Geometric Deformation Research Articles

Effect of Einasto Spike on the Gravitationally Decoupled Self-gravitating Dark Matter Halos

Abstract In this work, we consider the possibility of constructing
gravitationally bound, charged dark matter halos motivated by
Einasto density model. This model generalizes the concept of
charged, non-commutative mini-compact objects by including dark
matter as its primary component through the principles of the
minimal geometric deformation strategy. We point out that the
coupling of the non-commutativity inspired Einasto spike density
model with a non-isotropic fluid, within the context of gravitational
decoupling allows the formation of different minimally deformed
dark matter halos, corresponding to each value of the deformation
parameter. We assume the Tolman-Kuchowicz cosmological model as a
seed metric within the geometric deformation scheme to
initially generate an electrically charged isotropic solution.
Subsequently, we employ a density-like constraint to produce a
second anisotropic charged dark matter stellar model via the
Einasto density profile. A complete graphical analysis of the
structural variables and stability of both models indicate that,
for the considered choice of parameters, both cosmological models
are well-behaved, exhibiting expected physical behavior.

Origami multifunctional metagrating for a mechanically controlled electromagnetic wavefront

Metasurface or artificial electromagnetic (EM) structures offer viable options for manipulating EM waves with compact periodic structures. Tunable metasurfaces are ideal for many engineering and scientific applications because they can manipulate EM wavefronts. However, it is challenging to implement tunable metasurfaces that can achieve multiple functions for integration. In addition, integrated multifunctional metasurfaces are often structurally complicated and bulky. This paper proposes a simple spatial modulation mechanism that uses Miura origami reconfigurable one-dimensional metagrating to achieve multiple control of EM wavefront. Theoretical predictions, numerical simulations, and experiments confirm and validate the basic concepts. In particular, the continuous geometric deformation of the Miura-ori lattice is a promising method for compensating the dispersion of characters in gradient metasurfaces. Considering origami structures’ outstanding mechanical properties and strong deformation abilities, this discovery opens up another avenue for lightweight and deployable meta-devices.

Minimally deformed regular Hayward black hole solutions in Rastall theory

Abstract We profit from the minimal geometric deformation technique of
gravitational decoupling and extend the regular Hayward black hole,
to derive new black hole solutions in the context of Rastall theory.
The field equations with an extended matter source are decoupled
into two subsystems. The first of these are specified by the metric
components of the regular Hayward black hole while the second set
which contains the effects of the added source is solved by
utilizing a constraint imposed via a linear equation of state. By a
linear combination of the solutions of these two subsystems, we
obtain two cases of the extended solutions. For specified values of
the Rastall and decoupling parameters, we investigate some
physical/thermodynamical properties of the obtained models. It turns
out that only the first model preserves asymptotic flatness. It is
found that the first and second models are described by exotic and
ordinary matter, respectively. Finally, we obtain an acceptable
behavior of the Hawking temperature and thermodynamic stability for
both models.

SODD-YOLOv8: an insulator defect detection algorithm based on feature enhancement and variable row convolution

Abstract To address the detection challenges in defective images of insulators in transmission lines, including tiny object size, significant scale variations, a wide variety of defects, and complex background interference. In this study, an improved insulator defect detection algorithm is proposed, based on the YOLOv8s framework and combining feature enhancement and deformable convolution techniques. Firstly, to address the image feature distortion problem caused by aerial photography, a deformable convolutional feature extraction module (DCFEM) is introduced, which is designed to enhance the model’s ability to adapt to the local geometric deformation, so as to effectively recover the distorted feature information in the image. Moreover, to enhance the detection ability of the model for small objects, a small object feature enhancement module is designed, which adopts an efficient multi-scale attention mechanism, and aims to enhance the feature extraction ability of small objects, improve the sensitivity to small-size defects, and improve the detection accuracy. Eventually, to optimize the computational efficiency of the model, the average pooling-sparse convolution-batch normalization (BN) module is proposed. This module combines average pooling, sparse convolution and BN techniques to achieve a lightweight model while maintaining a high level of feature extraction capability. Experimental results on the China power line insulator dataset show that the improved model achieves a 4.3 percentage point improvement in the mAP metric compared to YOLOv8s, and the number of parameters in the model is reduced by 10%. The proposed scheme not only improves the accuracy and efficiency of defect detection, but also reduces the demand for computational resources, thus providing a more reliable and efficient solution for insulator defect detection in practical applications.

