Nonlinear Material Response Research Articles

A two-step dynamic FEM-FELA approach for seismic slope stability assessment

AbstractThe determination of the factor of safety (FoS) of slopes during seismic excitation can be complex if the relevant effects of pore water pressure accumulation, nonlinear material response and variable shear strength are duly accounted for. A rational two-step approach to tackle this task based on a hydro-mechanically coupled dynamic simulation and finite element limit analyses is henceforth introduced. To ensure accurate transfer of the hydro-mechanical soil state, a mapping concept is presented, accounting for spatial distributions of stresses, excess pore water pressures, inertial forces and shear strength. The proposed approach is compared to limit equilibrium method (LEM) for the case of a large-scale water-saturated open cast mine slope subjected to seismic loading. In comparison with LEM, the new approach to assess seismic slope stability proves to be simpler in its implementation and straightforward, which could be an important asset for practitioners.

Ultra-broadband all-optical nonlinear activation function enabled by MoTe2/optical waveguide integrated devices

All-optical nonlinear activation functions (NAFs) are crucial for enabling rapid optical neural networks (ONNs). As linear matrix computation advances in integrated ONNs, on-chip all-optical NAFs face challenges such as limited integration, high latency, substantial power consumption, and a high activation threshold. In this work, we develop an integrated nonlinear optical activator based on the butt-coupling integration of two-dimensional (2D) MoTe2 and optical waveguides (OWGs). The activator exhibits an ultra-broadband response from visible to near-infrared wavelength, a low activation threshold of 0.94 μW, a small device size (~50 µm2), an ultra-fast response rate (2.08 THz), and high-density integration. The excellent nonlinear effects and broadband response of 2D materials have been utilized to create all-optical NAFs. These activators were applied to simulate MNIST handwritten digit recognition, achieving an accuracy of 97.6%. The results underscore the potential application of this approach in ONNs. Moreover, the classification of more intricate CIFAR-10 images demonstrated a generalizable accuracy of 94.6%. The present nonlinear activator promises a general platform for three-dimensional (3D) ultra-broadband ONNs with dense integration and low activation thresholds by integrating a variety of strong nonlinear optical (NLO) materials (e.g., 2D materials) and OWGs in glass.

Hierarchical Modeling of the Nonlinear Optical Response of Composite Materials Based on Tetrathiafulvalene Derivatives.

The presented work concerns computational investigations of the physical properties of composite materials based on polymer matrix and nonlinear optical (NLO) active chromophores. The structural, electronic, and optical properties of selected tetrathiafulvalene (TTF)-based chromophores have been calculated using quantum chemical methods. The polymer matrix changes the physical properties of the inserted chromophores influencing their optical parameters. To explain the mechanism of the NLO signal occurrence from the composites based on poly(methyl methacrylate) (PMMA) matrix and TTF chromophores, their structures are modeled using the classical molecular dynamics. In consequence, the structural properties of the composites are discussed according to the NLO requirements. By developing the theoretical model based on a discrete multipole local field approach, the impact of polymer matrix on the optical properties of chromophores is explained.

Predicting and explaining nonlinear material response using deep physically guided neural networks with internal variables

Predicting and explaining nonlinear material response using deep physically guided neural networks with internal variables

Revealing a distortive polar order buried in the Fermi sea.

Polar metals are challenging to identify spectroscopically because the fingerprints of electric polarization are often obscured by the presence of screening charges. Here, we unravel unambiguous signatures of a distortive polar order buried in the Fermi sea by probing the nonlinear optical response of materials driven by tailored terahertz fields. We apply this strategy to investigate the topological crystalline insulator Pb1-xSnxTe, tracking its soft phonon mode in the time domain and observing the occurrence of inversion symmetry breaking as a function of temperature. By combining measurements across the material's phase diagram with ab initio calculations, we demonstrate the generality of our approach. These results highlight the potential of terahertz driving fields to reveal polar orders coexisting with itinerant electrons, thus opening additional avenues for material discovery.

