Nonlinear Mechanical Behavior Research Articles

Inverse design of periodic microstructures with targeted nonlinear mechanical behaviour

This paper introduces an inverse design framework for the precise tailoring of desired nonlinear mechanical responses in periodic microstructures, with particular focus on prescribed nonlinear stress–strain relationships. The topology optimization hinges on minimizing the error between the target and realized properties of the microstructures. A deformation-driven homogenization framework is setup. The periodic constraints needed for the microscale equilibrium equation are imposed through strongly enforced periodic boundary conditions and the removal of the translational nullspace, avoiding the need for Lagrange multipliers, greatly simplifying the implementation. Automatic differentiation is leveraged to efficiently calculate the necessary sensitivities for the gradient-based optimization. To further aid the design of discrete designs a intermediate density penalty constraint is proposed. Numerical examples underscore the efficacy of our methodology, showcasing microstructures that demonstrate targeted softening and stiffening as well as distinctive directional behaviour.

Performance analysis of acoustically actuated magnetoelectric antennas via equivalent circuit method

Acoustically actuated magnetoelectric (ME) antennas based on resonant magnetoelectric coupling within ferromagnetic/piezoelectric ME laminated composites have recently been considered as a promising solution for antenna miniaturization. However, its radiation performance has been theoretically overestimated, since the negative effects on performances due to the magnetization saturation and the nonlinear mechanical behavior that occur from high-field driving have not been paid enough attention. This work presents a unique equivalent-circuit-based numerical method to analyze the near-field resonance radiation performances of ME antennas driven by high electric fields. In this method, we establish an equivalent circuit of the converse magnetoelectric effect for a ME laminated composite to describe the operating principle of acoustically actuated electromagnetic radiation. The equivalent parameters related to resonance characteristics are determined by fitting the circuit model to the data from frequency response measurements of the near-field magnetic flux density. The validity of the model is verified by comparing the theoretical predictions with the experimental results, in the view of the volume fraction dependence of the mechanical resonance-related radiation characteristics of the fabricated ME composites. Based on the proposed model, the influence of driving voltage amplitude on near-field radiation performances is further analyzed by experimental fitting to the model, and the potential limiting factors of ME antennas are discussed according to the driving-amplitude dependence of parameters obtained from the fit. This work provides an effective and engineering-friendly approach to predict the evolution of ME antenna performances, leading a way to improve the performance limit for resonant magnetoelectric coupling.

Nonlinear dynamic analysis of opto-electro-thermo-elastic perovskite plates

AbstractPhotostrictive materials have attracted tremendous interest as the new generation of smart materials that can achieve a direct conversion from optical energy to mechanical energy. Understanding their nonlinear mechanical properties under light illumination is of paramount significance for their realistic optomechanical applications. This article proposes a novel opto-electro-thermo-elastic constitutive model that can consider the effects of photostriction, photothermal temperature, and electrostriction for metal halide perovskite crystals and investigates the nonlinear static and dynamic responses of the perovskite plates. The nonlinear governing equations are established based on the first-order shear deformation theory and von Kármán nonlinearity and are numerically solved by the differential quadrature method. A detailed parametric investigation is performed to analyze the effects of light and electricity on the nonlinear mechanical behaviors of perovskite plates. It is concluded that light illumination leads to the presence of optical stress and thermal stress in the perovskite plates, giving rise to increased static and dynamic deformations and stresses, as well as reduced postbuckling and free vibration characteristics. The research findings pave the way for the optomechanical applications of perovskite-based smart materials and structures.

Numerical modelling of the structural response of a novel hybrid densified wood filled-aluminium tube dowel for structural timber connections

This paper deals with the finite element modelling of the structural response of timber connections assembled using a novel hybrid dowel, made of densified wood filled aluminium tube, for the first time. Predictive and comprehensive finite element models, using the LS-Dyna Software, are developed to thoroughly investigate the non-linear 3D mechanical behaviour and optimize the design of the aluminium-to-timber connections. The materials parameters of the models are, first, identified based on experimental data from three-point bending tests. Then the models are validated by comparison to experimental data from slotted-in aluminium plate timber connections assembled either using steel dowel or hybrid densified wood filled aluminium tube dowel. The results are compared in terms of load-slip curves as well as in terms of failure modes. In addition, a parametrical study is conducted using the validated finite element model to investigate the influence of some material and geometrical parameters. The results showed that the hybrid densified wood filled aluminium tube dowels can be a potential substitute for conventional steel dowels. The study highlights the efficiency of the proposed finite element model in terms of quality of results and efficiency of use upstream the design process of such structures.

