Nonlinear Material Behavior Research Articles

Nonlinear analysis of three-dimensional hyperelastic problems using radial point interpolation method

Hyperelastic materials are primarily common in real life as well as in industry applications, and studying this kind of material is still an active research area. Naturally, the characteristic of hyperelastic material will be expressed when it undergoes large deformation, so the geometrical nonlinear effect should be considered. To analyze the behavior of hyperelastic material, the Neo-Hookean model is imposed in this study because of its simplicity. The model shows the nonlinear behavior when the deformation becomes large due to the nonlinear displacement-strain relation. This constitutive relation also gives a good correlation with experimental data. This study performs a meshless method, namely the radial point interpolation method (RPIM), to analyze the nonlinear behavior of Neo-Hookean hyperelastic material under a finite deformation state in three-dimensional space. The standard Newton-Raphson technique is applied to obtain the nonlinear solutions. Unlike mesh-based approaches, the meshless method shows its advantages in large deformation problems due to its mesh independence. In this paper, the numerical results of three-dimensional problems that undergo large deformation will be calculated and validated with solutions derived from previous studies. By investigating the obtained results, the superior ability of RPIM in hyperelastic problems can be proved.

Mechanical Analysis and Optimization of Concrete Structures Based on Advanced Finite Element Method

This article explores the mechanical analysis and optimization problems of concrete structures based on the Advanced Finite Element Method. By integrating advanced numerical techniques with practical engineering cases, this study aims to improve the safety and economy of concrete structure design. Firstly, the paper outlines the limitations of traditional finite element methods in concrete structure analysis, such as insufficient computational accuracy and low computational efficiency. Subsequently, by introducing AFEM, we significantly improved the accuracy and efficiency of the analysis. For example, when simulating a complex bridge structure, AFEM not only reduces the calculation time by about 25%, but also improves the accuracy of stress distribution prediction by more than 10%. In the optimization stage, we utilized the analysis results of AFEM and optimized the material consumption, cross-sectional dimensions, and reinforcement parameters of concrete structures through multi-objective optimization algorithms. A comprehensive data analysis underscores that the optimized concrete structure triumphantly meets all safety performance criteria while achieving a remarkable 12% reduction in material usage. This substantial material savings translates into a substantial 8% decrease in overall construction costs, significantly bolstering the project’s economic feasibility. Moreover, these cost savings not only amplify the project’s profitability but also play a pivotal role in enhancing the structure’s longevity and durability, thereby contributing to its sustainable performance over its entire service life. Furthermore, we delved into the capability of AFEM in simulating intricate phenomena such as the nonlinear behavior of concrete materials, crack propagation patterns, and the intricate interactions between steel reinforcements and concrete. These complex mechanical behaviors are crucial for the safety and stability of structures, and AFEM provides more comprehensive and accurate references for structural design by accurately simulating these behaviors. This article conducts in-depth research on the mechanical analysis and optimization of concrete structures based on AFEM, and demonstrates the significant advantages of AFEM in improving structural safety and economy through specific data. These research results not only provide new theoretical support and practical tools for concrete structure design, but also provide valuable references for future research and application in related fields.

On the imperfection sensitivity and design of buckling critical wind turbine towers

Wind turbine towers pose major challenges for design engineers due to their complex geometry, nonlinear material behavior and imperfection sensitivity. In service, these thin-walled shells are burdened by a combination of complex load cases and prone to buckling. In fact, one of the main design drivers of wind turbine towers is stability failure for which often the design recommendation of the EN-1993-1-6 are used.Recently an international shell buckling exercise was caried out by the team behind the EN-1993-1-6 design standard. Within this exercise 29 teams from academia and industry were asked to perform a series of linear and non-linear finite element simulations of an 8-MW multi-strake steel wind turbine support tower segment. In general, the linear and nonlinear analyzes posed no challenge for the shell buckling experts from around the world. However, the imperfection sensitivity analysis results scattered significantly among the participants. In addition, there was little consensus as to whether the given tower design is actually safe.The authors, whose background is aerospace engineering, participated in this exercise and show in this article how they overcome the challenges of this typical civil engineering problem. Among linear and non-linear analyzes the authors show the results of state-of-the-art shell buckling concepts which were developed for aerospace shells like interstage tanks and adapters but are also applicable to wind turbine towers.

