The legitimacy of decoupled forms in dynamic constitutive modeling has long lacked rigorous mathematical criteria. To address this, we propose a unified legitimacy-assessment framework based on Weighted Singular Value Decomposition (SVD) and CANDECOMP/PARAFAC (CP) tensor decomposition. This framework introduces an inverse-variance weighting strategy that quantifies experimental reliability from data dispersion, thereby enhancing the physical consistency of model diagnosis. Applied to annealed copper, our analysis reveals that the flow stress exhibits pronounced low-rank characteristics in both two-dimensional (strain–stress state) and quasi-static three-dimensional spaces, validating the use of decoupled models. However, under dynamic conditions and in the full four-dimensional space (incorporating temperature), the Rank-1 approximation error increases markedly, uncovering strong coupling among strain rate, temperature, and stress state. Furthermore, we demonstrate that a coupled constitutive model, informed by the CP decomposition results, significantly improves predictive accuracy. The proposed framework provides a theoretical foundation for simplifying and constructing high-fidelity, data-driven constitutive models.
{"title":"Coupling validity evaluation and constitutive modeling of annealed copper via weighted SVD and CP decomposition","authors":"Xinyu Sun, Yiding Wu, Rui Zhu, Wencheng Lu, Shuangqi Li, Bingzhuo Hu, Guangfa Gao","doi":"10.1016/j.ijimpeng.2026.105643","DOIUrl":"10.1016/j.ijimpeng.2026.105643","url":null,"abstract":"<div><div>The legitimacy of decoupled forms in dynamic constitutive modeling has long lacked rigorous mathematical criteria. To address this, we propose a unified legitimacy-assessment framework based on Weighted Singular Value Decomposition (SVD) and CANDECOMP/PARAFAC (CP) tensor decomposition. This framework introduces an inverse-variance weighting strategy that quantifies experimental reliability from data dispersion, thereby enhancing the physical consistency of model diagnosis. Applied to annealed copper, our analysis reveals that the flow stress exhibits pronounced low-rank characteristics in both two-dimensional (strain–stress state) and quasi-static three-dimensional spaces, validating the use of decoupled models. However, under dynamic conditions and in the full four-dimensional space (incorporating temperature), the Rank-1 approximation error increases markedly, uncovering strong coupling among strain rate, temperature, and stress state. Furthermore, we demonstrate that a coupled constitutive model, informed by the CP decomposition results, significantly improves predictive accuracy. The proposed framework provides a theoretical foundation for simplifying and constructing high-fidelity, data-driven constitutive models.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105643"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-09DOI: 10.1016/j.ijimpeng.2026.105642
Haifeng Ou, Wenkang Ye, Lingling Hu
Load-displacement curve is the essence of a material for the mechanical performances, which can normally not be changed once they are manufactured. In engineering, complex dynamic loads are usually sudden or unexpected. Great challenges remain for materials with alterable mechanical characteristics to meet various requirement of sudden dynamic protection. Here, we present a novel kind of metamaterial with rich types of load-displacement curves programmable, such as multiple snap-through to resist repeatable impact, stair-stepping for vibration isolation, long quasi-plateau for impact buffering or nonlinear damping, and mixture of above characteristics for complex dynamic loads. The metamaterial is composed of springs and rod mechanisms. The cells’ stiffness can be switched among zero, negative and positive, whilst the load amplitude is regulable. It is realized by the matching between the nonlinearity of rod mechanisms and the springs’ stiffnesses, with the former adjustable by the spring’s length. Thus the metamaterial’s mechanical characteristics can be programmed by only replacing several springs with different stiffness or length. The analytical expressions of the metamaterial’s load-displacement relationship under large deformation are established in an equation of parameters of springs and rods, which plays the guidance for the programming customization of the metamaterial. Experiments demonstrated the excellent buffering of the metamaterial under both repetitive impact and low-frequency vibrations even with indeterminate payload. The proposed spring-rod-based metamaterial and the ability of altering nonlinear load-displacement curves open up a new avenue to the self-adaptive protection under complex dynamic loads.