Beam theory of cellular microfilaments based on coarse-grained molecular force field

Microfilaments are the main component of the cell cytoskeleton and have a crucial influence on the morphology of living cells. The microfilaments provide mechanical support against applied loads and overcome competing forces that arise from various mechanisms, such as the elasticity of the cell membrane, binding reactions, and surface tension. However, modeling the mechanical properties of microfilaments is an open problem. In the present paper, we proposed a new continuum deformation energy density of microfilaments using the coarse-grained molecular force field and the local differential geometry of curves. In the new theory, the deformation energy density is a function of the microfilament’s strain and the curvature. This theory also unfolded the connections between the mechanical parameters and the coarse-grained force field. We found that the stretching stiffness and the bending stiffness are independent of the section of microfilaments. Microfilaments have a nonlinear stretching-bending term different from the classical beam theory. This means the classical beam theory cannot be directly applied to microfilaments with large deformations. Our theory provides the basis that the modified classical beam theory applies to the nonlinear mechanical behavior of cellular microfilaments.

Development and biomechanical testing of full-scale human brain simulant

In 21st century, traumatic Brain Injuries (TBI) due to blast exposure or head impacts in contact sports, accidents are one of most critical research area. But the area of TBI is poorly investigated due to the limitation of brain tissue availability and related ethical/biosafety issues. In general, the brain tissue is difficult to acquire after the autopsy and test in laboratorial settings. In this work, a full-size human brain simulant was developed using a biofidelic multi-part polymeric material poured into a negative mould which was designed and 3D printed. Based on the number of mild to moderate traumatic brain injury cases reported in the literature, three TBI prominent locations were chosen. The prefrontal cortex of frontal lobe, top portion of parietal lobe and temporal lobe of right hemisphere of the brain were the locations where the experiments were conducted under compressive loading conditions. The load versus displacement data was recorded and converted to the stress-strain plots to analyse the result responses and its implications. Two constitutive hyperelastic models (Yeoh model and Neo-Hookean) were selected for curve fitting and characterizing the non-linear mechanical behavior of the full-scale brain model. Such precisely developed and characterized full-scale brain simulant has not been reported in the literature to date and would be beneficial for simulating a wide range of traumatic brain injuries and surgical training.

Influence of temperature and nonlinear damping on mechanical properties of single-walled carbon nanotubes

Existing experiments have demonstrated that the nonlinear terms caused by damping impact the dynamical behaviors of single-walled carbon nanotubes (SWCNTs) significantly. Although, it is still an open question to precisely describe the vibrations of SWCNTs with the combined effects, such as the scale effect, the thermal effect, and the nonlinear damping. In the present research, we proposed a new nonlocal nonlinear Euler-Bernoulli theory to model an SWCNT's mechanical properties with the combined effect of three factors. A (10,10)SWCNT was brought to demonstrate the influence of the three factors on the elastic buckling and the forced bending vibrations. The results indicate for slender SWCNTs that the combined effects have some more remarkable impacts on nonlinear mechanical behaviors than individual factors, and dramatic deviation may emerge in the vibrations once nonlinear damping terms are absent.

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results. The improved model assumes that total strain is a combination of plastic, elastic, and crack strains. The constitutive relationship between the crack strain and the stress was further derived. The evolutions of mechanical parameters, i.e. strength parameters, dilation angle, unloading elastic modulus, and deformation parameters of crack, with the plastic strain and confining pressure were studied. With the increase in plastic strain, the cohesion, friction angle, dilation angle, and crack Poisson's ratio initially increase and subsequently decrease, and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease. The increasing confining pressure enhances the strength and unloading elastic modulus, and decreases the dilation angle and Poisson's ratio of the crack. The theoretical triaxial compressive stress-strain curves were compared with the experimental results, and they present a good agreement with each other. The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Seismic performance of confined prestressed hollow core wall panels part II: Numerical simulation and analysis