Thermomechanical Analysis of Cement Hydration Effects in Multi-layered Pier Head Concrete: Finite Element Approach

Mass concrete plays a crucial role in infrastructure development, yet its complex thermo-mechanical behavior poses challenges, especially in the construction of multi-layered structures like pier heads. This study investigated the thermo-mechanical behavior of a pier head during its concreting process in three stages, including the influence of temperature differences that impact the thermomechanical balance of the concrete. By utilizing the ABAQUS software, thermo-mechanical analysis was conducted to simulate temperature fluctuations during cement hydration. The model integrates thermal analysis to simulate temperature fluctuations during cement hydration and stress distribution during construction, validated through mesh convergence studies and field data comparison. The mechanical analysis considered concrete properties, temperature variations, and construction phase. Nonlinear material behavior and contact interactions between layers were incorporated to obtain a realistic simulation. The results indicated that a multi-layer system can balance temperatures, reducing thermal stress-induced cracking risks. Furthermore, specific test points within the pier head were assessed, revealing potential internal cracks by comparing thermal stresses to the concrete’s tensile strength. This research offers insight into pier head conditions during construction, highlighting critical stress zones, crack prediction, and construction sequence efficacy.

Measurement of the Static Nonlinear Third‐Order Elastic Moduli of Rocks: Problems and Applicability

AbstractThe third‐order elastic (TOE) model has been used to describe the widely observed nonlinear mechanical behaviors of earth materials. In addition to linear elastic constants (λ, μ), three nonlinear elastic moduli (A, B, C) are required for isotropic rocks. Contrary to previous research on dynamic TOE moduli, this study followed the protocol to measure strain and stress under uniaxial and hydrostatic compressive tests statically, which were later used to invert for the full set of TOE moduli for four standard rock types with differing pore structures of a porous oolitic limestone, quartz‐rich sandstones, and a dense crystalline basalt. The applicability of the TOE model to characterize nonlinearity depends on the fulfillment of path‐independence and small‐strain assumptions. Using the measured static TOE moduli, the finite element model demonstrates that the stress in the vicinity of the wellbore is more amplified than the stress in the linear elastic case, which leads to a wider zone of rock failure around the wellbore. Due to the long‐standing discrepancy between static and dynamic moduli, the rarely reported full set of static TOE moduli is necessary and will benefit future research in understanding the effect of rock nonlinearity on geophysical and geomechanical applications, such as long‐term safe storage of CO2 and generating process of geohazards.

Stress-strain curve estimation from micropillar compression with transverse contraction effect

The Focused Ion Beam (FIB) technique and the associated compression testing capabilities provide versatile access to understanding the microstructural behaviour of materials. Among many objectives, determining the stress-strain relationship from experimental or numerical force-displacement data remains a fundamental challenge. However, for micropillers under compression, the inside deformation constraint is complex like in components and the transformation of a measured force-displacement curve into an accurate uniaxial stress-strain curve is not straightforward. In this context, in a previous numerical based analysis for perfect volume constancy or incompressibility the determination of reliable and accurate stress-strain curves from nonlinear load-deformation curves of micropillers was already verified. In the case of transverse contractions, however, numerical simulations of micropillers provide unexpected force-displacement behaviour, i.e. their force-displacement curves are almost superimposing and are very close to the force-displacements for incompressibility. This effect implies, that transverse contraction would have no contributions in micropillar compression. In contrast, independent simulations using a single finite element accurately explore the true uniaxial stress-strain behaviour for the whole range of transverse contractions. These are considered as the reference behaviour and are also treated by an analytical expression. With the presented new stress-strain estimation approach, including transverse contraction, any force-displacement curve from a micropillar under compression can be stepwise corrected. The first step of the new stress-strain curve estimation method, including transverse contraction, is carried out in the same way as in the preceding analysis for incompressibility, followed by further steps to obtain the final true stress-strain curve. Although the presented numerical analysis is exemplarily performed for the behaviour of fused silica, but the stress-strain approach is in the same manner generally applicable for a material behaviour with other stress-strain curves. The assumption behind is isotropic and nonlinear material behaviour.

