Nonlinear Material Behavior Research Articles

A numerical two-scale approach for nonlinear hyperelastic beams and beam networks

We introduce a numerical framework for modeling hyperelastic slender trusses, oftentimes used as elementary building blocks in architected materials, which accounts for both the geometric nonlinearity inherent in thin structures and the nonlinear constitutive behavior of the base material. Akin to the FE2 method in homogenization, our approach is based on a formal, two-scale expansion. We decompose the three-dimensional (3D) description of a slender structure into a macroscale problem solving for the deformation of the beam center-line (based on an effective strain energy density, which depends on the stretching, bending, and torsional strains of the beam’s center-line) and a series of two-dimensional (2D) microscale boundary value problems (defined over the beam cross-section). We solve a series of 2D problems (covering a range of macroscopic strain combinations) for a given cross-sectional geometry and material distribution in an offline, pre-processing step. Using this pre-computed energy landscape, we solve the macroscopic boundary value problem within a geometrically exact, nonlinear discrete beam framework. We demonstrate the accuracy of this approach through a set of benchmark problems highlighting the nonlinear effects of the cross-sectional geometry and constitutive material, including material heterogeneity and pre-strains. We further illustrate how this technique is applied to truss-based architected materials consisting of networks of slender struts, which are typically made of polymeric base materials and thus allow for large nonlinear elastic deformation.

Semi‐crystalline polymers at finite strains: A thermo‐coupled constitutive model for varying degrees of crystallinity and temperatures

AbstractThermoplastics are gaining interest for various industrial applications, since they can be widely used for thermoforming and injection moulding processes due to their thermostable material behavior. In combination with the material's low density and high strength to mass ratio, they are especially of interest in times where an improved environmental balance is more and more important. Hence, why they are for example frequently used in the automotive industry to reduce the weight of automotive components.Semi‐crystalline polymers as a subcategory of thermoplastics, partly crystallize after cool‐down from the molten state. During the thermoforming process, they are subjected to large deformations as well as thermal loads and show strong thermo‐mechanical coupling effects in addition to the influence of the evolution of the crystalline phase on the macroscopic material behavior. Therefore, computational models are needed to predict the complex material response reliably and minimize production errors.This work presents a thermomechanically consistent material formulation at finite strains. In order to account for the highly nonlinear material behavior, elasto‐plastic and visco‐elastic contributions are combined in the Helmholtz free energy and a dependency on temperature as well as the degree of cristallinity (DOC) is incorporated. Special attention is devoted to the choice of yield function and hardening behavior.A comparison of the simulation results to experiments at varying degrees of crystallinity and temperatures is presented to review the changes in the formulation. Therefore a special blending technique is used to ensure stable crystallinity conditions in the test samples.

Finite element modeling of precast reinforced concrete wall with dual boundary elements under lateral load

This study aimed to stimulate the structural behaviour of the precast wall PC with dual boundary elements under constant axial load and incremental lateral load in terms of displacement control and assess its response based on the load–displacement response, stiffness degradation and modes of failure using Abaqus Software and validate the result of the tested specimen. Two approaches were used for defining the interaction between the steel reinforcement and the surrounding concrete where the high-stress regions are. Friction and cohesive behaviour using traction separation law were employed to define the interaction between the interfaces of the PC wall and post-cast concrete boundary elements. Furthermore, this study primarily focused on the nonlinear behaviour of concrete and steel materials, the bond-slip behaviour between concrete-to-steel interface, the interaction between precast and post-cast concrete interfaces, and load and boundary conditions. The concrete damage plasticity model was adopted to simulate the concrete behaviour and the cohesive and frictional behaviour to model the interaction between precast and post-cast concrete interfaces. The findings show that the initial response of both FE models agreed well with test rested specimen. However, Model I exhibited a stiffer response up to the yielding point. Furthermore, both FE models continued to exhibit ductile response, showing that the right-hand side post-cast cornet boundary element didn’t experience total crushing at the bottom right concrete.

Nonlinear micromechanical modeling of fully coupled piezo-elastic composite under large deformation and high electric field

This paper presents mathematical modeling and predictions of effective nonlinear electro-mechanical behavior of piezoelectric materials under large deformation and high electric field. The heterogeneous inclusion problem is extended to investigate the fields dependent electro-elastic behaviors under high fields. The associated strain field dependent Green tensors are introduced. The field dependent interaction tensors, related to Eshelby’s tensors, are explicitly formulated and used to derive micromechanical models based on the Mori–Tanaka approach and the self-consistent model. Due to electric-strain field dependence nonlinear algebraic tensors equations are resulted. Iterative incremental schemes based on the Newton–Raphson algorithm are elaborated and explicit semi-analytical formulations of electric-strain field dependent effective electro-elastic moduli of piezoelectric multi-phase composites are obtained for various inclusion types. Strain and electric field’s effects on effective properties can be analyzed for various electro-elastic composites. Numerical results of field dependent effective electro-mechanical properties are given for several inclusion’s volume fraction and shapes as well as types of matrix and inclusions phases.

