Nonlinear Material Research Articles

Effects of interfacial debonding on the stability of finitely strained periodic microstructured elastic composites.

Predicting failure initiation in nonlinear composite materials, often referred to as metamaterials, is a fundamental challenge in nonlinear solid mechanics. Microstructural failure mechanisms encompass fracture, decohesion, cavitation, compression-induced contact and instabilities, affecting their unconventional static and dynamic performances. To fully take advantage of these materials, especially in extreme applications, it is imperative to predict their nonlinear behaviour using reliable, accurate and computationally efficient numerical methodologies. This study presents an innovative nonlinear homogenization-based theoretical framework for characterizing the failure behaviour of periodic reinforced hyperelastic composites induced by reinforcement/matrix decohesion and interaction between contact mechanisms and microscopic instabilities. Debonding and unilateral contact between different phases are incorporated by employing an enhanced cohesive/contact model, which features a special nonlinear interface constitutive law and an accurate contact formulation within the context of finite strain continuum mechanics. The theoretical formulation is demonstrated using periodically layered composites subjected to macroscopic compressive loading conditions along the lamination direction. Numerical results illustrate the ways in which debonding phenomena, in conjunction with fibre microbuckling, may influence the critical loads of the examined composite solid. The sensitivity of the results obtained through the proposed contact-cohesive model at finite strain with respect to its implementation is also explored. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Polymerization-induced Chiral Self-assembly for the In-situ Construction, Modulation, Amplification and Applications of Asymmetric Suprastructures.

In the polymerization-induced chiral self-assembly (PICSA) process, chiral functional monomers undergo spontaneous supramolecular self-assembly and asymmetric stacking during living polymerization, leading to the in-situ generation of chiroptical polymer assemblies characterized by diverse morphologies. The PICSA strategy facilitates precise control and manipulation of both non-covalent supramolecular helices and covalent macromolecular helices within aggregated cores, thereby driving significant advancements in fields such as chiral recognition materials, asymmetric catalysts, nonlinear optical materials, and ferroelectric liquid crystals (LC). This minireview summarizes recent developments in the in-situ chiroptical construction and modulation associated with the PICSA methodology. Furthermore, it seeks to elucidate emerging PICSA systems founded on various living polymerization mechanisms, exploring hierarchical chirality transfer processes and the pathway complexities in both equilibrium and non-equilibrium conditions. This minireview also presents several illustrative examples that demonstrate the practical applications of chiral polymer materials synthesized through the PICSA approach, thereby illuminating future opportunities in this innovative field.

Polymerization‐induced Chiral Self‐assembly for the In‐situ Construction, Modulation, Amplification and Applications of Asymmetric Suprastructures

In the polymerization‐induced chiral self‐assembly (PICSA) process, chiral functional monomers undergo spontaneous supramolecular self‐assembly and asymmetric stacking during living polymerization, leading to the in‐situ generation of chiroptical polymer assemblies characterized by diverse morphologies. The PICSA strategy facilitates precise control and manipulation of both non‐covalent supramolecular helices and covalent macromolecular helices within aggregated cores, thereby driving significant advancements in fields such as chiral recognition materials, asymmetric catalysts, nonlinear optical materials, and ferroelectric liquid crystals (LC). This minireview summarizes recent developments in the in‐situ chiroptical construction and modulation associated with the PICSA methodology. Furthermore, it seeks to elucidate emerging PICSA systems founded on various living polymerization mechanisms, exploring hierarchical chirality transfer processes and the pathway complexities in both equilibrium and non‐equilibrium conditions. This minireview also presents several illustrative examples that demonstrate the practical applications of chiral polymer materials synthesized through the PICSA approach, thereby illuminating future opportunities in this innovative field.

A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines

Abstract In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in a space-time domain. Based on the Babuška–Nečas theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability and accuracy of the proposed approach.

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

AbstractThe 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.