In Part I of this research, confined prestressed hollow core wall structures were proposed and experimental tests of 19 specimens were conducted to study its mechanical behaviors. In this part, a detailed finite element model was developed in ANSYS to provide a tool for further investigating the seismic behaviors of confined prestressed hollow core wall structures. Contact elements were applied to simulate the interaction between material interfaces. Techniques in ANSYS including coupling of degrees of freedom (CP) of overlapped nodes and deactivation of concrete elements (EKILL) were adopted, along with restart analysis (REST) to simulate nonlinear mechanical behaviors of the structural system. The developed modeling method was verified by the experimental test results and was shown to accurately predict the global and local behaviors such as failure modes and load bearing capacities of precast hollow core walls. Parametric analysis on shear span ratio, axial load ratio, rigidity of floor systems as well as strength of vertical wall-wall joints was conducted, and relevant design recommendations were provided for prestressed hollow core wall structures. Results show that for a ductile prestressed hollow core wall structure, the axial load ratio is recommended to be smaller than 0.06 and the story number less than 5. Influence of rigidity of floor systems requires further study with dynamic tests, but low-strength vertical wall-wall joint is highly recommended for this system. Two analytical mechanisms that are shear-flexural mechanism and truss mechanism were proposed for calculation of load bearing capacities. These two mechanisms provide good predictions for an upper bound and a lower bound for load bearing capacities of prestressed hollow core walls, respectively. From Part I and II of this research, the mechanical behaviors of prestressed hollow core wall structures are verified experimentally, numerically, and theoretically, and it is concluded that they can be used as a potential choice for low-rise buildings in rural areas.

Curvature Analysis in a Bi-layered Non-linear Elastic Bar under Uniform Heating

The present theoretical paper is concerned with analysis of the curvature in a bi-layered bar of rectangular cross-section. The bar is subjected to uniform heating. The two layers of the bar have different thickness and material properties. Besides, the layers exhibit non-linear elastic mechanical behaviour that is treated by applying a power-law stress-strain constitutive relationship. The bi-layered bar curvature is studied analytically. For this purpose, the mechanical response of the bar to uniform heating is investigated. The strains in the two layers due to heating are analyzed. An equation is compiled by using the fact that the prolongations of the bar layers are equal. Two equations are worked out by considering the equilibrium of the layers. The analysis of the curvature presented in this paper is checked-up by comparing with a known solution for the curvature in a bi-layered linear-elastic bar under uniform heating. The uniform heating induced curvature in a bi-layered bar whose layers are continuously inhomogeneous in longitudinal direction is also studied.

Nonlinear mechanical behavior and stress amplification effect correction of thin plate welded structure considering initial deformation

With the continuous development of light weight of ships, thin plate welded structures are widely used in superstructure of large hull structures and high-speed boats. However, the thin-plate welded structure has a special nonlinear mechanical behavior because of its small stiffness, more complicated welding deformation. The nonlinear mechanical behavior of thin plate welded structure is mainly caused by large slenderness ratio and complex initial buckling deformation, which can be characterized and quantified by defining global deformation angle αG and local deformation angle αL. Because of the welding angle deformation and welding dislocation, there is obvious stress amplification effect at the welding corner, but the traditional stress amplification correction formula is only suitable for thick plate welding structure. Aiming at the nonlinear mechanical behavior and secondary bending moment effect of thin plate welded structure, an analytical model of thin plate welded structure with initial deformation is established by combining theoretical derivation and numerical method. The results show that the additional bending moment effect caused by local welding deformation angle cannot be ignored. Finally, combined with a series of fatigue tests, the additional bending moment caused by bending deformation and angular deformation of typical welded joints is analyzed, and the notch stress field and fatigue strength correction of thin plate welded structures with initial defects are realized.

Regulatory provisions for determining parameters of nonlinear mechanical behavior in hardening soil models

Presently, nonlinear mechanical soil models are widely used in the geotechnical practice. They are implemented in geotechnical finite-element software PLAXIS, MIDAS GTS NX, Z-Soil, Optum, etc. Notwithstanding the fact that International regulatory documents mainly recommend nonlinear models for calculating foundations, they do not specify methods for defining their parameters because nonlinear models are actually commercial products of various software manufactures and cannot be normalized in any country. For this very reason, specialists of Gersevanov Research Institute of Bases and Underground Structures (department of JSC "Research center of Construction") developed Standard of Organization STO 36554501-067-2021. The Standard is based on the world experience in assessing nonlinear model parameters defined with using advanced laboratory equipment. The article describes the most significant provisions of this Standard. Thus, depending on the problem to be solved, four groups of models are introduced: I - a model includes volumetric isotropic hardening (Soft Soil); II - a model includes volumetric isotropic hardening and rheological properties of the soil (Soft Soil Creep); III - a model includes double isotropic hardening (Hardening Soil) and IV - a model includes double isotropic hardening and stiffness at small strain (Hardening soil with small strain). Requirements to the necessary and sufficient types and scope of tests, which define model parameters, are reported. Taking into account that only laboratory tests define model parameters, Standard provides requirements for specimens' quality evaluation performed basing on measurements of the volumetric strain under effective natural stress. Specimens of poor and very poor quality cannot be considered. It is shown that power-law coefficient m , which indicates the relationship between soil stiffness and stress-strain-state in the models of III and IV groups can be received from triaxial compression and oedometer tests and shall be prescribed depending on prevailing deformation (shear or compression). Stiffness parameters at small strains can be defined wit in-situ tests (seismoacoustic profiling) or with laboratory tests (resonant column test, seismoacoustic profiling of specimens in triaxial cell equipped with bender element and strain gauges on the local base). The developed Standard specifies requirements for laboratory definition of stiffness at small strains.