Nonlinear elastic behavior of 2D materials using molecular statics and comparisons with first principles calculations

Nonlinear elastic behavior of 2D materials using molecular statics and comparisons with first principles calculations

Effect of nonlinear material behavior on progressive failure analysis of pin-joint composites

In this study, the mechanical performances of glass fiber-reinforced notched and pin-connected composite plates were investigated experimentally and numerically. For this purpose, composite plates with a circular hole, semicircular double-edge notched, U-edge notched, and single and double pin joints were prepared from layer glass fiber composites. Tensile tests were carried out on the obtained specimens. The effect of notch type, number of pins, and position of pins on plate damage load and type was investigated for linear and non-linear material behavior. Progressive failure analysis was performed using the Hashin damage criteria. Subprogram codes were written in the Ansys program using the finite element method. According to the obtained data, it was determined that the type of notch and the number of pins have a significant effect on the damage loads of the plates and the behavior of the material is important in terms of convergence to the experimental results in numerical solutions. In single-pin composites, the type of damage changed from net-tension to shear out as the pin approached the free edge of the plate. It was observed that the distance between the pins did not have any effect on the damage type of the composites in the double-pin joint structure. Compared to single-pin joint composites, double-pin joint composites were found to carry a maximum of 34% more damage load. The convergence rate of experimental and numerical data was obtained as a minimum of 92.1% for nonlinear material behavior and a minimum of 73.4% for linear material behavior

A Continuum Damage-Based Anisotropic Hyperelastic Fatigue Model for Short Glass Fiber Reinforced Polyamide 66

A phenomenological 3D anisotropic nonlinear fatigue damage model has been developed for a short glass fiber-reinforced polyamide. The model is formulated within the framework of continuum damage mechanics and is based on a proposed anisotropic hyperelastic strain energy function. The proposed model accounts for the effects of fiber content and nonlinear material behavior. The mechanical behavior of polyamide reinforced with 20% and 30% wt short glass fiber has been experimentally investigated under quasi-static and fatigue loading. Fatigue tests under bending loading are carried out on rectangular specimens cut in the parallel and perpendicular direction to the mold flow direction. The proposed fatigue damage model allows predicting the fatigue damage of composite materials reinforced with short fiberglass, considering fiber orientation and fiber content. The model is used to predict the damage evolution and the number of cycles to failure, and good agreement between predicted values and experimental data is observed.

Adaptive control of a soft pneumatic actuator using experimental characterization data.

Fiber reinforced soft pneumatic actuators are hard to control due to their non-linear behavior and non-uniformity introduced by the fabrication process. Model-based controllers generally have difficulty compensating non-uniform and non-linear material behaviors, whereas model-free approaches are harder to interpret and tune intuitively. In this study, we present the design, fabrication, characterization, and control of a fiber reinforced soft pneumatic module with an outer diameter size of 12mm. Specifically, we utilized the characterization data to adaptively control the soft pneumatic actuator. From the measured characterization data, we fitted mapping functions between the actuator input pressures and the actuator space angles. These maps were used to construct the feedforward control signal and tune the feedback controller adaptively depending on the actuator bending configuration. The performance of the proposed control approach is experimentally validated by comparing the measured 2D tip orientation against the reference trajectory. The adaptive controller was able to successfully follow the prescribed trajectory with a mean absolute error of 0.68° for the magnitude of the bending angle and 3.5° for the bending phase around the axial direction. The data-driven control method introduced in this paper may offer a solution to intuitively tune and control soft pneumatic actuators, compensating for their non-uniform and non-linear behavior.