An extended lumped damage mechanics IGABEM formulation for quasi-brittle material failure

This study proposes a new formulation for the mechanical modeling of quasi-brittle materials. The material degradation due to cracking is addressed through the Extended Lumped Damage Mechanics (XLDM) approach. The model is inserted into an IGABEM formulation, where Non-Uniform Rational B-Splines (NURBS) are the basis functions. A novel nonlinear solution technique has been developed for the numerical implementation. Crack propagation is captured using the initial stress field approach, widely utilized by the BEM community to account for nonlinear material behavior. The XLDM is coupled into an IGABEM formulation by discretizing part of the domain into cells, placed only where damage is expected to grow. Classical benchmark problems are presented to demonstrate the method’s capability and effectiveness. The results show excellent agreement with both experimental and numerical findings from the literature. Damage evolution is assessed through the band thickness opening, leading to material degradation. This method offers a new way of addressing damage mechanics problems within the BEM framework. It could benefit the BEM community, as traditional damage analysis within this numerical method often leads to significant time-consuming and elevated computational costs, which are mitigated by the formulation proposed herein.

Experimental investigation and micromechanical analysis of glass fiber reinforced polyamide 6

Achieving process stability in the thermoforming of fiber reinforced polymer materials (FRPs) for aerospace or automotive manufacturing is usually associated with a costly trial-and-error process, where experimental boundary conditions and other influencing factors, such as, for example, material composition, need to be adjusted over time. This is especially true when material phenomena on the microlevel, such as the crystallization kinetics of the polymer matrix or resulting stresses from temperature gradients, are the cause of the process instability. To reduce the experimental effort and reliably predict the material behavior during thermoforming, finite element simulation tools on multiple scales are a useful solution. Hereby, incorporating micromechanical phenomena into the model approaches is crucial for an accurate prediction by further reducing the deviation between simulation and experiment, in particular with regard to the underlying nonlinear material behavior. In this work, unit cell simulations on the microscale of a unidirectional glass fiber reinforced polymer (UD GFRP) are conducted to predict effective thermomechanical properties of a single material ply and ascertain the effect of individual ply constituents on the homogenized material behavior. The polymeric matrix material model used was identified in a prior publication with experimental data at various temperatures for polyamide 6 blends with varying degrees of crystallinities. Various randomization methods are tested to generate the unit cells and replicate the composites’ random fiber distribution, with a focus on process automation. The simulative results are successfully compared to an experimental study on glass fiber reinforced polyamide 6 tested at various temperatures, demonstrating the potential of the approach to reduce both time and cost required for material characterization. Finally, the unit cells are used to generate a database to predict untested load cases that will be used in future work to characterize a homogenized macroscopic material model.

Towards a Fracture Mechanics-Based Assessment for Fatigue Life Prediction of Ni–Ti Stents

The fatigue failure of Ni–Ti peripheral stents still represents an open issue of major concern due to the non-linear material behavior, the complex loads acting in vivo, and the manufacturing process. The fatigue assessment currently exploits total-life methodologies devoted to preventing crack nucleation. This work investigates a complementary fracture mechanics-based approach accounting for crack propagation from pre-existing manufacturing defects. Fatigue crack growth tests were performed on rolled Ni–Ti samples with a thickness and microstructure comparable to that of stents. A fracture mechanics-based assessment was implemented to predict the fatigue durability of surrogate samples tested at different mean and alternate strains. The fracture surfaces of the samples were inspected to determine a statistical distribution of defect size at the fracture origin. The cyclic J-integral was adopted as the crack driving force parameter, and it allowed to account for the complex response of the material, undergoing energy dissipations during phase transformation. Encouraging fatigue life predictions conforming to experimental data were obtained in the finite-life regime, whereas conservative estimates were computed below the fatigue threshold. This approach can be reverted to determine the maximum acceptable material defects for specific applications, providing a useful tool to manufacturing companies.