Pose Estimation of a Cobot Implemented on a Small AI-Powered Computing System and a Stereo Camera for Precision Evaluation.

The precision of robotic manipulators in the industrial or medical field is very important, especially when it comes to repetitive or exhaustive tasks. Geometric deformations are the most common in this field. For this reason, new robotic vision techniques have been proposed, including 3D methods that made it possible to determine the geometric distances between the parts of a robotic manipulator. The aim of this work is to measure the angular position of a robotic arm with six degrees of freedom. For this purpose, a stereo camera and a convolutional neural network algorithm are used to reduce the degradation of precision caused by geometric errors. This method is not intended to replace encoders, but to enhance accuracy by compensating for degradation through an intelligent visual measurement system. The camera is tested and the accuracy is about one millimeter. The implementation of this method leads to better results than traditional and simple neural network methods.

Thermal and thermo-mechanical post-buckling analysis of GNP-reinforced composite laminated plates

This research utilizes isogeometric analysis (IGA) method to analyze buckling and post-buckling responses of composite laminated plates embedded with graphene nanoplatelets (GNPs) subjected to three-dimensional (3D) conduction of heat or combined 3D heat conduction and mechanical edge compression. A formulation to determine temperature profile produced by 3D conduction of heat in the GNP-reinforced laminate is established, and a new function with smooth transition form of GNP volume fraction across the thickness is presented for dictating the volume fraction of layer. Shear deformable quasi-3D theory with the von Kármán type nonlinearity which takes initial geometric deformation and thermal effect into consideration is employed to construct the nonlinear equilibrium states. Four types of GNP arrangements encompassing uniform, O, X and V shapes are considered. The IGA approach presented, through the benchmark test, is evidenced to estimate the thermal buckling temperature accurately and to successfully trace the thermal post-buckling path. Additional parametric study is carried out to scrutinize the thermal and the thermo-mechanical post-buckling features of the GNP-reinforced composite laminated plates, and the new findings are sure to be served as the benchmark solutions.

Braneworld black bounce to transversable wormhole

We provide a way for embedding a 4-dimensional geometry corresponding to the Simpson-Visser (SV) spacetime — which is capable of representing a traversable wormhole, a one-way wormhole, or a regular black hole — into a Randall-Sundrum setup. To achieve this, we linearly deform the bulk geometry and the bulk matter distribution concerning a coupling constant. These deformations induce a transition from a 5D vacuum AdS state to an anisotropic matter distribution. The latter results in the induced geometry on the brane transitioning from a singular Schwarzschild spacetime to a regularized SV spacetime. Since there are no sources or matter fields on the brane, we can assert that the induced SV geometry on the brane arises from the influence of geometrical and matter deformations in the bulk. Thus, the central singularity is suppressed. We determine the cases where the energy conditions are either satisfied or violated. Our spacetime is asymptotically radial AdS, which is intriguing given the absence of a global AdS box that would prevent instability under larger wavelength perturbations. Therefore, it is no longer appropriate to claim that instability exists for very small perturbations near the AdS horizon. Thus, we propose that the stability of the solution can be analyzed by examining the speed of sound due to the presence of matter fields in the energy momentum tensor.

Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in f(T)-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for f(T)-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure f(T) gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.

Preferred Electric Field Mechanism for Frustrated Lewis Pair Reactivity.

This study employs computational methods to investigate the mechanism of H2 activation by frustrated Lewis pair (FLP) species, including both intermolecular and intramolecular nitrothane/borane FLP systems. Previous studies have proposed two qualitative reactivity mechanism models to explain the facile cleavage of H2 by FLPs. The findings of this study support the electric field mechanism as the favorable pathway for H2 cleavage. Utilizing frontier molecular orbital theory and energy decomposition analysis, the study explores the electronic structure and nature of the reactions under an external electric field (EEF). Analysis using the activation strain model highlights the significant influence of geometrical deformation energies of FLPs on the activation barriers of H2 activation reactions. Computational results suggest that H2 activation by FLP molecules follows the electric field mechanism, indicating the potential of the FLP/EEF combination as an effective activator for inert molecules.