Debonding model for nonlinear Fe-SMA strips bonded with nonlinear adhesives

The application of adhesively-bonded joints for strengthening of structures using iron-based shape memory alloys (Fe-SMAs) has recently emerged in construction. Fe-SMAs and the majority of structural adhesives exhibit a pronounced nonlinear material behavior, which may result in a favorable ductile failure mechanism. The development, however, of a mechanical model to predict the structural behavior of the joint is non-trivial due to the presence of nonlinearity in the adherent and adhesive. This study aims to propose a semi-analytical and semi-numerical model for describing the mechanical behavior of Fe-SMA-to-steel adhesively bonded joints. The developed model serves three main functions: (i) estimating the bond capacity for a given interfacial fracture energy, and vice versa; (ii) processing the bond–slip (τ−s) behavior directly from the load–displacement (F−Δ) curve, and vice versa; and (iii) delivering a numerical method to simulate the full-range mechanical behavior of the bonded joints, namely the behavior at different loading stages. The model is validated using the experimental testing of 26 Fe-SMA-to-steel lap-shear joints, as well as 24 further bonded joints subject to shear with different adherents (e.g., stainless steel strips and Nickel–Titanium SMA wires) and base materials (e.g., concrete and composite polymer). An experimental data processing protocol, on the basis of the experimentally measured force–displacement (F−Δ) behavior and the distributed displacement along the bond line (s−x) via the Digital Image Correlation (DIC) technique, is further proposed to assess the full-range behavior of bonded joints.

Seismic Dynamic Response and Lining Damage Analysis of Curved Tunnel under Shallowly Buried Rock Strata

It is still challenging to anticipate with accuracy how tunnels will behave and if they will fail when subjected to an earthquake load. In this study, assuming nonlinear material behavior and a three-dimensional inelastic rock medium, the theory of damage mechanics is applied to numerical simulation to build a curved tunnel-surrounding rock model, whose correctness was verified in laboratory experiments. To better understand the influence of surrounding rock strength on the seismic performance of a curved tunnel, the stratum parameters of the curved tunnel-surrounding rock system are quantified. The findings demonstrate that the damage process in curved tunnels is a circular process of damage change, and the model accurately captures these structural aspects of the damage evolution process. In addition, structural damage can be identified using displacement detection because the displacement of a curved tunnel is directly related to its compression damage. Finally, the seismic response of the curved tunnel-surrounding rock system is studied parametrically to determine the extent to which different parameters affect the seismic response. These parameters, including elastic modulus, friction angle, cohesion, and Poisson’s ratio, are characteristics of rock-medium materials. We then created multi-factor evaluation formulas to direct the surrounding rock to reinforce.

Thermal thin shell approximation towards finite element quench simulation

Superconducting electromagnets commonly exhibit thin layers with high aspect ratio such as insulation layers or turn-to-turn contacts. A finite element (FE) analysis of these devices can lead to unfavorable meshes in these thin layers, either because of a high number of degrees of freedom or mesh elements of poor quality which decrease the accuracy of the simulation results. To mitigate these issues when conducting a thermal FE analysis solving the heat equation, this work proposes to collapse thin volume layers into surfaces by using a thermal thin shell approximation (TSA). The proposed method uses one-dimensional Lagrange elements across the thickness of the thin layer and can handle a variety of interface conditions, multi-layered structures, heat sources, nonlinear material behavior or coupling to physics other than heat transfer. The efficiency of the proposed approximation is highlighted by comparison with a reference model with a conventionally meshed insulation for a model problem exhibiting a brick wall structure where a stationary heat equation is solved. The formulation is then verified against reference models with meshed insulation solving a transient heat equation for an insulated high-temperature superconductor pancake coil exhibiting a local defect which causes a thermal runaway. The benefit of using the model with the TSA is studied by analyzing pancake coils with different ratios of the insulation layer to the coated conductor thickness. It is shown that the smaller the ratio, the shorter the solution time and the lower the number of unknowns of the thin shell model when compared to the conventionally meshed insulation in order to reach the same numerical accuracy. The method is implemented in an open-source FE framework and a reference implementation for a simple model problem is shared alongside this paper.

Deep learning-based wave digital modeling of rate-dependent hysteretic nonlinearities for virtual analog applications

Electromagnetic components greatly contribute to the peculiar timbre of analog audio gear. Indeed, distortion effects due to the nonlinear behavior of magnetic materials are known to play an important role in enriching the harmonic content of an audio signal. However, despite the abundant research that has been devoted to the characterization of nonlinearities in the context of virtual analog modeling over the years, the discrete-time simulation of circuits exhibiting rate-dependent hysteretic phenomena remains an open challenge. In this article, we present a novel data-driven approach for the wave digital modeling of rate-dependent hysteresis using recurrent neural networks (RNNs). Thanks to the modularity of wave digital filters, we are able to locally characterize the wave scattering relations of a hysteretic reluctance by encapsulating an RNN-based model into a single one-port wave digital block. Hence, we successfully apply the proposed methodology to the emulation of the output stage of a vacuum-tube guitar amplifier featuring a nonlinear transformer.