Numerical investigation of knee prosthesis stresses in daily activities: Insight into knee rehabilitation and Creation of a new optimal model

Total knee arthroplasty (TKA) is a cornerstone in addressing knee joint disorders, significantly enhancing patients' quality of life. However, despite technological advancements, a comprehensive understanding of the dynamic stresses experienced by knee prostheses during daily activities, particularly under rehabilitation interventions, remains elusive. This study aims to bridge this gap by employing numerical simulations and finite element analysis to elucidate these dynamic stresses and their interaction with rehabilitation protocols.A real-life knee replacement prosthesis model was meticulously constructed through coordinate measuring and 3D scanning, facilitating detailed finite element analysis in ANSYS Workbench version 17.1. Two distinct boundary conditions and loading scenarios were applied, with comparisons made between linear and nonlinear material assumptions. The simulation results using these different boundary condition methods revealed minimal differences. Specifically, at a knee angle of 0°, the relative stress error rate between the two boundary condition types was approximately 1 % (1.11 MPa and 1.099 MPa, respectively). At 15° and 90°, the error rates were 1.9 % and 0.56 %, respectively (10.275 MPa and 10.078 MPa at 15°; 10.275 MPa and 10.078 MPa at 90°). Given these minimal differences, the first type of boundary condition was adopted for the subsequent scenarios to enhance convergence efficiency in the analysis.Moreover, comparative analyses between linear and nonlinear material behaviors demonstrated acceptable agreement, offering insights into potential efficiency gains in simulation methodologies. Building on this foundation, an optimized tibial model was proposed, incorporating geometric alterations to the tray. Quantitative assessments revealed significant reductions, with von Mises stress decreasing by 23.35 % and equivalent strain by 17 % at a knee angle of 140°. Further evaluations at varying angles, including 60°, consistently showed positive influences on stress and strain. These quantitative findings not only contribute valuable insights into the mechanical behavior of knee prostheses but also provide tangible evidence for the efficacy of linear material behavior assumptions. The proposed optimized model exhibits promising potential for enhancing the design and performance of knee prostheses, particularly under critical loading conditions.In conclusion, these results underscore the importance of a nuanced understanding of knee prosthesis behavior during rehabilitation, offering a quantitative foundation for refining existing designs and informing the development of next-generation prostheses.

Fretting fatigue life of galvanized bridge support cable wire: Experimental study and strain-based fracture mechanics analysis

The galvanized wires used in cable bridges can fail due to fretting fatigue. Experimental results have shown that defects resulting from the galvanization process are a possible source of initiation for fatigue cracks and make the life shorter than that of a wire without a galvanized layer. The investigation presented in this paper uses strain-based fracture mechanics to analyze the influence of these defects on the fatigue life of galvanized wire. The presented analysis considers nonlinear material behaviour. A 3D finite element model is used to compute the required stress field. Stress intensity factors are obtained by a proposed numerical point load weight function, and shape factors are found for the surface and deepest points of the semielliptical crack. Plain fatigue tests of galvanized wires are performed to calibrate key model parameters. The calibrated model is then shown to provide reasonably accurate but systematically conservative estimates of the fatigue life under fretting conditions typical of bridge stay cable saddle supports.