N-(1H-Benzo[d]imidazol-2-yl)-1-(3-substituted phenyl) methanimines as optoelectronic and nonlinear optical materials: spectroscopic and computational approaches

N-(1H-Benzo[d]imidazol-2-yl)-1-(3-substituted phenyl) methanimines as optoelectronic and nonlinear optical materials: spectroscopic and computational approaches

A comparative theoretical study on the structural, spectral, microtopology exploration ( ELF, RDG, IRI, TDM), NBO and nonlinear optical properties of Red170 from different solvents and substituents

The effect of solvents and substituents on the C.I. Pigment PR170, the best known member of the naphthol red family, is investigated. Both PR170 and its alkoxy derivatives were analyzed using FTIR, 1H-NMR and UV-Vis spectroscopy. The study included the evaluation of the average local ionization energy (ALIE), MEP, HOMO-LUMO analysis. The nature of intra- and intermolecular contacts in the crystal structure was also investigated using crystal packing and Hirshfeld surface analysis. Covalent and non-covalent interactions in PR170 were comprehensively described by IRI, RDG and ELF. In addition, Natural Bonding Orbital (NBO) and Fukui function calculations were performed. An analysis of the UV-Vis electronic transitions for different solvents was carried out, providing insight into the charge transfer processes within both PR170 and its derivatives. In particular, the research indicated a CT-type excitation at the S2 level during the hole-electron transfer analysis. The NLO results showed that PR170 is a promising candidate for nonlinear optical materials.

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 factorsRWTHblau such as, for example, material composition RWTHblau 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. RWTHblauHereby, 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 distributionRWTHblau 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 RWTHblauboth time and cost required for material characterization. Finally, the unit cells are used to generate a RWTHblaudatabase RWTHblauto predict untested load cases that will be used in future work to characterize a homogenized macroscopic material model.

Fire after earthquake assessment of 3D reinforced concrete structures

Despite that, an earthquake's occurrence can lead to dramatic effects with significant damage in urban areas, including human and material losses. Fire after an earthquake amplifies the overall impact and becomes a catastrophic event. Most constructions in Algeria are made of reinforced concrete, and current regulations overlook fires after earthquakes. Structural designs are inadequate to handle such events. This study aims to investigate the behaviour of 3D reinforced concrete frames, as part of a residential building, designed according to internal codes, CBA93 and RPA99 v2003. This 3D RC structure is exposed to several load levels of its vertical load bearing capacity. The structural system is assumed to undergo seismic scenarios characterised by various levels of story drift and damage level types. The structure is then exposed to the standard fire ISO834 model. Numerical investigations are carried out for thermo-mechanical analysis using the finite element software ANSYS, taking into account geometric and material non-linearities. Results highlight the significant impact of vertical loads, story drifts, fire scenarios, and structural damage on a building's response to fire following an earthquake. These factors collectively influence the collapse probabilities, underlining the importance of holistic risk assessment in structural design.

Makers across computers and heliotropic algorithms and can we talk about what to become?

Digitalization needs to be storied for me to become critical of and creative with its functionings. In today’s algorithmic condition, knowledge production and learning are complex posthuman entanglements: the human as materially affective has become fabricated hybrids of organism and machine. Storying is seen as simultaneous processes of fictionalizing and functionalizing hence enabling celebrations of alterations and of irreducible plural logics possibilizing nonlinear material arrangements of concepts creating alliances between the environment, technology and the social. Storying thus making trajectories and becomings present in the other rendering their mutual presence perceptible, asking if we can talk about what to become – together? Storying on the premises of the child and me, that is, highlighting the subject position instead of that of technology. It implies a view of technology that should serve humanity and being oriented toward life-affirming, human-centric goals. Always asking about what we want, and do we want it? And what is it that we currently do not seem to understand? In the posthuman project, humans as affective are significant and I suggest a view of algorithms as heliotropic designed as life engendering tools only. Ignoring the affective dimension of becoming, digitalized environments give way to an ethical and conceptual vacuum, wherein education risk being sacrificed at the altar of technology and development. The primary task for the digital spacemakers/makerspace is thus being to train the imagination through teaching critical and creative encounters affirming intradisciplinary perspectivists ethos. Makerspace/spacemaking first and foremost being an onto-epistemological endeavour pointing paradoxically towards the importance of the teacher. The child being the knower however, the teacher has sadly been trained not to. I address the need for studies approaching digitalization by way of affects and storying: the child seen as a metaphysical political being, as knowing and knowers of affect. Therefore, I meander through some complex ideas and discuss data as bioinformatical practices of data simultaneously situated and fictional. Instead of speaking about evidence-based teaching, research, analysis, and results, I speak of something imperceptible and inclusive that collectivizes digital freedom as processes of subjective becomings, teaching towards moments of non-governance.