{"title":"Spring-rod-based mechanical metamaterials with programmable nonlinear load-displacement curves","authors":"Haifeng Ou, Wenkang Ye, Lingling Hu","doi":"10.1016/j.ijimpeng.2026.105642","DOIUrl":"10.1016/j.ijimpeng.2026.105642","url":null,"abstract":"<div><div>Load-displacement curve is the essence of a material for the mechanical performances, which can normally not be changed once they are manufactured. In engineering, complex dynamic loads are usually sudden or unexpected. Great challenges remain for materials with alterable mechanical characteristics to meet various requirement of sudden dynamic protection. Here, we present a novel kind of metamaterial with rich types of load-displacement curves programmable, such as multiple snap-through to resist repeatable impact, stair-stepping for vibration isolation, long quasi-plateau for impact buffering or nonlinear damping, and mixture of above characteristics for complex dynamic loads. The metamaterial is composed of springs and rod mechanisms. The cells’ stiffness can be switched among zero, negative and positive, whilst the load amplitude is regulable. It is realized by the matching between the nonlinearity of rod mechanisms and the springs’ stiffnesses, with the former adjustable by the spring’s length. Thus the metamaterial’s mechanical characteristics can be programmed by only replacing several springs with different stiffness or length. The analytical expressions of the metamaterial’s load-displacement relationship under large deformation are established in an equation of parameters of springs and rods, which plays the guidance for the programming customization of the metamaterial. Experiments demonstrated the excellent buffering of the metamaterial under both repetitive impact and low-frequency vibrations even with indeterminate payload. The proposed spring-rod-based metamaterial and the ability of altering nonlinear load-displacement curves open up a new avenue to the self-adaptive protection under complex dynamic loads.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105642"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-19DOI: 10.1016/j.ijimpeng.2026.105661
Xiaolong Chen , Li Chen , Huu-Tai Thai , Qin Fang
Existing models have not consistently captured the scaling effects associated with deformable penetration of flat-nosed long rods into concrete. This paper proposes a novel semi-analytical model that explicitly incorporates the projectile diameter-to-aggregate size ratio. The projectile is treated as a control volume. Based on conservation laws and wave impedance conditions, an analytical model for the residual diameter is derived. A scaling-informed penetration resistance is used to define a yield velocity that accounts for the projectile diameter-to-aggregate size ratio. This velocity is then incorporated into a Forrestal-type resistance model, resulting in a closed-form solution for penetration depth. The model was validated against experimental data and numerical simulations. It captures the transition to the deformable regime and the subsequent reduction in penetration depth due to nose bulging. The model also captures two key scaling laws: (1) the normalized residual diameter decreases as the projectile diameter increases, and (2) the normalized penetration depth increases monotonically. Overall, the proposed model provides a unified framework that links scaling effects with deformable penetration behavior, and can be used as a useful tool for practical protective design.