Modelling insertion behaviour of PVP (Polyvinylpyrrolidone) and PVA (Polyvinyl Alcohol) microneedles

A comprehensive investigation into the effects of nonlinear material behaviour of polymeric (MN) and skin on the dynamics of the MN insertion in skin was undertaken in this study using experiments and numerical simulations. The nonlinearity of the material behaviour was incorporated by employing the Ramberg–Osgood and neo-Hookean equations for stress–strain relationships for the MN materials and skin, respectively. For this purpose, a characteristic type of dissolving MN array was selected. This type of MN is made by a combination of poly(vinyl alcohol) and poly(vinyl pyrrolidone). The numerical simulations were validated using experimental investigations where the MNs were fabricated using laser-engineered silicone micromould templates technology. Young’s modulus, Poisson’s ratio, and compression breaking force for the MN polymers were determined using a texture analyser. The alignment between experimental findings and simulation data underscores the accuracy of the parameters determined through mechanical testing and mathematical calculations for both MN materials (PVP/PVA) and skin behaviour during the MN insertion. This study has demonstrated a strong alignment between the experimental findings and computational simulations, confirming the accuracy of the established parameters for MNs and skin interactions for modelling MN insertion behaviour in skin, providing a solid foundation for future research in this area.

Non-linear mechanical behaviour of thermoplastic elastomeric materials and its vulcanizate under tension/tension fatigue deformation by fourier transform rheological studies

Fourier transform (FT) rheology opens up novel frontiers in understanding non-linear mechanical behaviours of polymeric materials under sustained long-term dynamic load. The prediction of the exact point of appearance of a crack in a sample under dynamic mechanical strains of large amplitude and the fatigue analysis has been made possible to such degrees of precision, previously not possible through conventional rheological and mechanical analysis. In this work, the fatigue behaviour of a thermoplastic elastomeric material (TPE) and a thermoplastic vulcanizate (TPV) from thermoplastic polyurethane (TPU) and epichlorohydrin− ethylene oxide−allyl glycidyl ether (GECO) rubber is investigated by Fourier transform studies under oscillatory strain-controlled tensional test to understand the linear and non-linear mechanical behaviour. Fatigue analysis is performed through the fingerprint harmonics of the material’s stress response, i.e., the second and third harmonics, ( I 2/1 and I 3/1) to establish the stress nonlinearity, asymmetry, and the formation of macrocracks. Furthermore, these higher harmonics are fitted with the Neo-Hooke and Mooney-Rivlin model to fundamentally understand the mode of fatigue failure, and a close agreement between theoretical fitting and experimental outcomes is established. Strain-life curves were utilized for the thorough investigation of the fatigue behaviour of the specimens and more than 9-fold enhancement in the strain life of the TPV is observed over TPU at a strain amplitude of ∼1.05 indicating an increasing ductility. Finally, the necessity of FT rheology was further emphasised as it is observed that I 2/1 and I 3/1 harmonics are more sensitive towards fatigue response as compared to the storage modulus and the complex modulus. Henceforth, the FT rheology analysis has enabled the current study to efficiently establish the ductility of each individual specimens and for prediction of the dynamic service lifetime of the developed materials.

Precision improvement of robotic bioprinting via vision-based tool path compensation

Robotic 3D bioprinting is a rapidly advancing technology with applications in organ fabrication, tissue restoration, and pharmaceutical testing. While the stepwise generation of organs characterizes bioprinting, challenges such as non-linear material behavior, layer shifting, and trajectory tracking are common in freeform reversible embedding of suspended hydrogels (FRESH) bioprinting, leading to imperfections in complex organ construction. To overcome these limitations, we propose a computer vision-based strategy to identify discrepancies between printed filaments and the reference robot path. Employing error compensation techniques, we generate an adjusted reference path, enhancing robotic 3D bioprinting by adapting the robot path based on vision system data. Experimental assessments confirm the reliability and agility of our vision-based robotic 3D bioprinting approach, showcasing precision in fabricating human blood vessel segments through case studies. Significantly, it minimizes the printing layer width disparity to just 0.15 mm compared to the 0.6 mm in traditional methods, and it decreases the average error for curved filaments to 7.0 mm2 from the previous 12.7 mm2 in conventional printing. While these results underscore the significant potential of our innovation in creating precise biomimetic constructs, further investigation is necessary to tackle challenges such as accurately distinguishing closely stacked layers using a vision system, especially under varying lighting conditions. These limitations, coupled with issues of computational complexity and scalability in larger-scale bioprinting, emphasize the importance of enhancing the reliability of the vision-based approach across various conditions. Nonetheless, our innovation demonstrates substantial promise in creating precise biomimetic constructs and paves the way for future advancements in vision-guided robotic bioprinting, including the integration of multi-material printing techniques to enhance versatility.

