid parametric sweeps, sensitivity studies, uncertainty quantification, and integration into multi-physics design workflows. The Octave code and benchmark cases are provided to support a reproducible early-stage intake design.

This paper introduces a novel non-linear friction model for ice that incorporates melting effects. By coupling frictional heating with a dynamic melting process, the model effectively captures the reduction in friction resulting from the formation of a lubricating melt film and shear-thinning behaviour at the contact interface. Validation against established literature models and experimental data demonstrates that the formulation accurately characterises the transition from static to dynamic friction over a broad range of sliding velocities (emphasising high sliding velocities) and temperatures. Sensitivity analyses further reveal that the power-law index and shear-thinning coefficient are critical parameters in tuning the model response, ensuring its applicability from low- to high-velocity regimes. This versatile analytical tool has significant implications for predicting ice friction in applications spanning winter sports, transportation safety, and the design of advanced friction-modulating surfaces.

We present a compact semi-analytic framework that couples solid-target energy-deposition physics with two-temperature plasma hydrodynamics to model the earliest stages of a fission-driven fireball. Starting from spherically symmetric conservation laws, the approach replaces cold-matter constitutive closures with a two-temperature equation of state that explicitly includes ionization enthalpy and radiative energy loss, and systematically reduces the full PDE system to a thin-shell ODE model for the shell radius and mean ionization fraction. The manuscript documents the step-by-step asymptotic reduction, derives closed-form limits, and quantifies model uncertainty through analytic sensitivities and example-propagated bounds. A stability study of the reduced dynamics includes analytic results for the ionization subsystem and numerical recipes for instantaneous eigenvalues, finite-time multipliers, and Lyapunov exponents useful for experimental design. Representative parameter sweeps reveal rapid ionization (sub-picosecond) and nanosecond-scale hydrodynamic expansion, characterized by velocities on the order of 106 m·s⁻¹. Comparisons with classical blast scaling solutions and recommended validation pathways (radiation-hydrodynamic benchmarks and targeted laser-plasma experiments) demonstrate the model’s value as a fast, efficient, and physically grounded tool for parametric studies, uncertainty quantification, and experiment planning.

This study investigates a composite double-layer structure for improved thermal shock resistance. A modified Hugoniot elastic limit model is presented for the composite, followed by a 2D thermo-elastic impact simulation using commercial software. The simulation focuses on a composite material under initial extreme low temperature conditions with alternating metallic (Steel, Aluminum) and non-metallic layers (Kevlar 49, Graphite). The frozen target is subjected to pre- heated projectile. The objective is to optimize the composite's durability by strategically placing reinforcement particles within specific layers. The analysis explores the effect of different particle types (oil, water, Aluminum, Steel) and sizes (0.3mm, 0.5mm, 1mm) on the composite's stress response. It was found that aluminum and steel particles significantly reduce stress compared to fluid/gas particles, confirmed qualitatively by literature. Kevlar particles within the SiCp layer enhance its resistance, while Aluminum particles within the Kevlar layer offer weight reduction benefits. Moreover, for Kevlar, larger particles improve resistance, and vice versa for the SiCp case. Considering weight, a particle size of 0.5mm is chosen for both layers. Moreover, a finite element analysis of the optimized composite model subjected to thermoelastic impact loading demonstrates its superior performance compared to the non-reinforced composite. Specific layer combinations (SiCp with Kevlar particles, Graphite or Kevlar with Aluminum particles) show the most significant stress reduction. Finally, separate 3D ballistic analysis was performed for Tungsten having 600m/sec projectile into 5 layered target with thickness of 2.8mm each layer and appropriate interaction friction (SiCp - Steel 304 - Al 7075-T651 - Kevlar 49 - Graphite Crystalline) during penetration time of 0.006sec at 300K. The dynamic explicit transient analysis was confirmed with the predecessors' analytic calculations.

The current paper calculates analytically the minimum required torque for cylinder movement together with the optimal (maximum) capturing velocity allowed to operate over a 2D rigid cylinder mass body that is placed inside a rigid general asymmetric shaped v-groove rigid bracket with asymmetric wall. The parametric analytic solution has been derived using generalized equations of motion – body-force derivations and kinematics alongside angular momentum equation for five cases scenarios: pure slip state, slip state that turn into rotational state, pure rotational state during the cylinder motion and the minimum required torque to initiate rotational movement and initial slip movement conditions, respectively. The motivation is to understand carrying devices better designing through cylindrical loading-bracket relationships.