{"title":"A semi-analytical model incorporating scaling effects for deformable penetration of flat-nosed long rods into semi-infinite concrete targets","authors":"Xiaolong Chen , Li Chen , Huu-Tai Thai , Qin Fang","doi":"10.1016/j.ijimpeng.2026.105661","DOIUrl":"10.1016/j.ijimpeng.2026.105661","url":null,"abstract":"<div><div>Existing models have not consistently captured the scaling effects associated with deformable penetration of flat-nosed long rods into concrete. This paper proposes a novel semi-analytical model that explicitly incorporates the projectile diameter-to-aggregate size ratio. The projectile is treated as a control volume. Based on conservation laws and wave impedance conditions, an analytical model for the residual diameter is derived. A scaling-informed penetration resistance is used to define a yield velocity that accounts for the projectile diameter-to-aggregate size ratio. This velocity is then incorporated into a Forrestal-type resistance model, resulting in a closed-form solution for penetration depth. The model was validated against experimental data and numerical simulations. It captures the transition to the deformable regime and the subsequent reduction in penetration depth due to nose bulging. The model also captures two key scaling laws: (1) the normalized residual diameter decreases as the projectile diameter increases, and (2) the normalized penetration depth increases monotonically. Overall, the proposed model provides a unified framework that links scaling effects with deformable penetration behavior, and can be used as a useful tool for practical protective design.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105661"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Repeated impact events are frequently encountered in engineering structures, where the cumulative effects may influence structural precision, vibration control, and long-term stability. In repeated impact problems, the dynamic complexity introduced by multiple sub-impacts has not yet been sufficiently addressed. To gain insight into the mechanism of repeated impacts, this study investigates the multiple sub-impact phenomenon and its influences on the repeated impact responses using a finite element method. A nonlinear finite element model is developed to investigate the repeated impact problem on slender elastic-viscoplastic beams. The model incorporates the effects of strain rate dependence, residual deformation, and stress wave propagation, and it is validated against experimental results with good agreement. Numerical results reveal that multiple sub-impacts, caused by insufficient sphere rebound and strong beam vibration, are ubiquitous in every repeated impact. Compared with single-impact predictions, multiple sub-impacts alter repeated impact dynamics significantly by introducing additional excitation into the impact system. The occurrence of multiple sub-impacts leads to random variations in force and displacement histories, alters energy dissipation patterns, and increases the impact numbers required for achieving pseudo-shakedown state. Moreover, the characteristics of sub-impacts are strongly dependent on impact location, leading to distinct repeated impact responses at different locations. Therefore, this study demonstrates that multiple sub-impacts significantly influence the repeated impact responses, and these findings highlight the importance of accounting for the multiple sub-impact effects in the design, optimization and analysis of engineering structures under repeated impacts.
{"title":"Influences of multiple sub-impacts on the repeated impact responses of flexible beams","authors":"Liang Jiang , Yuanyuan Guo , Xiaochun Yin , Panpan Weng , Huaiping Ding , Cheng Gao","doi":"10.1016/j.ijimpeng.2026.105653","DOIUrl":"10.1016/j.ijimpeng.2026.105653","url":null,"abstract":"<div><div>Repeated impact events are frequently encountered in engineering structures, where the cumulative effects may influence structural precision, vibration control, and long-term stability. In repeated impact problems, the dynamic complexity introduced by multiple sub-impacts has not yet been sufficiently addressed. To gain insight into the mechanism of repeated impacts, this study investigates the multiple sub-impact phenomenon and its influences on the repeated impact responses using a finite element method. A nonlinear finite element model is developed to investigate the repeated impact problem on slender elastic-viscoplastic beams. The model incorporates the effects of strain rate dependence, residual deformation, and stress wave propagation, and it is validated against experimental results with good agreement. Numerical results reveal that multiple sub-impacts, caused by insufficient sphere rebound and strong beam vibration, are ubiquitous in every repeated impact. Compared with single-impact predictions, multiple sub-impacts alter repeated impact dynamics significantly by introducing additional excitation into the impact system. The occurrence of multiple sub-impacts leads to random variations in force and displacement histories, alters energy dissipation patterns, and increases the impact numbers required for achieving pseudo-shakedown state. Moreover, the characteristics of sub-impacts are strongly dependent on impact location, leading to distinct repeated impact responses at different locations. Therefore, this study demonstrates that multiple sub-impacts significantly influence the repeated impact responses, and these findings highlight the importance of accounting for the multiple sub-impact effects in the design, optimization and analysis of engineering structures under repeated impacts.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105653"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-03DOI: 10.1016/j.ijimpeng.2026.105636
Canwei Zhu, Tianbao Ma
Metallic materials are widely employed as armor target materials, making the investigation of their penetration mechanisms critically important. In this study, we develop a novel theoretical model of rigid projectile penetrating into semi-infinite metal target. The model constructs a two-dimensional velocity field in the target material based on the mass conservation equation, while incorporating the effects of strain hardening, strain rate, and thermal softening into the radial stress formulation within the plastic region. Using the above mentioned velocity field, the momentum equation is accurately solved in the elastic and plastic region, the stress field is obtained, the force exerted on the projectile is approximated, and the equation of motion is solved numerically to ultimately determine the penetration depth. Subsequently, the theoretical predictions of the proposed approximation method are compared with experimental data on normal penetration in metal target. The results demonstrate that the calculations using the explicit Johnson–Cook constitutive relationship exhibit excellent agreement with the experimental penetration depths of ogive–nosed rigid long rods penetrating into semi–infinite metal targets. Moreover, a comparison of different constitutive models in the plastic region reveals their influence on the deformation resistance. When the related to nose shape correlation parameter, falls within the range , the effect of strain rate on deformation resistance increases with , whereas the effect of thermal softening first decreases and then increases slightly as increases. In addition, the proposed theoretical model proves that the inertial effect of the rigid projectile penetrating the semi-infinite metal target is negligible. However, a significant nonlinear correlation is observed between the penetration resistance and the impact velocity, the physical mechanism of which arises from the strain rate effect in the target material.