Dynamic acoustoelastic testing (DAET) with a thermal strain pump for characterization of closed fatigue cracks

Dynamic acoustoelastic testing (DAET) is a nonlinear acoustic technique used to characterize the nonlinear elastic behavior of materials. To enable the in-situ implementation of DAET, we propose a modification to the conventional DAET setup by replacing the mechanical strain pump with a thermal strain pump. This study presents the feasibility of the proposed thermal-pump DAET setup for in-situ detection of closed fatigue cracks in an aluminum test specimen. Our setup employs a hot air blower to induce a small (∼4 °C) thermal gradient near the surface of the specimen. The surface temperature evolution is captured by an infrared camera allowing thermal strain evaluation on the surface. A pair of high frequency angle-beam Rayleigh surface wave transducers are used to probe the thermal strain-induced changes in near-surface elastic properties. The slope of the relative change in Rayleigh wave speed with the applied thermal strain is taken as a measure of nonlinearity (γ) evaluated at several locations across the specimen along the intact and cracked regions. Our results show that γ measures higher near the crack and decreases as the probe moves towards the crack tip, demonstrating the potential of thermal-pump DAET for in-situ evaluation of closed fatigue cracks.

Modeling the damage-induced softening behavior of brain white matter using a coupled hyperelasticty-damage model

White matter in the brain is structurally anisotropic consisting of large bundle of aligned axonal fibers. Hyperelastic, transversely isotropic constitutive models are typically used in the modeling and simulation of such tissues. However, most studies constrain the material models to describe the mechanical behavior of white matter in the limit of small deformation, without considering the experimentally observed damage initiation and damage-induced material softening in large strain regime. In this study, we extend a previously developed transversely isotropic hyperelasticity model for white matter by coupling it with damage equations within the framework of thermodynamics and using continuum damage mechanics method. Two homogeneous deformation cases are used to demonstrate the proposed model's capability in capturing the damage-induced softening behaviors of white matter under uniaxial loading and simple shear, along with the investigation of fiber orientation effect on such behaviors and material stiffness. As a demonstration case of inhomogeneous deformation, the proposed model is also implemented into finite element codes to reproduce the experimental data (nonlinear material behavior and damage initiation) from an indentation configuration of porcine white matter. Good agreement between numerical results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of white matter considering damage at large strain.

Multi-criteria decision-making analysis and numerical simulation of the low-velocity impact response of inter-ply S2-glass/aramid woven fabric hybrid laminates

Hybrid composites have gained a lot of attention due to their superior mechanical performance and energy absorption capacity compared to single-fibre counterparts, but studies on the hybridization of aramid and S2-glass fabrics are still scarce. This paper presents a multi-criteria decision-making analysis and numerical simulation applied to the study of the performance of asymmetric inter-ply hybrids of plain-weave aramid and satin-weave S2-glass fabrics/epoxy laminates subjected to low-velocity impact. Different aramid/glass fibre ratios, impact sides and impact energies (19 J, 37 J and 72 J) were investigated. A multi-criteria decision-making analysis was performed to identify the best laminate design based on the technique for order of preference by similarity to the ideal solution which considered areal density, deformation and absorbed energy as design criteria. A novel numerical FE model based on continuum damage mechanics was developed considering non-linear material constitutive behaviour and different interlaminar and intralaminar failure modes. The material model was implemented in Abaqus/Explicit solver using a user-defined material model, and the non-linear material behaviour in the normal direction is considered by defining instantaneous stiffnesses using third-degree polynomials. The results identified single fibre laminates as the worst designs and hybrid laminates with aramid on the impact side as the best design. Besides, for similar fibre ratios, the total delamination area was larger for the impact on aramid layers.

Модели бетона и арматуры при взрывных нагрузках

In this article, the mathematical models of structural materials describing their dynamic properties are considered for calculating building structures for the action of dynamic loads. Physical and mechanical properties are described related to reinforcing steel and concrete under the action of explosive loads, as well as the influence of the loading rate and other factors on the deformation diagram of steel and concrete. The analysis is carried out concerning the reasons for the increase in the resistance of concrete and reinforcement under rapidly increasing loads. The relevance of the topic is determined by its compliance with the main goals and objectives of the Russian state policy in the field of improving the safety of buildings and structures when exposed to explosive loads. The article describes the methods of mathematical description of the structural materials behavior under the action of explosive loads. A simplified method for modeling the dynamic properties of reinforcing steel and concrete by multiplying the calculated resistance by the dynamic strengthening factor, as well as a more time-consuming method based on the equations of gas-hydrodynamics and implemented in the LS-DYNA software package, are considered. The authors used the method of taking into account the dynamic strengthening of reinforcing steel and concrete based on the nonlinear behavior of materials using diagrams with a piecewise linear description. Dynamic hardening was considered using hardening factors. The purpose of the study is to compare the results of numerical calculation according to the method proposed by the authors with the data obtained during the experimental program Blind Blast Test. The calculation was carried out by the finite element method using the Lira 10.12 calculation complex. The DYNAMICS+ system was used to simulate the load from the action of an external explosion. The experimental model is a reinforced concrete slab reinforced with ASTM Grade 60#3 rods. The results of numerical calculation showed high convergence with the experimental program. The use of the method of accounting for the dynamic hardening of reinforcing steel and concrete, based on the nonlinear behavior of materials using diagrams with a piecewise linear description, is the most optimal model that allows to get a fairly accurate solution and at the same time is acceptable from the point of view of labor intensity. This article is of interest to design engineers engaged in the calculation of structures for explosive loads.