FlexScale: Modeling and Characterization of Flexible Scaled Sheets

We present a computational approach for modeling the mechanical behavior of flexible scaled sheet materials---3D-printed hard scales embedded in a soft substrate. Balancing strength and flexibility, these structured materials find applications in protective gear, soft robotics, and 3D-printed fashion. To unlock their full potential, however, we must unravel the complex relation between scale pattern and mechanical properties. To address this problem, we propose a contact-aware homogenization approach that distills native-level simulation data into a novel macromechanical model. This macro-model combines piecewise-quadratic uniaxial fits with polar interpolation using circular harmonics, allowing for efficient simulation of large-scale patterns. We apply our approach to explore the space of isohedral scale patterns, revealing a diverse range of anisotropic and nonlinear material behaviors. Through an extensive set of experiments, we show that our models reproduce various scale-level effects while offering good qualitative agreement with physical prototypes on the macro-level.

On the Schapery nonlinear viscoelastic model: A review

Among the various models presented so far to describe the nonlinear viscoelastic behavior of materials, the model proposed by Schapery in the 1960s stands out for its wide acceptance and significant contributions to the field. Through a detailed inspection of the main articles presented by Schapery and other related studies, the present paper reviews the Schapery nonlinear viscoelastic model. One-dimensional and three-dimensional formulations of the model for both isotropic and anisotropic materials, along with model accuracy, are discussed. The present article highlights the challenges of material characterization methods, such as creep-recovery testing, stress relaxation testing, and dynamic mechanical analysis. The article also addresses the issues of characterizing the material's behavior under non-recoverable strain and varying temperatures. Finally, the future research needs in this field are outlined, emphasizing the potential for further advancements in our understanding of nonlinear viscoelasticity.

Topological derivatives for shell structure optimization considering crash loadcases with material nonlinearities and large deformations

The topological derivatives for shell structures in dynamic loadcases, which are often used in lightweight designs, are developed. These sensitivities consider the highly nonlinear material behavior and large deformations of the structure. The aim of the investigation is the support of an efficient topology optimization for crashloaded structures. The considered functionals can in general be described by displacements, velocities and accelerations. In particular, the semi-analytical sensitivity calculations for the internal deformation energy and for single point displacements in arbitrary directions in the shell structure are presented. These functionals cover the most important functions for the development of crash structures. Using the material derivative in combination with the adjoint method, a terminal value problem has to be solved. Depending on whether first differentiation and then discretization in the time domain is performed or first discretization and then differentiation, a separate solution scheme for the adjoint is derived. Both schemes are presented in a comparable description. For the numerical evaluation of the topological derivatives, the basic equations for large deformed shell elements are included as well as a phenomenological material interpolation, which represents the tangential material behavior resulting from plastic strain and isotropic hardening. All assumptions made for the derivation are described in detail and their influences are discussed. The elaborated equations and the procedure for the calculation of the topological derivatives are applied, discussed and checked for plausibility on two clearly defined loading conditions for the internal deformation energy and single point displacements on different locations.