{"title":"Investigation into the penetration mechanism of a rigid long rod into a semi-infinite metallic target","authors":"Canwei Zhu, Tianbao Ma","doi":"10.1016/j.ijimpeng.2026.105636","DOIUrl":"10.1016/j.ijimpeng.2026.105636","url":null,"abstract":"<div><div>Metallic materials are widely employed as armor target materials, making the investigation of their penetration mechanisms critically important. In this study, we develop a novel theoretical model of rigid projectile penetrating into semi-infinite metal target. The model constructs a two-dimensional velocity field in the target material based on the mass conservation equation, while incorporating the effects of strain hardening, strain rate, and thermal softening into the radial stress formulation within the plastic region. Using the above mentioned velocity field, the momentum equation is accurately solved in the elastic and plastic region, the stress field is obtained, the force exerted on the projectile is approximated, and the equation of motion is solved numerically to ultimately determine the penetration depth. Subsequently, the theoretical predictions of the proposed approximation method are compared with experimental data on normal penetration in metal target. The results demonstrate that the calculations using the explicit Johnson–Cook constitutive relationship exhibit excellent agreement with the experimental penetration depths of ogive–nosed rigid long rods penetrating into semi–infinite metal targets. Moreover, a comparison of different constitutive models in the plastic region reveals their influence on the deformation resistance. When the <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> related to nose shape correlation parameter, falls within the range <span><math><mrow><msup><mrow><mn>0</mn></mrow><mrow><mo>∘</mo></mrow></msup><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>9</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>∘</mo></mrow></msup></mrow></math></span>, the effect of strain rate on deformation resistance increases with <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, whereas the effect of thermal softening first decreases and then increases slightly as <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> increases. In addition, the proposed theoretical model proves that the inertial effect of the rigid projectile penetrating the semi-infinite metal target is negligible. However, a significant nonlinear correlation is observed between the penetration resistance and the impact velocity, the physical mechanism of which arises from the strain rate effect in the target material.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105636"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145895839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-10DOI: 10.1016/j.ijimpeng.2026.105645
Seven Burçin Çellek , Alper Taşdemirci , Gülden Çimen , Fakı Murat Yıldıztekin , Ahmet Kaan Toksoy , Mustafa Güden
This study investigates the ballistic performance of silicon carbide (SiC) ceramic armor systems reinforced with single and hybrid metallic cover plates composed of Ti-6Al-4V (Ti64) and copper. Controlled ballistic experiments combined with validated LS-DYNA simulations were conducted to examine how cover-plate material, thickness, and stacking sequence influence penetration resistance, energy dissipation, and failure mechanisms. The experimental results revealed that metallic cover plates significantly enhance protection by improving projectile erosion and extending dwell time. While both Ti64 and copper single layers increased the anti-penetration capability (APC) compared with bare SiC, hybrid configurations achieved the highest performance. The optimal design, consisting of a 2 mm Ti64 plate placed in front of a 1 mm copper plate, produced the greatest reduction in penetration depth and the highest APC value. Numerical analyses closely replicated the experimental trends and provided insight into stress-wave interactions, pressure evolution, and damage progression within the ceramic. The findings demonstrate that hybrid Ti64-Cu systems not only improve initial impact resistance but also redistribute energy toward the front layers, reducing stress transmission to the backing and mitigating catastrophic ceramic failure. The combined experimental and numerical results establish a clear design framework for developing lightweight, high-efficiency ceramic armor through tailored hybrid layering strategies.