Ferroelectric nematic fluids as spontaneous polarization field for enhanced orientational-dependent second-harmonic generation

ABSTRACT Second-order nonlinear optical effects have piqued researchers’ interest in fundamental physics and practical perspectives. The ferroelectric nematic liquid crystals (NF LCs) have recently drawn attention to LC nonlinear optical applications due to their relatively high second-harmonic generation output. Further improving the nonlinear optical properties to get closer to the performance of inorganic nonlinear optical materials is challenging. Here, we take a blending strategy to enhance the nonlinear optical response of a prototype NF LC, DIO. We mixed an organic nonlinear optical crystalline material, 3,5,5-trimethyl (cyclohex-2-enylidene) malononitrile (TCM), with DIO and investigated the effects of TCM doping at various concentrations. We quantitatively determined the second-harmonic generation and spontaneous polarization as functions of temperature and concentration. We found that, compared with the pure DIO, the second-harmonic generation performance increased by about 130% at maximum, 93% in maximum for the nonlinear optical coefficient, and 10% in maximum for spontaneous polarization.

Stress-controlled medium-amplitude oscillatory shear (MAOStress) of PVA–Borax

We report the first-ever complete measurement of MAOStress material functions, which reveal that stress can be more fundamental than strain or strain rate for understanding linearity limits as a function of Deborah number. The material used is a canonical viscoelastic liquid with a single dominant relaxation time: polyvinyl alcohol (PVA) polymer solution cross-linked with tetrahydroborate (Borax) solution. We outline experimental limit lines and their dependence on geometry and test conditions. These MAOStress measurements enable us to observe the frequency dependence of the weakly nonlinear deviation as a function of stress amplitude. The observed features of MAOStress material functions are distinctly simpler than MAOStrain, where the frequency dependence is much more dramatic. The strain-stiffening transient network model was used to derive a model-informed normalization of the nonlinear material functions that accounts for their scaling with linear material properties. Moreover, we compare the frequency dependence of the critical stress, strain, and strain-rate for the linearity limit, which are rigorously computed from the MAOStress and MAOStrain material functions. While critical strain and strain-rate change by orders of magnitude throughout the Deborah number range, critical stress changes by a factor of about 2, showing that stress is a more fundamental measure of nonlinearity strength. This work extends the experimental accessibility of the weakly nonlinear regime to stress-controlled instruments and deformations, which reveal material physics beyond linear viscoelasticity but at conditions that are accessible to theory and detailed simulation.

Practice-oriented numerical model for seismic response of cold-formed steel-framed mid-rise buildings