The current paper presents a finite element method (FEM) axisymmetric solution based on commercial software for an isotropic closed-ended container filled with fluid, located in the triple point phase (liquefied gas) while being converted into gas through a phase transition to critical point phase by a simultaneously rapid change of pressure and temperature to their critical values. The whole chemical process will be simulated through thermo-elastic analysis that is controlled by temperature-displacement dynamic coupling and subjected to step function boundary conditions alongside liquefied triple point initial conditions. In the process, the maximum principal stresses will be determined and illustrated as dependent on the container thickness. In the process, investigation will be carried out for prominent parameters, like, container hollow geometry type (spherical, ellipsoidal, and cylindrical) and raw material of the container. Commercial software solution calibration against existing literature solutions has been performed. Also, the solution accuracy was examined by element size mesh analysis to be coherent. In conclusion, the best materials to use were Molybdenum TZM and Tungsten while the preferred shape is the ellipsoidal shape. However, a typical vessel that is still durable with sufficient thermal strength for gas storage purposes is a cylinder body container with spherical ended cups made from Aluminum 6061 T6.

This paper presents the thermoelastic shock wave model components of projectile, target, and muzzle tube during the initial start of penetration. The penetration model is combined using pressure and temperature (e.g., mechanical and thermal shock) that act separately at the moment of penetration (a few microseconds) into a homogeneous or first-layer armor body. The armor’s shape and material will be investigated based on contact principal stress. The reciprocal influence between the penetrator and the armor in the aspect of the projectile nose shape will also be demonstrated. Moreover, the penetrator thermoelastic material’s durability will be examined, based on von Mises criterion. The examination for the initial elastic contact stress impact will be performed by using the explicit solution to temperature-displacement coupling equilibrium, based on commercial finite elements modeling. In addition, a modified impact contact stress model based on both mechanical and thermal energies was proposed and found to agree with the literature. Brief conceptual analysis of projectile–shield interactions was examined. Finally, shooting tube muzzle thermoelastic analysis was performed alongside a literature comparison, which was found to agree qualitatively and quantitatively. Muzzle tube material impact analysis was performed. Finally, it was concluded that muzzle tubes obey the rule that a shorter cylinder length tube develops higher muzzle tube principal stresses.

An approximate simplified analytic solution is proposed for the one DOF (degree of freedom) static and dynamic displacements alongside the stiffness (dynamic and static) and damping coefficients (minimum and maximum/critical values) of a parallel spring-damper suspension system connected to a solid mass-body gaining its energy by falling from height h. The analytic solution for the prescribed system is based on energy conservation equilibrium, considering the impact by a special G parameter. The formulation is based on the works performed by Timoshenko (1928), Mindlin (1945), and the U. S. army-engineering handbook (1975, 1982). A comparison between the prescribed studies formulations and current development has led to qualitative agreement. Moreover, quantitative agreement was found between the current prescribed suspension properties approximate value - results and the traditionally time dependent (transient, frequency) parameter properties. Also, coupling models that concerns the linkage between different work and energy terms, e.g., the damping energy, friction work, spring potential energy and gravitational energy model was performed. Moreover, approximate analytic solution was proposed for both cases (friction and coupling case), whereas the uncoupling and the coupling cases were found to agree qualitatively with the literature studies. Both coupling and uncoupling solutions were found to complete each other, explaining different literature attitudes and assumptions. In addition, some design points were clarified about the wire mounting isolators stiffness properties dependent on their physical behavior (compression, shear tension), based on Cavoflex catalog. Finally, the current study aims to continue and contribute the suspension, package cushioning and containers studies by using an initial simple pre – design analytic evaluation of falling mass- body (like cushion, containers, etc.).