{"title":"The effect of layered cover plate material on the ballistic performance of ceramic armors: Experimental and numerical study","authors":"Seven Burçin Çellek , Alper Taşdemirci , Gülden Çimen , Fakı Murat Yıldıztekin , Ahmet Kaan Toksoy , Mustafa Güden","doi":"10.1016/j.ijimpeng.2026.105645","DOIUrl":"10.1016/j.ijimpeng.2026.105645","url":null,"abstract":"<div><div>This study investigates the ballistic performance of silicon carbide (SiC) ceramic armor systems reinforced with single and hybrid metallic cover plates composed of Ti-6Al-4V (Ti64) and copper. Controlled ballistic experiments combined with validated LS-DYNA simulations were conducted to examine how cover-plate material, thickness, and stacking sequence influence penetration resistance, energy dissipation, and failure mechanisms. The experimental results revealed that metallic cover plates significantly enhance protection by improving projectile erosion and extending dwell time. While both Ti64 and copper single layers increased the anti-penetration capability (APC) compared with bare SiC, hybrid configurations achieved the highest performance. The optimal design, consisting of a 2 mm Ti64 plate placed in front of a 1 mm copper plate, produced the greatest reduction in penetration depth and the highest APC value. Numerical analyses closely replicated the experimental trends and provided insight into stress-wave interactions, pressure evolution, and damage progression within the ceramic. The findings demonstrate that hybrid Ti64-Cu systems not only improve initial impact resistance but also redistribute energy toward the front layers, reducing stress transmission to the backing and mitigating catastrophic ceramic failure. The combined experimental and numerical results establish a clear design framework for developing lightweight, high-efficiency ceramic armor through tailored hybrid layering strategies.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105645"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-03DOI: 10.1016/j.ijimpeng.2025.105630
Alexandria Rogers , Jacob A. Rogers , Camden Clark , Justin W. Wilkerson
This study introduces a novel experimental technique for probing how prestress affects penetration dynamics in soft matter. The superimposed-shear impact (SSI) test introduces torsional preloading to an annular gel sample using a Taylor-Couette cell (TCC) prior to projectile impact. To validate the approach, two triblock copolymer gels of differing stiffness were subjected to four levels of TCC inner cylinder rotation (). Steel spheres of two diameters were used as projectiles. High-speed imaging tracked the projectile’s depth-time trajectory from contact through cavity pinch-off and rebound. Results demonstrate that increasing consistently reduced the maximum depth of penetration (DoP), independent of gel formulation or projectile size. The stiffer PMMA19 gel exhibited consistently lower DoP values than the PMMA gel for a given projectile size and . The smaller projectile produced shallower penetration and shorter interaction times with the material. Pre-shear also influenced cavity symmetry and projectile rebound behavior: higher caused pinch-off to occur more abruptly and, in some cases, enabled projectile escape via enhanced elastic recoil. Lastly, the classical elastic Froude number () was reformulated into a nonlinear elastic Froude number () to account for strain stiffening effects that are ubiquitous in soft matter. Plotting normalized DoP against resulted in the data from all test conditions collapsing onto a single curve, aligning with established DoP- scaling trends. The SSI technique thus provides a framework for studying penetration mechanics in preloaded viscoelastic solids that can support understanding, modeling, and control of biological tissues, engineered soft materials, and impact-resistant protective systems.