Cold-formed steel (CFS) framed buildings are becoming increasingly common, notably in the high seismic regions of the United States (US). However, research to understand the seismic performance of CFS-framed buildings specifically using large-scale (building-level) specimens has begun only recently. Therefore, efforts to validate and improve numerical modeling of whole building systems have been limited due to this lack of experimental data. A recently completed experimental program, conducted at the Large High-Performance Outdoor Shake Table at the University of California, San Diego, involved earthquake testing of a full-scale 6-story CFS-framed building. The test building adopted an assembly of continuous tie-rod and built-up compression stud pack at the ends of individual shear walls to resist seismic overturning moment and uplift forces within the building. The objective of this paper is to present a practice-oriented phenomenological finite element modeling approach intended for design engineers and compare the predictions from this model against the measured seismic response of the 6-story building. The model aims to provide a robust, yet computationally efficient approach, with minimal degrees-of-freedom, while also capturing the salient features of seismic response of mid-rise CFS-framed buildings suitable for nonlinear time history analyses-based design. The building model, developed within the OpenSeesPy finite element platform, includes the shear walls and gravity walls as well as the lateral strength and stiffness contribution from exterior and interior gypsum sheathing. The continuous tie-rod system is also modeled to capture the cumulative floor displacements caused by the axial elongation in the steel rods. The effect of built-up compression stud packs on the lateral behavior of a shear wall was estimated using available experimental data and a detailed numerical model of an isolated shear wall, then subsequently incorporated in the nonlinear hysteretic material model. The numerical model captured the natural frequencies of the translation modes of the building in its undamaged state with <3% error. It also predicted the peak roof drift ratio within an error of 0.03% drift ratio under the design earthquake event. These results provide confidence in the proposed numerical modeling approach as a tool for seismic response prediction of mid-rise CFS-framed buildings with similar structural detailing features.

Propagation buckling failure of a buried offshore pipeline with integral arrestors under external overpressure and strike-slip faulting disturbance

In this study, the propagation buckling failure of a buried offshore pipeline under external overpressure and strike-slip faulting disturbances was investigated numerically. A nonlinear shell model, accounting for geometric, material, self-contact, and pipe-soil interaction nonlinearities, was developed using the vector form intrinsic element method. The arresting performances of the single- and double-integral arrestors were analyzed based on a series of simulations considering various combinations of arrestor diameter-to-thickness ratios, lengths, and sub-arrestor intervals. A comparative analysis was conducted between single- and double-integral arrestors, focusing on their arresting performance, material usage, and manufacturing complexity. The results revealed that pipelines under external overpressure are prone to local collapse and bidirectional buckling propagation under small fault displacements. Reverse ellipticities occur downstream of the buckling propagation and their development leads to flipping propagation. Buckling arrestors function by exhausting the upstream flattening propagation and inhibiting the development of reverse ellipticities downstream. The material consumption of each single-integral arrestor was significantly higher than that of a double-integral arrestor with the same diameter-to-thickness ratio. The weld count of the double-integral arrestors was lower than that of the single scheme, but this difference narrowed as the pipeline mileage increased. These results can serve as valuable guidelines for the design and construction of pipelines crossing seismic zones.

Effects of stiffeners on anchor rod flexural strength in column base-plate connections

The present paper reports results of a numerical investigation of the mechanical behavior of a column base plate connection subjected to an axial compression force and a bending moment. A three-dimensional nonlinear model was developed, using the Cast3M software, and validated against experimental data. In addition, the material nonlinearity as well as contact conditions between the different components of the connection were thoughtfully considered. Based on the validated model, an extensive parametric analysis was conducted to investigate the effect of stiffeners on the forces in the anchor rods. The results clearly indicate that the design approaches that consider only the tensile strength of anchor rods while neglecting the bending moments can lead to a poor estimation of the forces applied to these rods. They also suggest that adding stiffeners provides additional strength and reduces the anchor rod bending in one direction. However, it is important to note that the stiffeners also induce an additional moment in the opposite direction. This could make the anchor rod more susceptible to biaxial bending with tension. Furthermore, this study proposes a new specific shape of stiffener is suggested (cbp5). It was concluded that the proposed shape of stiffeners allows a more uniform distribution of forces and avoids excessive stress concentrations, effectively prevents the biaxial bending in the anchor rod.

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.