This paper presents, aerodynamics coefficients calculation (Lifting & drag coefficients, pressure central location) of Trapeze wing shape configurations for different aspect ratios (ARs) values by using improved vortex lattice method (VLM), compared with finite-wing and slender body theories. The planar wing was divided into N panels of the size: 6X6 with trapezoid shape panels. As expected, for high ARs the VLM solution for the lifting coefficient is coincided with the finite wing theory whereas for small ARs (<1) it is coincided with the slender body theory (~1). Afterwards, we obtained that the calculated VLM induced drag becomes closer to the finitewing theory as the AR value is increased.

This paper describes the numerical solution of time dependent, two coupled substances in one-dimensional field that participate in a chemical reaction with two kinds of different concentrations that affect each other. It is necessary to find the final state solution of the component variability concentrations in numerical form. The equations are conjugated and dependent on the radius and time (the existing physical model is a drop). In order to obtain a solution, we used the explicit method for the second-order equation, which is very easy to program and understand, but requires some preliminary mathematical work. We examined the convergence of the solution in aspects of longitudinal (h) and lateral integration (s), as well as depending on the problem parameters. Thus, we have found that the (substances) components can reach an equilibrium state in which the concentrations would no longer change in time, or this state of equilibrium will not be existing due to the nature of the process and the concentrations will change in a cyclic or other form. Finally, qualitative support was found in literature.

This paper presents analytical adaptive expressions for the two distinct cases of tank leakage estimations for gas (sonic and subsonic) and liquid flows under specific measurements data that assists to evaluate a circular hole/slit/orifice (crack) diameter and area. The analytic process is performed by equalization between analytic reformulation of the traditional mass flow formulations and the test formulation for mass flow dependent driven pressure differential over time multiplied by volume. In case of uniform environment conditions, the slit diameter might also represent the total sum of numerous exit holes/slits possible existence. Finally, a qualitative agreement was found between literature and current results in the context of orifice diameter versus pressure differential.

We present a theoretical study of the hydrodynamic and electrokinetic response of both metallic spherical polarized colloids as well as metallodielectic Janus particles, which are subjected to an arbitrary non-uniform ambient electric field (DC or AC forcing). The analysis is based on employing the linearized ‘standard’ model (Poisson–Nernst–Planck formulation) and on the assumptions of a ‘weak’ field and small Debye scale. In particular, we consider cases of linear and helical time-harmonic travelling-wave excitations and provide explicit expressions for the resulting dielectrophoretic and induced-charge electrophoretic forces and moments, exerted on freely suspended particles. The new analytic expressions thus derived for the linear and angular velocities of the initially uncharged polarizable particle are compared against some available solutions. We also analyze the levitation problem (including stability) of metallic and Janus particles placed in a cylindrical (insulating or conducting) pore near a powered electrode.

The following work describes the process of finding the flow and the temperature fields for a given ventilation system configuration. In order to simplify the problem, the flow was characterized as 2D, incompressible, viscous and in constant state. First, the governing equations in terms of the stream function, vorticity and Reynolds number have been developed. The obtained mathematical model for the flow field is actually a pair of coupled elliptical partial differential equations. Solving the resulting equations was performed using SOR (successive over-relaxation) methods following upwind second-order finite differences. In the second stage, the temperature field was numerically calculated using the flow field data obtained in the first stage. In fact, as expected, the flow has been advanced from the left inlet opening to the right outlet opening. Also, the main flow was creating a vortex while above the main flow large vortex has been generated and surrounded by several small vortices around it. Last but not least, Reynolds (Re) number influence on the solution nature has been expressed by flow expansion in the whole ventilation cell. Finally, comparison between different Re numbers have proved the flow type dependency on the Re number and its effect on the temperature field.

This paper presents a new fresh theoretical study of the ballistic penetration phenomena into hard materials due to low-energy bodies' motion. This model based on the energy balance between the kinetic energy of the piercing body and the protective body thermal energy. Following this equilibrium alongside the equation of the projectile motion, the resulting deceleration value is analytically calculated. Substituting the obtained deceleration value into the kinematic equilibrium results with the penetration thickness expression as well as the time of penetration inside the mono and multi layers materials (like, monolithic and composite materials). In addition, equivalently to the Johnson-Cook model, a proposed impact stress for penetrative and non-penetrative cases was developed. Additionally, a residual velocity expression alongside the evaluation of the total energy and deceleration parameters were also determined. Key parameters are the projectile effective length, which defines the projectile geometry alongside the material strength parameters (heat capacity, Yield, compressive and tensile strengths). Finally, good numerical agreement (order of magnitude and numerical values) has been found between various literature experimental tests and current analytic solution for the kinematic parameters.