Hierarchical Mechanical Transduction of Precision-Engineered DNA Hydrogels with Sacrificial Bonds.

Engineering the response to external signals in mechanically switchable hydrogels is important to promote smart materials applications. However, comparably little attention has focused on embedded precision mechanisms for autonomous nonlinear response in mechanical profiles in hydrogels, and we lack understanding of how the behavior from the molecular scale transduces to the macroscale. Here, we design a nonlinear stress-strain response into hydrogels by engineering sacrificial DNA hairpin loops into model network hydrogels formed from star-shaped building blocks. We characterize the force-extension response of single DNA hairpins and are able to describe how the specific topology influences the nonlinear mechanical behavior at different length scales. For this purpose, we utilize force spectroscopy as well as microscopic and macroscopic deformation tests. This study contributes to a better understanding of designing nonlinear strain-adaptive features into hydrogel materials.

Nanocolloidal hydrogel mimics the structure and nonlinear mechanical properties of biological fibrous networks.

Fibrous networks formed by biological polymers such as collagen or fibrin exhibit nonlinear mechanical behavior. They undergo strong stiffening in response to weak shear and elongational strains, but soften under compressional strain, in striking difference with the response to the deformation of flexible-strand networks formed by molecules. The nonlinear properties of fibrous networks are attributed to the mechanical asymmetry of the constituent filaments, for which a stretching modulus is significantly larger than the bending modulus. Studies of the nonlinear mechanical behavior are generally performed on hydrogels formed by biological polymers, which offers limited control over network architecture. Here, we report an engineered covalently cross-linked nanofibrillar hydrogel derived from cellulose nanocrystals and gelatin. The variation in hydrogel composition provided a broad-range change in its shear modulus. The hydrogel exhibited both shear-stiffening and compression-induced softening, in agreement with the predictions of the affine model. The threshold nonlinear stress and strain were universal for the hydrogels with different compositions, which suggested that nonlinear mechanical properties are general for networks formed by rigid filaments. The experimental results were in agreement with an affine model describing deformation of the network formed by rigid filaments. Our results lend insight into the structural features that govern the nonlinear biomechanics of fibrous networks and provide a platform for future studies of the biological impact of nonlinear mechanical properties.

Melt electrowritten scaffold architectures to mimic tissue mechanics and guide neo-tissue orientation

All human tissues present with unique mechanical properties critical to their function. This is achieved in part through the specific architecture of the extracellular matrix (ECM) fibres within each tissue. An example of this is seen in the walls of the vasculature where each layer presents with a unique ECM orientation critical to its functions. Current adopted vascular grafts to bypass a stenosed/damaged vessel fail to recapitulate this unique mechanical behaviour, particularly in the case of small diameter vessels (<6 mm), leading to failure. Therefore, in this study, melt-electrowriting (MEW) was adopted to produce a range of fibrous scaffolds to mimic the extracellular matrix (ECM) architecture of the tunica media of the vasculature, in an attempt to match the mechanical and biological behaviour of the native porcine tissue. Initially, the range of collagen architectures within the native vessel was determined, and subsequently replicated using MEW (winding angles (WA) 45°, 26.5°, 18.4°, 11.3°). These scaffolds recapitulated the anisotropic, non-linear mechanical behaviour of native carotid blood vessels. Moreover, these grafts facilitated human mesenchymal stem cell (hMSC) infiltration, differentiation, and ECM deposition that was independent of WA. The bioinspired MEW fibre architecture promoted cell alignment and preferential neo-tissue orientation in a manner similar to that seen in native tissue, particularly for WA 18.4° and 11.3°, which is a mandatory requirement for long-term survival of the regenerated tissue post-scaffold degradation. Lastly, the WA 18.4° was translated to a tubular graft and was shown to mirror the mechanical behaviour of small diameter vessels within physiological strain. Taken together, this study demonstrates the capacity to use MEW to fabricate bioinspired scaffolds to mimic the tunica media of vessels and recapitulate vascular mechanics which could act as a framework for small diameter graft development to guide tissue regeneration and orientation.