Exploring the possibility of testing the no-hair theorem with Minkowski-deformed regular hairy black holes via photon rings

In this paper, we investigate the optical appearance of a regular static spherically symmetric hairy black hole within the context of Minkowski deformation governed by the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. This black hole describes a hairy black hole with geometric deformations in the radial and temporal metric components, parameterized by α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. The optical appearance of the black hole, illuminated by a static thin accretion disk in three toy emission function models, exhibits distinctive shadows and photon rings. Our findings reveal that for static spherically symmetric hairy Minkowski-deformed regular black holes, the event horizon radius rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_h$$\\end{document}, photon sphere radius rph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ph}$$\\end{document}, critical impact parameter bph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{ph}$$\\end{document}, and innermost stable circular orbit radius risco\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{isco}$$\\end{document} all have a positive correlation with α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. These parameters affect the null geodesic trajectories, shadows, and the optical appearance of the photon rings illuminated by a static thin accretion disk around the black hole. Utilizing this, we obtained the optical appearance of this black hole when observed in the forward direction of the optical and geometric thin accretion disk models. In all three models, the radius of the photon ring images also shows a positive correlation with the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Therefore, under the static spherically symmetric hairy Minkowski-deformed regular black hole, there is no degeneracy of photon rings dependent on the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Theoretically, this allows for the distinction of different spacetime metrics of hairy Minkowski-deformed regular black holes, providing a potential method for testing the no-hair theorem through future observations of black hole photon rings.

Anisotropic interior models with Kohler–Chao–Tikekar-like complexity factor

This work explores the construction of spherically symmetric models of stellar interiors by incorporating the null complexity factor (CF) as an additional constraint. This supplementary condition helps us to close an array of stellar structure equations resulting from the process of gravitational decoupling. By making use of MGD-type gravitational decoupling we analyze the role of gravitational decoupling and its impact on the complexity of static, self-gravitational systems. We begin by considering an anisotropic seed solution described by the Kohler–Chao–Tikekar metric ansatz. We then apply the minimal geometric deformation technique to this seed solution, imposing the constraint that the effective anisotropic factor vanishes. This constraint leads to the generation of an isotropic stellar solution. Furthermore, we construct a second family of solutions in which the CF, remains the same for both the seed solution and its minimally deformed counterpart. Our analysis further investigated the influence of both the deformation parameter and the CF on the structural properties of the static and spherically symmetric stellar objects.

Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff–Sagnotti counter-terms, and geometric flows

Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.

A new shape reconstruction method for monitoring the large deformations of offshore wind turbine towers

Offshore wind turbine (OWT) upsizing has become an inevitable trend. Compared with small OWTs, large OWT rotors exert greater horizontal loads and bending moments on the tower. These factors make a large OWT tower more prone to geometric nonlinear deformations, which can affect the normal operation of a wind turbine and even lead to damage to the wind turbine tower. Therefore, monitoring the deformation of large OWT towers is necessary. Shape sensing is a technique that uses surface strains to reconstruct deformed shapes. Currently, there is a lack of effective methods for geometric nonlinearity deformation shape sensing. In addition, the tower of OWT is a variable cross-section structure. The influence of varying cross-sections further increases the difficulty of developing a large deformation reconstruction algorithm. To solve this problem, this paper proposes a new method called rotation angle approximation (RAA). This method establishes a least-squares error functional using analytic curvature and section curvature. The rotation angles of the tower axis are obtained via this function. The deformed shape is then predicted via the boundary conditions and the rotation angles along the tower axis. Numerical simulations demonstrated this method can accurately predict the large deformations of a tower under different load conditions.