{"title":"Effect of azimuthal prestress on kinetic penetration into soft matter","authors":"Alexandria Rogers , Jacob A. Rogers , Camden Clark , Justin W. Wilkerson","doi":"10.1016/j.ijimpeng.2025.105630","DOIUrl":"10.1016/j.ijimpeng.2025.105630","url":null,"abstract":"<div><div>This study introduces a novel experimental technique for probing how prestress affects penetration dynamics in soft matter. The superimposed-shear impact (SSI) test introduces torsional preloading to an annular gel sample using a Taylor-Couette cell (TCC) prior to projectile impact. To validate the approach, two triblock copolymer gels of differing stiffness were subjected to four levels of TCC inner cylinder rotation (<span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>). Steel spheres of two diameters were used as projectiles. High-speed imaging tracked the projectile’s depth-time trajectory from contact through cavity pinch-off and rebound. Results demonstrate that increasing <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> consistently reduced the maximum depth of penetration (DoP), independent of gel formulation or projectile size. The stiffer PMMA<sub>19</sub> gel exhibited consistently lower DoP values than the PMMA<span><math><msub><mrow></mrow><mrow><mn>9</mn></mrow></msub></math></span> gel for a given projectile size and <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. The smaller projectile produced shallower penetration and shorter interaction times with the material. Pre-shear also influenced cavity symmetry and projectile rebound behavior: higher <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> caused pinch-off to occur more abruptly and, in some cases, enabled projectile escape <em>via</em> enhanced elastic recoil. Lastly, the classical elastic Froude number (<span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span>) was reformulated into a nonlinear elastic Froude number (<span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi><mi>e</mi></mrow></msub></math></span>) to account for strain stiffening effects that are ubiquitous in soft matter. Plotting normalized DoP against <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi><mi>e</mi></mrow></msub></math></span> resulted in the data from all test conditions collapsing onto a single curve, aligning with established DoP-<span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> scaling trends. The SSI technique thus provides a framework for studying penetration mechanics in preloaded viscoelastic solids that can support understanding, modeling, and control of biological tissues, engineered soft materials, and impact-resistant protective systems.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105630"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-10DOI: 10.1016/j.ijimpeng.2026.105644
Bilin Zheng , Xiao Kang , Xiaoyu Zhang , Mengchuan Xu , Yuan Li , Ying Li
With the advancement of 3D printing technology, there is a growing trend toward employing intricate selective laser melted (SLM) lightweight lattice structures as hypervelocity impact-resistant devices, potentially replacing traditional Whipple shield configurations. However, systematic analysis of the hypervelocity mechanical performance of SLM-manufactured materials—particularly the widely used AlSi10Mg aluminum alloy—remains insufficient. To investigate the dynamic response mechanisms of SLM AlSi10Mg aluminum alloy under hypervelocity impact, this study systematically quantifies the material's mechanical behavior and pore defect effects through integrated porosity-incorporated numerical simulations and hypervelocity shock compression experiments. A quantitative predictive model correlating porosity with shock wave propagation was established through micro-CT-based pore reconstruction. The study identifies dual attenuation mechanisms mediated by pore networks, involving both energy dissipation through pore collapse and impedance mismatch effects at pore-matrix interfaces. These coupled mechanisms reduce shockwave velocity, attenuate pressure amplitude, and ultimately decrease the equation-of-state (EOS) parameters compared to those of defect-free theoretical values. Hypervelocity shock compression experiments were then conducted at pressures of 14.76 GPa-58.45 GPa, with maximum velocities exceeding 5 km/s, validating the reliability of numerical simulations and enabling the pioneering experimental determination of Hugoniot EOS parameters for SLM AlSi10Mg under hypervelocity conditions. The experimental results demonstrate that compared to conventional wrought aluminum alloys, the SLM material exhibits slight reductions in EOS parameters (1%-10%) alongside systematic degradation of compressive resistance. The scientific innovations of this work include quantitative elucidation of additive manufacturing (AM) defect-shockwave interactions through energy redistribution mechanisms; the pioneer experimental acquisition of Hugoniot EOS parameters for SLM aluminum alloys under extreme dynamic loading.