Flexibility, toughness, and load bearing of 3D-printed chiral kerf composite structures

Chiral kerf structures are formed by arranging chiral and coiled unit cells which allows for multi-dimensional and multi-scale shape configurations under mechanical loadings. In this study, we investigate how the mechanical properties of materials and microstructural topologies interact to control the flexibility, toughness, and load bearing of 3D-printed chiral kerf structures. We explore chiral kerf structures with two different kerf patterns, i.e., square and hexagon, and three coiling densities. We consider three materials, namely brittle Polylactic Acid (PLA), compliant thermoplastic polyurethane (TPU), and a ductile composite made by alternating PLA and TPU, referred to as a programmable composite. The chiral kerf structures undergo two deformation mechanisms when subjected to mechanical loadings. The first one results from reconfigurations of kerf cells such as uncoiling, rotation of cells, and cell packing, and the second mechanism arises from nonlinear and inelastic material responses. The use of brittle material limits cell reconfigurations before material failure, reducing the overall flexibility and toughness of kerf structures. While the compliant material enables full cell reconfigurations, it results in low load bearing. The use of PLA:TPU composite allows for cell reconfigurations and inelastic material response, enhancing flexibility and toughness while maintaining a relatively high load bearing. We demonstrate that stress distribution in kerf structures can be controlled by using multiple materials or coil densities. This strategy can delay failure and improve the toughness and load-bearing capabilities of kerf structures.

Fractal Circuit Architectures for Spatially Controlled Heating and Multi-Modal Shape Programming of Electro-Active Shape Memory Polymers

Shape memory polymers (SMPs) are commonly activated through external heating or rigid embedded heaters, which lack precise temperature control and restrict programmable shape transformations. This study demonstrates integrating thin films of hard electronic materials patterned in fractal designs into SMPs yields novel thermomechanical responses, enabling flexible implementation of stretchable electronic functionality. Space-filling Hilbert, Moore and Peano fractal curves generate distributed electronic circuitry patterns within the SMP matrices. To investigate the coupled electro-thermal-mechanical behavior, a multi-physics modeling approach is adopted. A nonlinear thermo-visco-hyperelastic constitutive model captures the SMP’s shape memory characteristics. Governing equations for the multi-physics problem are formulated. Experimental data validates the model’s predictions of the SMP’s nonlinear material response under uniaxial loading. This validated framework analyzes SMP composites with integrated fractal circuits. Findings reveal composites with higher-order fractal circuits’ exhibit faster, more uniform resistive heating and smaller electrical resistance changes during stretching, enabling consistent and predictable shape recovery under various deformations. Notably, these advantageous heating and resistance characteristics enhance the force recovery rate during the shape memory cycle. Furthermore, the composites demonstrate excellent shape recovery under bending. Remarkably, uniaxial stretching can induce controlled out-of-plane shape transformations, enabling novel actuation modalities. This work provides insights into leveraging fractal circuit integration to enhance SMP performance and expand capabilities, enabling multi-functional actuators, sensors and programmable soft grippers.

Plasma etching promoting the saturable absorption of BiOI

Materials exhibiting exceptional saturable absorption performance and etching compatibility are significant in the context of advanced optical devices. Our study demonstrates that plasma etching can effectively promote the saturable absorption of BiOI nanosheets because of defect formation. Remarkably, the BiOI nanosheet subjected to the optimized H2/Ar-plasma treatment manifests a substantial nonlinear absorption coefficient (βeff) of (−5.5 ± 0.7) × 103 cm GW−1 under laser excitation at 800 nm, while the pristine BiOI sample exhibits no discernible nonlinear optical response. The βeff of plasma-treated BiOI samples is (−4.2 ± 0.9) × 103 cm GW−1 at 515 nm, surpassing that of the untreated counterpart by more than fourfold. A comprehensive structural and spectroscopic analysis indicates that oxygen vacancies serve to increase the density of in-gap states, thereby narrowing the bandgap of the BiOI. This reduced bandgap effectively facilitates the Pauli-blocking effect and, in turn, augments the saturable absorption properties of the samples. In contrast to oxygen vacancies, iodine vacancies make a negligible contribution to the performance enhancement of BiOI. Our result would provide a promising way to improve the nonlinear optical response of materials.

Enormous and Tunable Bulk Charge/Spin Photovoltaic Effect in Piezoelectric Binary Materials T-IV-VI and T-V-V.

Understanding the nonlinear response of light and materials is crucial for fundamental physics and next-generation electronic devices. In this work, we have investigated the second-order nonlinear bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) effects in the piezoelectric binary materials T-IV-VI and T-V-V (IV = Ge, Sn; VI = S, Se; and V = P, As, Sb, Bi). The independent nonzero conductivity tensors of charge current are derived for these binaries through the symmetry analysis, along with the mechanism for generating pure spin current. These binaries, with their unique folded structure, exhibit significant charge and spin currents under illumination. Furthermore, we find that strain engineering can effectively modulate charge/spin currents by influencing charge density distribution and built-in electric field due to the piezoelectric effect. Our research suggests that the piezoelectric binary materials possess enormous and tunable charge/spin currents, underscoring their potential for applications in nonlinear flexible optoelectronics and spintronics.