Geometrical morphology and deformation measurement of long-span suspension bridge based on terrestrial laser scanning

Long-span suspension bridges necessitate deformation measurements for proper evaluation and upkeep. However, conventional approaches are unable to collect continuous spatial deformation data, which severely restricts their application in structural research. This paper presents a reliable and efficient method for measuring the deformation of suspension bridges using 3D laser scanning, including planning the scanning route, preprocessing the point cloud data, and extracting the deformation indicators. The method plans the scanning route based on experience and basic path planning principles to achieve both efficiency and precision, preprocesses the point cloud data by 3-stage denoising and curvature-based downsampling to preserve valuable point data better, and then proposes an extraction procedure for different types of deformation indicators. A field test on a typical long-span suspension highway bridge is performed, and the data processing and results extraction details are introduced. The accuracy and consistency of measurement results are discussed to verify the reliability of the proposed approach. The verified data provides useful information for the evaluation and maintenance of the bridge.

Analytical solutions for static longitudinal displacements of suspension bridges under a moving vertical concentrated load

The longitudinal displacement at the girder ends of long-span suspension bridges is a crucial issue that affects structural safety, durability, as well as traffic safety and ride comfort. The primary cause of these reciprocating displacements is the action of moving live loads, which induces quasi-static displacements in the longitudinal direction. This paper theoretically investigates the static longitudinal displacements of suspension bridges under a moving vertical concentrated load and elucidates the underlying deformation mechanisms. Considering geometrical nonlinearity, analytical equations are established for the longitudinal deformations of the main cable and stiffening girder under a vertical concentrated load. By analyzing the geometrical deformation conditions of the suspenders, the relationship between the longitudinal displacements of the stiffening girder and the main cable is derived. Due to the coupling between longitudinal and vertical displacements, the vertical displacement of the stiffening girder must be solved to obtain its longitudinal displacement. Based on deflection theory and considering the bending stiffness of the stiffening girder, this paper derives the vertical deformations of the stiffening girder for single-span suspension bridges and those with short continuous side spans under a vertical concentrated load, which is then used to calculate the longitudinal displacement. Finite element models are used to verify the accuracy of the analytical solutions. Differences between the proposed solutions and previous solutions neglecting the bending stiffness of the stiffening girder are compared and analyzed. The effects of neglecting the longitudinal displacement at the bridge tower top and the presence of short continuous side spans on the longitudinal displacement of stiffening girder are also investigated. The results demonstrate the high accuracy of the proposed analytical solution for the longitudinal displacement at the girder ends of suspension bridges. Importantly, the bending stiffness of the stiffening girder cannot be neglected in calculating the longitudinal displacement. The longitudinal displacement at the girder ends is primarily caused by the longitudinal deformation of the main cable, while the contribution from the flexural deformation of the girder is negligible. Furthermore, the longitudinal displacement at the bridge tower top has a negligible effect on the longitudinal displacement of the girder, and the presence of short continuous side spans is beneficial for reducing the longitudinal displacement of the stiffening girder. The proposed analytical solution method provides a rapid approach for calculating the static longitudinal displacement at the girder ends of suspension bridges under passing live loads and reveals the deformation mechanism. This is beneficial for preliminary design and structural optimization, as it avoids the complex finite element modeling and solution process.

Minimally deformed regular Bardeen black hole solutions in Rastall theory

In this study, we utilize the minimal geometric deformation technique of gravitational decoupling to extend the regular Bardeen black hole, leading to the derivation of new black hole solutions within the framework of Rastall theory. By decoupling the field equations associated with an extended matter source into two subsystems, we address the first subsystem using the metric components of the regular Bardeen black hole. The second subsystem, incorporating the effects of the additional source, is solved through a constraint imposed by a linear equation of state. By linearly combining the solutions of these subsystems, we obtain two extended models. We then explore the distinct physical properties of these models for specific values of the Rastall and decoupling parameters. Our investigations encompass effective thermodynamic variables such as density and anisotropic pressure, asymptotic flatness, energy conditions, and thermodynamic properties including Hawking temperature, entropy, and specific heat. The results reveal that both models violate asymptotic flatness of the resulting spacetimes. The violation of energy conditions indicate the presence of exotic matter, for both models. Nonetheless, the energy density, radial pressure, as well as the Hawking temperature exhibit acceptable behavior, while the specific heat and Hessian matrix suggest thermodynamic stability.