Influence of geometric imperfections on the seismic performance of unanchored liquid storage tanks

This paper investigates the inelastic buckling of imperfect unanchored cylindrical steel tanks subjected to seismic loads. A pushover-based seismic analysis was conducted considering the impulsive hydrodynamics pressures on the wall and base plate of the tank. Material and geometric nonlinearities were considered in the seismic analysis of the tanks. Three types of imperfections were analyzed: imperfections due to impacts, imperfections located at the bottom of the tank wall, and imperfections with the first buckling mode shape. The buckling analysis was performed for two tank geometries (one slender and one broad), and the effect of the imperfections was correspondingly evaluated. The considered imperfection amplitudes were established according to the New Zealand seismic design code for storage tanks. Additionally, amplitudes that exceed the normative limit were evaluated to further analyze the sensitivity to imperfection. The analysis revealed that geometric imperfections reduce the peak ground acceleration needed to induce buckling failure. Specifically, the critical peak ground acceleration for the slender tank decreased from 0.195 g to 0.180 g for the slender tank and from 0.600 g to 0.535 g for the broad tank. This buckling capacity reduction due to geometric imperfections were about 8 % and 11 % for the slender and the broad tanks, respectively.

Local strain inhomogeneities during electrical triggering of a metal–insulator transition revealed by X-ray microscopy

Electrical triggering of a metal-insulator transition (MIT) often results in the formation of characteristic spatial patterns such as a metallic filament percolating through an insulating matrix or an insulating barrier splitting a conducting matrix. When MIT triggering is driven by electrothermal effects, the temperature of the filament or barrier can be substantially higher than the rest of the material. Using X-ray microdiffraction and dark-field X-ray microscopy, we show that electrothermal MIT triggering leads to the development of an inhomogeneous strain profile across the switching device, even when the material does not undergo a pronounced, discontinuous structural transition coinciding with the MIT. Diffraction measurements further reveal evidence of unique features associated with MIT triggering including lattice distortions, tilting, and twinning, which indicate structural nonuniformity of both low- and high-resistance regions inside the switching device. Such lattice deformations do not occur under equilibrium, zero-voltage conditions, highlighting the qualitative difference between states achieved through increasing temperature and applying voltage in nonlinear electrothermal materials. Electrically induced strain, lattice distortions, and twinning could have important contributions in the MIT triggering process and drive the material into nonequilibrium states, providing an unconventional pathway to explore the phase space in strongly correlated electronic systems.

Micromechanical analysis of magnetoelectric coupling of composites containing nonlinear magnetostrictive and piezoelectric constituents

This paper is a reformulation of the simplified unit-cell and Mori-Tanaka micromechanics theories in their applications to nonlinear magnetoelectric analysis of two-phase composite materials with 0–3, 1–3, and 2–2 connectivity types, respectively. We elucidate the similarity between the two models insofar as concentration-factor matrices are concerned. The representations of the bulk magnetostrictive and piezoelectric phases are based on nonlinear constitutive equations. Due to material nonlinearity, the mathematical frameworks are accomplished via incremental formulation that provides a system of linear algebraic equations at each increment which is obviously a great advantage over nonlinear one. The derived nonlinear composite constitutive relations that govern the hysteresis behavior of composites are implemented to study the composite composed of Terfenol-D and PZT constituents. The responses of this composite to a complete cycle of magnetic field are shown and the micromechanics predictions are compared in light of existing experimental data.

Enhanced analytical solution of magnetic field dynamics in nonlinear magnetic materials

This work presents two new analytical approaches developed to describe magnetic field penetration into nonlinear magnetic materials commonly found in transformers and electrical machines. These new analytical models are designed to achieve a balance between precision and mathematical simplicity, which allows them to be easily implemented in the finite element method and analytical analysis of electromagnetic devices. The use of these advances can significantly reduce the computational costs of numerical calculations. In addition, the influence of a curved surface on the dynamics of the magnetic field inside magnetic materials is also studied, which makes it possible to extend the new results to magnetic objects of various shapes.