Material optimization of reinforced concrete structures in multiple limit states

AbstractA common limitation in current material optimization methods for reinforced concrete structures is that they often concentrate solely on either the serviceability limit state (SLS) or the ultimate limit state (ULS). In response, this paper introduces a novel approach to optimize the material layout in planar reinforced concrete structures in plane stress, accounting for both limit states simultaneously. The proposed method employs an iterative strategy, integrating criteria for serviceability and ultimate limit states while approximating the elastoplastic behavior of cracked reinforced concrete. Here, the criteria for the limit states are incorporated as limits on the strains. The methodology initiates with a finite element limit analysis for the preliminary layout. The minimum potential energy principle is utilized to determine the strains for the nonlinear material response, and subsequently, an iterative linearized method is applied for material optimization. The research showcases the successful application of this approach to simple examples and presents improved and optimized solutions that adhere to the limit criteria for more complex structural scenarios.

Optical non-linearities and applications of ZnS phosphors

Optical non-linearities play a crucial role in enabling efficient and ultrafast switching applications that are essential for next-generation photonic devices. ZnS phosphor material produces the best results in terms of increased luminescence quantum yield when doped with certain impurities. Nevertheless, the investigation of the third-order non-linear optical susceptibility of the phosphor materials can be exploited for various switching applications. In this regard, we review the recent advancements in the investigation of non-linear optical properties of ZnS phosphors, where the knowledge of absorption and refraction is utilized in various optical and detector applications. Furthermore, the review highlights strategies employed to enhance the non-linear optical response of phosphor materials as well as a general discussion of an attosecond optical switching scheme which can be used to fabricate devices with petahertz speeds. Consequently, we provide a solution to the unsolved problem of the significant extension of optical limiting applications to switching applications by developing design strategies to manipulate conventional ZnS phosphor material. The potential challenges and future prospects of utilizing phosphor materials for switching applications are also addressed. The strategies for manipulating ZnS phosphor can be generalized for a broad range of other materials by minimizing linear and non-linear losses, while enhancing the values of the non-linear refractive index coefficient. We propose that the figure-of-merit of ZnS material can be enhanced by using a suitable combination of pump and probe wavelength values, which can be useful for optical switching applications.

Generation of entangled waveguided photon pairs by free electrons.

Entangled photons are a key resource in quantum technologies. While intense laser light propagating in nonlinear crystals is conventionally used to generate entangled photons, such schemes have low efficiency due to the weak nonlinear response of known materials and losses associated with in/out photon coupling. Here, we show how to generate entangled polariton pairs directly within optical waveguides using free electrons. The measured energy loss of undeflected electrons heralds the production of counter-propagating polariton pairs entangled in energy and emission direction. For illustration, we study the excitation of plasmon polaritons in metal strip waveguides that strongly enhance light-matter interactions, rendering two-plasmon generation dominant over single-plasmon excitation. We demonstrate that electron energy losses detected within optimal frequency ranges can reliably signal the generation of plasmon pairs entangled in energy and momentum. Our proposed scheme is directly applicable to other types of optical waveguides for in situ generation of entangled photon pairs.

Modelling of hybrid biocomposites for automotive structural applications

The demand for environmentally friendly materials is at its peak, and government legislations have become stricter and no longer tolerate violations. With biocomposites emerging as structural components instead of being hidden as non-structural applications and interiors, the automotive and motorsport sector started considering them for structural body parts. Natural fibres abundance, commercial availability, renewability, low density, low cost, and high tensile strength make biocomposite materials excellent candidates for eco-friendly vehicles. Several studies reported the utilisation of biocomposites as high-performance components and structural applications. However, current computer-aided engineering and modelling tools are insufficient to explore the vast field of possibilities during biocomposite materials selection to accurately predict the components' behaviour and analyses. Therefore, this study focuses on creating a material model to predict the behaviour of biocomposite materials. Additionally, the model is numerically implemented to illustrate the deformation and bending stiffness capabilities of a motorsport monocoque chassis structure application. A micromechanics modelling combining rate-dependant constitutive laws and multi-site interactions of inclusions is developed for studying the nonlinear response of composite materials. To avoid numerical instabilities when increments of time become very small, a regulation procedure concerning the visco-plastic function is adopted in the computation of the consistent tangent modulus. Based on the Generalised Mori–Tanaka (GMT) scheme, the effective properties are obtained for the nonlinear composite. The accuracy of the model is evaluated and validated by comparison results from the open literature. Finally, the developed constitutive equations are implemented as a user-defined material UMAT in a Finite Element code, leading to an application on a bio-based composite for the bamboo/flax fibre-reinforced epoxy hybrid composite materials.