A case study of preliminary damage detection of two heritage vaults through geometric deformation analysis on 3D point clouds

Masonry vaults are common structural elements in heritage buildings that, given their long lifespan, are susceptible to the accumulation of damages and deformations from diverse actions such as overloads, support movements, seismic action, etc. The use of 3D point clouds from terrestrial laser scanners and structure from motion photogrammetry survey to investigate these deformations can offer valuable information for structural assessment and conservation, particularly when historical information is limited. The analysis of the deviation measured between the surveyed as-built point cloud of a vault and a reference geometry could reveal deformation patterns. Those, compared with recurring damage mechanisms discussed in literature, can provide a preliminary identification of the damage mechanisms affecting a structure, and the evaluation guide the recognition of the underlying action. The aim of this paper is to investigate how to generate different reference geometries and the impacts of their choice as reference geometry for the identification and quantification of different deformations. Deviation analyses were performed on the main vaults of two different churches with different reference geometries (i.e., geometries derived from the survey and geometrical primitives fitted on point-cloud), and the results were discussed by comparing the deviation maps obtained with the crack pattern and the already known deformations of the buildings.

Cosmological solution through gravitational decoupling in [formula omitted] gravity

This paper aims to formulate anisotropic cosmological solution of a non-static spherical structure with the help of gravitational decoupling scheme through minimal geometric deformation in f(G,T) gravity. This technique transforms only the radial metric function while the temporal component remains unchanged. Consequently, the field equations are separated into two independent arrays: one is related to the seed source and the other characterizes the extra sector. In order to derive the solution corresponding to the isotropic sector, we use the Friedmann–Lemaitre–Robertson–Walker cosmic model and employ the barotropic equation of state as well as power-law model. Finally, we study the impact of decoupling parameter to describe different eras of the universe through graphical analysis. It is found that physically viable and stable trends of the resulting solution are achieved for both radiation-dominated as well as matter-dominated epochs in this modified theory.

Imprints of dark matter on the structural properties of minimally deformed compact stars

In this manuscript, we investigate the possibility of constructing anisotropic dark matter compact stars motivated by the Einasto density profile. This work develops analytical solutions for an anisotropic fluid sphere within the framework of the well-known Adler–Finch–Skea metric. This toy model incorporates an anisotropic fluid distribution that includes a dark matter component. We use the minimal geometric deformation scheme within the framework of gravitational decoupling to incorporate anisotropy into the pressure profile of the stellar system. In this context, we model the temporal constituent of the Θ-field sector to characterize the contribution of dark matter within the gravitational matter source. We present an alternative approach to studying anisotropic self-gravitating structures. This approach incorporates additional field sources arising from gravitational decoupling, which act as the dark component. We explicitly verify whether the proposed model satisfies all the requirements for describing realistic compact structures in detail. We conclude that the modeling of the Einasto density model with the Adler–Finch–Skea metric gives rise to the formation of well-behaved and viable astrophysical results that can be employed to model the dark matter stellar configurations.

On energy mechanism of rate-dependent failure mode evolution in plain weave composite

The intricate failure modes and the yet unclear rate dependency of carbon fiber reinforced plain weave composite materials pose a challenge to mechanics researchers. This study establishes an energy-based evolution mechanism for the compressive failure modes of plain weave composite materials as the strain rate varies. This mechanism illustrates how the rate dependency of failure modes arises from the competitive relationship between strain potential energy and deformation kinetic energy. At low loading rates, the specimen exhibits a progressive crushing failure mode characterized by low peak stress and significant geometric deformation. As the loading strain rate increases, the energy required for this geometric deformation also increases. When the energy expenditure surpasses that needed to elevate the stress level of the specimen, it transitions to an instantaneous failure mode with high peak stress. In this mode, the specimen fractures into multiple small fragments immediately upon failure, lacking the large geometric deformations observed at lower rates. Through calculating this energy mechanism, a transition strain rate of 180 s−1 was determined for both failure modes. The accuracy of this mechanism was further verified by tests conducted near the critical strain rate. The energy-based evolution mechanism for failure modes provides a simplified and concise framework for simplifying complex models of composite material failures.