{"title":"Hypervelocity impact response and equation-of-state characterization of selective laser melted AlSi10Mg alloy","authors":"Bilin Zheng , Xiao Kang , Xiaoyu Zhang , Mengchuan Xu , Yuan Li , Ying Li","doi":"10.1016/j.ijimpeng.2026.105644","DOIUrl":"10.1016/j.ijimpeng.2026.105644","url":null,"abstract":"<div><div>With the advancement of 3D printing technology, there is a growing trend toward employing intricate selective laser melted (SLM) lightweight lattice structures as hypervelocity impact-resistant devices, potentially replacing traditional Whipple shield configurations. However, systematic analysis of the hypervelocity mechanical performance of SLM-manufactured materials—particularly the widely used AlSi10Mg aluminum alloy—remains insufficient. To investigate the dynamic response mechanisms of SLM AlSi10Mg aluminum alloy under hypervelocity impact, this study systematically quantifies the material's mechanical behavior and pore defect effects through integrated porosity-incorporated numerical simulations and hypervelocity shock compression experiments. A quantitative predictive model correlating porosity with shock wave propagation was established through micro-CT-based pore reconstruction. The study identifies dual attenuation mechanisms mediated by pore networks, involving both energy dissipation through pore collapse and impedance mismatch effects at pore-matrix interfaces. These coupled mechanisms reduce shockwave velocity, attenuate pressure amplitude, and ultimately decrease the equation-of-state (EOS) parameters compared to those of defect-free theoretical values. Hypervelocity shock compression experiments were then conducted at pressures of 14.76 GPa-58.45 GPa, with maximum velocities exceeding 5 km/s, validating the reliability of numerical simulations and enabling the pioneering experimental determination of Hugoniot EOS parameters for SLM AlSi10Mg under hypervelocity conditions. The experimental results demonstrate that compared to conventional wrought aluminum alloys, the SLM material exhibits slight reductions in EOS parameters (1%-10%) alongside systematic degradation of compressive resistance. The scientific innovations of this work include quantitative elucidation of additive manufacturing (AM) defect-shockwave interactions through energy redistribution mechanisms; the pioneer experimental acquisition of Hugoniot EOS parameters for SLM aluminum alloys under extreme dynamic loading.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105644"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-03DOI: 10.1016/j.ijimpeng.2026.105634
Tianyu Ren , Xiaoliang Deng , Fei Han , Qian Wang
This paper presents a mechanical-thermal-chemical coupled multiphysics non-ordinary state-based peridynamics (NOSBPD) computational framework for investigating the non-shock ignition behavior of polymer-bonded explosives (PBXs). To combine the rate-dependent Johnson-Cook plastic constitutive model and the Arrhenius chemical reaction heat release model with nonlocal peridynamic enables the rigorous modeling of non-shock ignition behaviors of PBX charge, overcoming the challenges faced by the existing simulation techniques. Within such framework, a series of complicated processes such as dynamic deformation and fracture, crack nucleation and propagation, friction between crack surfaces, plastic dissipation, heat conduction, and crystal chemical reaction can be simulated in a simultaneous manner. The proposed approach is validated through classic examples including Kalthoff-Winkler (KW) impact and Taylor-bar impact tests. The predictive capability of the proposed approach is further demonstrated by modeling of the Steven test of PBX. The simulation results exhibit good agreement with both previous experimental and numerical results with respect to temperature evolution, pressure history, as well as critical impact velocity for ignition. In addition, the influences of impact velocities, explosive thicknesses, and projectile shapes on the ignition response of the PBX were analyzed, providing a deep and thoughtful understanding of ignition behaviors of PBX. The proposed multiphysics computational framework advances the development of non-shock ignition models and also can be utilized to guide the design of PBXs charges.