Momentum-dependent intraband high harmonic generation in a photodoped indirect semiconductor

Nonlinear optical response of solid-state materials exposed to strong non-resonant light fields leads to the generation of harmonic frequencies as a consequence of interband polarization and coherent intraband dynamics of the electrons. The efficient production of a macroscopic wave requires the preservation of the mutual phase between the driving wave and the individual microscopic sources of radiation. Here, we experimentally and theoretically show that the yield of high harmonic generation in a photodoped silicon crystal is enhanced by the nonlinear intraband current whose amplitude depends not only on the volume density of the photogenerated carriers but also on their momentum distributions within the bands. The strongest enhancement is reached when the carrier system is relaxed to the band minima before interacting with the strong nonresonant wave, which drives the high harmonic generation. These results extend the possibilities of high harmonic spectroscopy towards the investigation of ultrafast carrier relaxation in condensed matter.

Efficient second-harmonic generation of quasi-bound states in the continuum in lithium niobate thin film enhanced by Bloch surface waves

Abstract Nonlinear optics has generated a wide range of applications in the fields of optical communications, biomedicine, and materials science, with nonlinear conversion efficiency serving as a vital metric for its progress. However, the weak nonlinear response of materials, high optical loss, and inhomogeneous distribution of the light field hamper the improvement of the conversion efficiency. We present a composite grating waveguide structure integrated into a Bragg reflector platform. This design achieves high Q in the spectral range by exploiting the unique properties exhibited by the bound states in the Bloch surface wave-enhanced continuum, and efficient second-harmonic generation by close-field amplification with the optical field tightly localized in a nonlinear material. By manipulating the symmetry of the grating, a precise tune over the near field within a designated wavelength range can be achieved. Specifically, we select a photonic crystal configuration supporting surface waves, employing TE polarization conditions and an asymmetry factor of −0.1 between the composite gratings. This configuration resonates at a fundamental wavelength of 783.5 nm, exhibiting an impressive Q-factor of 106. Notably, at an incident light intensity of 1.33 GW/cm2, we achieve a normalized electric field strength of up to 940 at the fundamental frequency and a second-harmonic conversion efficiency of up to 6 × 10−3, significantly amplifying the second-harmonic response. The proposed configuration in this investigation has the potential to be integrated into the field of nonlinear optics for sensing frequency conversion applications.

Prominent Nonlinear Optical Absorption in SnS2‐Based Hybrid Inorganic–Organic Superlattice

AbstractNonlinear optical materials hold great promise for applications in advanced opto‐/opto‐electronic devices. However, achieving a substantial nonlinear absorption coefficient and modulation depth concurrently remains challenging. This study proposes an effective strategy for enhancing the nonlinear optical response of materials through the construction of hybrid inorganic–organic superlattices via convenient organic intercalation. Synthesizing SnS2 intercalated with various tetra‐alkylammonium cations, it is revealed that the optimized sample (SnS2/CTA: SnS2 intercalated with cetyltrimethylammonium, CTA+) exhibits a substantial enhancement of nonlinear absorption across a broad wavelength range (from 515 to 1550 nm) and for diverse nonlinear optical processes (saturable absorption, two‐photon absorption, and three‐photon absorption). Specifically, the SnS2/CTA demonstrates a third‐order nonlinear absorption coefficient of (9.847 ± 0.084) × 103 cm GW−1 and a 69% modulation depth under laser excitation at 800 nm. Under 1550 nm excitation, it displays a fifth‐order nonlinear absorption coefficient of (45.3 ± 1.2) cm3 GW−2 and a 62% modulation depth. Notably, these values surpass those of the majority of non‐exfoliated materials. Structural, spectral, and density functional theory calculations indicate no induced structure defects post‐organic intercalation. The observed bandgap reduction is attributed to the electron injection associated with the organic molecule intercalation. The calculated performance enhancement, based on dielectric enhancement and bandgap reduction, qualitatively aligns with experimental findings.