This paper presents a simulation-based solution for calculating rocket engine performance with liquid-type propellants of Paraffin and Kerosene for oxidizer to fuel ratio that is given by a linear formula. The engine was divided into two main stages: combustion chamber and a nozzle. In the first phase, conditions were found in the combustion chamber, based on the assumption of equilibrium according to Barrere. Next, the flow in the nozzle was calculated based on the fluid in the combustion chamber. Three main theories were examined in order to find the flow conditions in the nozzle: equilibrium, frozen and mixed flows (Bray conditions). While the latter assumes the existence of the "Sudden Freezing Point" found by Bray, so that from this point to the end of the nozzle, the flow is assumed to be frozen. The use of the proposed simulation might contribute for multiple calculations performance (e.g., fuels with multiple intermediate reactions). Comparison between both types of fuels/propellants for the three described types of flow is presented alongside CEA software results, whereas good agreement between solutions was found. Also, the greater the ratio between hydrogen and carbon atoms, the better the engine performance for a particular oxidizer. Finally, it was found that an equilibrium flow model throughout the nozzle has a better nozzle performance compared to the other types of flows.

The current paper deals with the problem of the simply supported thin rectangular plate subjected to the intermediate strip in-plane loading. Based on the strain energy method (Fourier ansatz), the critical (minimum value) of buckling stress occurrence was determined in a general form dependent only on the strip thickness, strip location, plate width and stress magnitude. Compatible with the classical columns Euler method it was found that the plate stability is decreased with the increasing of the plate width due to larger induced stresses. Also, strip location relative to the support region was found to influence the buckling (same analogy to the Euler buckling theory; consider the strip as a both sides pressed rod). Additionally, the strip width parameter increase is likely to cause larger buckling stress. Moreover, expressions that includes both axial and transverse loads for different extended cases configurations were also derived and examined based on the strain energy method alongside explanation for possible applications (thin aluminum plate welding). In a general view, it was found that the cases of combined axial and perpendicular loading action are less stabilized than cases where only one kind of loading configuration is participated. Finally, the buckling stress was found to agree qualitatively with the cited literature.

This paper describes the numerical solution of flow analysis in a two‐dimensional combustion chamber with two parallel inlets aided for propellants entrance, addressing a number of different problems that depend on each other: the flow affected by a discrete point in‐cell vortex, the velocity affected by the flow regime in the cell, and the combustion problem affected by the oxygen and fuel entries from the cell walls. The shape geometry of the combustion chamber is made from a square section connected with a semi‐circular one. The mathematical model of the problem consists of an inhomogeneous stream function Laplace equation coupled to partial differential mass conservation equation subjected to a wall non‐intrusion condition and known mass values in the wall openings. Algebraic conformal mapping transformation has been used for modeling the complex cell geometry. The solution was obtained by using the iterative Gauss–Seidel method for both the current function and the mass calculation. Comparison with another modeling method for calibration purpose was performed; considering each geometrical component separately whereas continuous conditions were applied between the two sections. The grid types are: (1) a uniform grid in Cartesian coordinates in the square part, and (2) a uniform circular grid in polar coordinates. It was found that different initial guesses have not effect on the final solution, but an informed initial guess affects the solution time convergence iterations number to solve the problem. Finally, the effect of the mixing vortex on the location of the flame front in the chamber was investigated.

A theoretical study is provided for determining the effective stress and viscosity of ideally conducting uncharged polarized freely spherical solid particles suspended in a Stokes fluid under a uniform DC electric field and constant shear. Due to polarization electric double layer (EDL) is formed in the symmetric electrolyte around the spherical (perfect conductor) particle. Assuming a dilute suspension (ignoring particle-particle interaction) we employ a generalized effective stress formulation which considers the case of applied pure shear (no electric field), the case of ambient electric field (no shear) and finally the coupling between both cases. Comparison between the current analysis and literature has shown commendable agreement. Our analytical predictions can be further simplified for the case of a thin EDL utilizing the Helmholtz-Smoluchowski (HS) slip-velocity model in accordance with the generalized cell- method.