Deformation analysis of friction welded hybrid structures

AbstractThe purpose of this paper is to present a framework for modelling the deformation behaviour of friction welded hybrid structures. The constitutive model is developed for large deformations and nonlinear material behaviour. Moreover, to demonstrate the model's applicabilities, it was implemented into a finite element system (ABAQUS). Subsequently, the simulation results were critically evaluated using experimental data.

LS-DYNA Machine Learning–Based Multiscale Method for Nonlinear Modeling of Short Fiber–Reinforced Composites

Short-fiber-reinforced composites (SFRC) are high-performance engineering materials for lightweight structural applications in the automotive and electronics industries. Typically, SFRC structures are manufactured by injection molding, which induces heterogeneous microstructures, and the resulting nonlinear anisotropic behaviors are challenging to predict by conventional micromechanical analyses. In this work, we present a machine learning-based multiscale method by integrating injection molding-induced microstructures, material homogenization, and Deep Material Network (DMN) in the finite element simulation software LS-DYNA for structural analysis of SFRC. DMN is a physics-embedded machine learning model that learns the microscale material morphologies hidden in representative volume elements of composites through offline training. By coupling DMN with finite elements, we have developed a highly accurate and efficient data-driven approach, which predicts nonlinear behaviors of composite materials and structures at a computational speed orders-of-magnitude faster than the high-fidelity direct numerical simulation. To model industrial-scale SFRC products, transfer learning is utilized to generate a unified DMN database, which effectively captures the effects of injection molding-induced fiber orientations and volume fractions on the overall composite properties. Numerical examples are presented to demonstrate the promising performance of this LS-DYNA machine learning-based multiscale method for SFRC modeling.

Macro-scale modeling of finite strain viscoplasticity in irradiated F/M steels: a continuum thermodynamic framework

The European reduced activation ferritic/martensitic steel Eurofer97 in irradiated states displays significant nonlinear material behavior involving irradiation hardening, loss of strain hardening, and uniform elongation, as well as irradiation-induced embrittlement. Nonlinear behavior of irradiated steel modeled on the continuum scale will help to estimate the maximum operating range of the irradiated components beyond the onset of localized plastic flow. In this work, a thermodynamic framework for modeling irradiation-influenced deformation is established based on irradiation defect density and a thermodynamically consistent finite strain formulation of an existing viscoplastic model using the Dual Variables concept is presented. The model is implemented in ABAQUS allowing the simulation of tensile tests conducted on irradiated and unirradiated materials which shows the model’s ability to capture the post-yield and post-necking behavior observed in experiments up to ductile failure.

Development and experimental validation of finite element models for a prestressed lead extrusion damper

The emerging trend in earthquake-resistant structural design is to dissipate some part of the seismic input energy through energy-dissipating devices (EDDs). A prominent candidate to serve this purpose is the lead extrusion damper (LED), which dissipates seismic energy by the extrusion of lead through the displacement of a bulged shaft. The LEDs should be designed as they meet the demands of the host structural system. Hence, predicting the force–displacement relation and energy dissipation characteristics of the LED is essential. To serve this purpose, comprehensive three-dimensional finite element models (FEMs) were developed in this study to simulate the cyclic behavior of a prestressed LED. The methodology consisted of performing coupon tests, the development of FEMs, and experimental verification. Coupon tests were performed for lead and steel to simulate the nonlinear material behaviors better. The models were validated against the experimental results of the LED and a steel beam-to-column connection. In general, the adapted model satisfactorily captured the experimental results. The maximum differences in the maximum force and dissipated energy predictions were about 7.5% for the generated FEMs. In addition, the mean relative difference in predicting damper forces for eight LEDs selected from the literature was about 6%. The low relative differences between the models and experiments demonstrated that the adapted FEM could reliably estimate the cyclic response of the LEDs. It can be stated that the adapted three-dimensional finite element modeling strategy can be utilized robustly for design purposes.