{"title":"Multiphysics non-ordinary state-based peridynamics for modeling non-shock ignition of PBX","authors":"Tianyu Ren , Xiaoliang Deng , Fei Han , Qian Wang","doi":"10.1016/j.ijimpeng.2026.105634","DOIUrl":"10.1016/j.ijimpeng.2026.105634","url":null,"abstract":"<div><div>This paper presents a mechanical-thermal-chemical coupled multiphysics non-ordinary state-based peridynamics (NOSBPD) computational framework for investigating the non-shock ignition behavior of polymer-bonded explosives (PBXs). To combine the rate-dependent Johnson-Cook plastic constitutive model and the Arrhenius chemical reaction heat release model with nonlocal peridynamic enables the rigorous modeling of non-shock ignition behaviors of PBX charge, overcoming the challenges faced by the existing simulation techniques. Within such framework, a series of complicated processes such as dynamic deformation and fracture, crack nucleation and propagation, friction between crack surfaces, plastic dissipation, heat conduction, and crystal chemical reaction can be simulated in a simultaneous manner. The proposed approach is validated through classic examples including Kalthoff-Winkler (KW) impact and Taylor-bar impact tests. The predictive capability of the proposed approach is further demonstrated by modeling of the Steven test of PBX. The simulation results exhibit good agreement with both previous experimental and numerical results with respect to temperature evolution, pressure history, as well as critical impact velocity for ignition. In addition, the influences of impact velocities, explosive thicknesses, and projectile shapes on the ignition response of the PBX were analyzed, providing a deep and thoughtful understanding of ignition behaviors of PBX. The proposed multiphysics computational framework advances the development of non-shock ignition models and also can be utilized to guide the design of PBXs charges.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105634"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-03DOI: 10.1016/j.ijimpeng.2026.105635
Genlin Mo , Haitao Lu , Li Liu , Weiyu He
This study investigates the wounding potential of spherical fragments using numerical simulation with ballistic gelatin, a standard tissue simulant in wound ballistics. The large deformation of the gelatin was simulated utilizing the Arbitrary Lagrangian-Eulerian (ALE) formulation. Impacts of two spherical fragments were analyzed: one with a diameter of 3 mm at an initial velocity of 651 m/s, and the other with a diameter of 4.76 mm at 1150 m/s. The simulation results demonstrated that the 3 mm fragment was trapped within the gelatin block, whereas the 4.76 mm fragment penetrated through it. The evolution of the temporary cavity showed good agreement with experimental observations. The relationship between the fragment's velocity and the maximum pressure preceding it was elucidated. The model also revealed that high volumetric tensile stresses, which are capable of inducing severe tissue injury, can develop in the gelatin. Furthermore, the simulations highlight that atmospheric pressure is a critical factor that must be accounted for in accurate modeling of temporary cavity formation.
{"title":"Numerical simulation of temporary cavity dynamics in ballistic gelatin using the arbitrary Lagrangian-Eulerian Method","authors":"Genlin Mo , Haitao Lu , Li Liu , Weiyu He","doi":"10.1016/j.ijimpeng.2026.105635","DOIUrl":"10.1016/j.ijimpeng.2026.105635","url":null,"abstract":"<div><div>This study investigates the wounding potential of spherical fragments using numerical simulation with ballistic gelatin, a standard tissue simulant in wound ballistics. The large deformation of the gelatin was simulated utilizing the Arbitrary Lagrangian-Eulerian (ALE) formulation. Impacts of two spherical fragments were analyzed: one with a diameter of 3 mm at an initial velocity of 651 m/s, and the other with a diameter of 4.76 mm at 1150 m/s. The simulation results demonstrated that the 3 mm fragment was trapped within the gelatin block, whereas the 4.76 mm fragment penetrated through it. The evolution of the temporary cavity showed good agreement with experimental observations. The relationship between the fragment's velocity and the maximum pressure preceding it was elucidated. The model also revealed that high volumetric tensile stresses, which are capable of inducing severe tissue injury, can develop in the gelatin. Furthermore, the simulations highlight that atmospheric pressure is a critical factor that must be accounted for in accurate modeling of temporary cavity formation.</div></div>","PeriodicalId":50318,"journal":{"name":"International Journal of Impact Engineering","volume":"212 ","pages":"Article 105635"},"PeriodicalIF":5.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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