A practical guide to mitigate edge fracture instability in sheared polymer melts

The measurement of nonlinear shear response of viscoelastic materials is often hindered by edge fracture instabilities. The phenomenon was first addressed theoretically by Tanner and Keentok and ever since has attracted the interest of experimentalists and theorists alike. Despite progress, accounting for or mitigating edge fracture remains a challenge, in particular when dealing with strongly viscoelastic materials such as entangled polymer melts. Here, we present and compare different experimental attempts to delay edge fracture in a cone-and-plate (CP) geometry, including the use of an immiscible fluid bath around the sample (that reduces the stress and interfacial gradients in comparison with the sample/air interface), a cone-partitioned plate (CPP) fixture, and an outer collar attached to the sample's edge (in a CP or CPP fixture). Focusing on the torque signal, we find that the combination of CPP and collar provides the best results. This may indeed help measuring highly elastic materials over an extended range of shear rates and, importantly, contribute to reliably measuring the normal stress coefficients in a cone-partitioned plate tool. It is, therefore, hoped that this simple idea will be further pursued in the direction of improving our current rheometric capabilities.

Arching development above active trapdoor: insight from multi-scale analysis using FEM–SPH

AbstractUnderground excavation is usually accompanied by complex soil-structure interaction problems in practical engineering. This paper develops a novel multi-scale approach for investigating the soil arching effect through trapdoor tests. This approach adopts the finite element method (FEM) and smoothed particle hydrodynamics (SPH) method to handle the particle-rigid body interaction in the trapdoor tests, incorporating a micromechanical 3D-H model to derive the nonlinear material response required by the SPH method. The variation of the earth pressure on the trapdoor in simulations exhibits good agreement with those of the experiments. Extensive parametric analyzes are performed to assess the effects of soil height and inter-particle friction angle on the evolution of load transfer and soil deformation. Three deformation patterns are observed under different buried conditions, including the trapezoid, the triangle, and the equal settlement pattern. Results indicate that the planes of equal settlement develop progressively with the trapdoor movement and then enter the range of experimentally observed values. Additionally, three failure mechanisms are identified that correspond to the three deformation patterns. Due to the advantages of the micromechanical model, mesoscale behavior is captured. The anisotropy of stress distribution in the plastic region is found during the arching process.

Description of the constitutive behaviour of stainless steel reinforcement

This paper presents a comprehensive analysis of the constitutive relationship of stainless steel reinforcement and proposes new material models for both austenitic and duplex stainless steel bars. These are an advancement on existing models which have largely been developed for structural stainless steel plate, rather than for reinforcement bars. Current design guidance for material modelling of reinforcing bars does not include representative stress-strain relationships which capture the unique mechanical properties of stainless steel reinforcement. Codes include idealised elastic-plastic material models which are inappropriate and inefficient for the highly nonlinear and ductile material response of stainless steel. The present study aims to address this issue by first conducting a series of tensile tests to ascertain the stress-strain material responses and then employing this data to examine the validity of existing approaches and propose new material models where required. It is shown that new material models are required and those that are developed are able to accurately capture the stress-strain response of stainless steel reinforcement, and provide a better, more accurate, representation than existing methods.

Physics-Based Self-Learning Spiking Neural Network enhanced time-integration scheme for computing viscoplastic structural finite element response

The present study introduces a new physics-based self-learning spiking neural framework to compute geometrically and physically nonlinear structural response. While the so-called traditional or second-generation deep neural networks are used in many applications in the class of physics-informed neural networks, we propose a hybrid model that consists of third-generation Leaky-Integrated and Fire (LIF) neurons, Recurrent Leaky-Integrated and Fire (RLIF) neurons and second-generation dense transformation. The third-generation neurons are inspired by the human brain’s energy-efficient functioning which introduces inherent temporal and sparse behavior leading to a more sustainable AI approach. However, the sparse nature of the spiking neurons poses a challenge to tackle nonlinear regression tasks. Thus, in the present study, we use an autoencoding strategy that converts the real-valued signals to its spiking representation and enables the spiking neurons to learn nonlinear material response. The proposed hybrid network is firstly pretrained with combined data-driven and physics-based loss functions and then deployed in the plastic corrector step of the implicit integration which is used in the Finite Element solver and is validated on a series of Boundary Value Problems (BVPs) consisting of plate elements. A self-learning strategy is introduced for the hybrid network to train itself during FE simulation using the proposed physics-based loss function. Two major advantages were observed: an overall computational gain in the excess of 30% and the self-learning/online training ability of the model that bolsters its convergence behavior. Finally, the proposed third-generation layers are deployed on the Xylo-Av2 neuromorphic chip and its energy performance is compared with the second-generation Recurrent Neural Networks (RNNs).