Analysis procedures accounting for load redistribution mechanisms in masonry earth retaining structures under traffic loading

This paper introduces novel analysis procedures for the structural assessment of masonry earth retaining structures subjected to traffic loading. Given their substantial presence, particularly in transportation networks of historical cities, and the challenges posed by ageing, deterioration, and exposure to loads beyond their original design considerations, this research highlights the necessity of accounting for potential load redistribution mechanisms during their assessment. This can prevent overly conservative interventions that may not be necessary and also contravene sustainability and heritage preservation principles. Four distinct analysis procedures – 2D monotonic, 3D monotonic, 3D static moving load and 3D dynamic moving load – are developed, each progressively more refined than its predecessor in capturing potential load redistribution mechanisms in masonry earth retaining structures. These mechanisms may develop due to the dynamic loading conditions of the vehicular passage, the 3D structural configuration of retaining structures, and non-linear material behaviour. By comparing the structural capacity evaluated using the four procedures, contributions from different sources of load redistribution can be separately quantified, aiding in the reduction of conservatism inherent in less refined assessment procedures. The application of the developed procedures and consequent quantification of load redistribution is demonstrated through a case study of an existing masonry retaining structure in Amsterdam, the Netherlands.

A novel hydro-elastoplastic constitutive model incorporating hydrostatic damage for predicting high-pressure performance of concrete under blast loading

The evolution of damage and failure modes of concrete under blast or impact loads are the outcomes of stress wave propagation. The stress state at a point within the concrete changes instantaneously with time and space. Establishing a constitutive model that can cover the nonlinear behavior of materials under complex loading paths and histories is an extremely challenging task. The main difficulty lies in the construction of the damage model, which has not yet been fully resolved in commonly used concrete models. This paper, based on the mechanisms of damage and failure of concrete under hydrostatic pressure, constructs a state equation that includes the description of crushing and compaction damage due to the collapse and closure of pores, as well as their interactive model, negative pressure degradation caused by hydrostatic pressure, and nonlinear volumetric behavior under loading/unloading/reloading. By introducing independent shear and tensile deviatoric damage scaling functions and a damage scaling function under isotropic tension, the coupling relationship between deviatoric and volumetric damage is considered. Corresponding strength models and element erosion criteria are developed based on the new state equation and damage models. Then, single-element numerical experiments of unconstrained uniaxial compression and tension, triaxial compression under different confining pressures, monotonic and cyclic hydrostatic compression, and isotropic tension were conducted to verify the predictive accuracy of the proposed model under single loading paths. Finally, numerical experiments of contact explosion on plain concrete thick and thin targets were carried out using the proposed model, revealing the propagation laws and failure processes of the loading compression wave, unloading tensile wave, and reflected tensile wave within the concrete target. The predicted final failure modes are consistent with the experimental results.

Chemically reactive flow of non‐Newtonian nano‐liquid over different magnetized and slippery inclined surfaces

AbstractFlow behavior of nonlinear materials over magnetized and contracting and extending inclined surfaces is described specifically by Jeffery–Hamel type flow, where the flow is caused by a convergent/divergent channel with the appearance of a source or sink. The role of the conversion of more than one species to more than every other species is significant in the flow conduct of such types of nonlinear materials. However, for the desired higher thermal conductivity, the Brownian motion and thermophoretic forces are incorporated in this particular work. Moreover, the impacts of first‐order chemical reaction and slips on the velocity, thermal, and concentration distributions, respectively presented to portray the importance of the entire study. The liquid motion on such surfaces is further addressed with the involvement of viscous dissipation and solar radiation. The newly mathematically formulated work is then approximated via one of the built‐in approaches based on collocation methods. The key findings are determined through graphical illustration. The physically interesting growing velocity of the liquid motion is noticed with variation in the slippery motion parameter during the convergent channel case. The opposite trend is noted for the divergent channel case. Furthermore, the Brownian motion‐related parameter escalated the temperature of the liquid, and the reverse status of the liquid concentration is determined with variation in the same parameter. The mass fraction is determined in a declining conduct with the ascending variation in first‐order chemical reaction factor. At the end of the work, a comparison with existing results is provided with excellent agreement.