Mathematical model for the nonlinear mechanical behavior of shape memory alloy springs

Mathematical model for the nonlinear mechanical behavior of shape memory alloy springs

High-temperature mechanical behavior and thermal shock resistance of eco-friendly periclase-Mg1.08Al1.84Ti0.08O4 spinel refractories used in RH degassing process

RH degassing device is a crucial high-temperature equipment used for the production of high-quality and environmentally friendly steel. The majority of steel metallurgical companies utilize magnesia-chrome (MgO-Cr2O3) refractories as linings in the RH degassing device. However, MgO-Cr2O3 refractories have the potential risk of generating hexavalent chromium ions during usage, which have a carcinogenic effect. We developed novel periclase-Mg1.08Al1.84Ti0.08O4 spinel (M-MATss) refractories, as a replacement for conventional MgO-Cr2O3 refractories. Investigations focused on the effect of MATss content on the mechanical strength at ambient and high temperatures and thermal shock resistance of the M-MATss refractories. The results showed that MATss significantly improved the modulus of rupture at 1500 ℃ (HMOR) and the refractoriness under load (RUL), which exhibited comparable or even superior performance compared to MgO-Cr2O3 refractories. M-MATss refractories with 15 wt% MATss content displayed the highest HMOR and RUL values of 4.6 MPa and 1655 ℃, respectively. This can be attributed to the reduction in silicate phase, which reduced the formation of liquid phase. Furthermore, the M-MATss refractories exhibited exceptional resistance to thermal shock due to the nonlinear mechanical behavior of microcracks caused by the thermal expansion mismatch between periclase and MATss, which contributed to enhanced resistance against crack propagation.

Experimentally validated numerical analyses on the seismic responses of extra-large LNG storage structures

Extra-large liquefied natural gas (LNG) storage tanks are comprised by a steel inner tank and an outer protective tank of prestressed reinforced concrete (PRC), both being very thin. These important lifeline infrastructures are prone to damage and even failure under earthquake during their service life. Convincing numerical simulation, verified by shake table tests, is a feasible tool to quantify the seismic responses and to mitigate the potential damage/failure of LNG storage structures. This work addresses systematically the three-dimensional finite element (FE) modeling, experimental validation and numerical simulations of such structures, with the soil–pile interaction of the foundation, the fluid–structure interaction of the inner tank and damage of the outer tank all properly accounted for. For the sake of computational efficiency with no loss of too much precision, the soil–pile interaction is described by the mass–damper–spring model, and the fluid–structure interaction by the mass–spring model with both the convective and impulsive components accounted for. Moreover, the nonlinear mechanical behavior of concrete is considered by the damaged-plasticity model regularized with the fracture energy. The concrete–steel interaction in PRC is practically dealt with by modifying the constitutive relations of concrete and steel rebars/tendons properly with the equilibrium and compatibility conditions accounted for. The FE modeling strategy is validated against the recently conducted benchmark shaking table test of a scaled extra-large LNG storage structure. The capability in capturing the overall dynamic responses, e.g., the hydrodynamic pressure and structural vibrations under seismic actions, etc., is sufficiently verified. Finally, the dynamic responses and structural reliability of an extra-large LNG storage tank under deterministic and stochastic seismic actions are numerically studied in details.

A modified HJC model for geological materials subjected to blasting loadings

In this paper, a modified HJC model is proposed to address the problem that the HJC model cannot simulate tensile damage cracks. The modified HJC model modifies the strength surface, strain rate effect and damage model of the original HJC model, respectively. The modified model is embedded in LS-DYNA software for single and multiple finite element validation. The effects of different parameters on the modified HJC model stress–strain curves are analyzed in the single finite element validation. In multiple finite element verification, uniaxial and triaxial compression experiments, Brazilian disc splitting experiments, SHPB dynamic compression experiments, and SHPB dynamic splitting experiments are performed. The results of single and multiple finite element numerical validation illustrate that the modified HJC model can well simulate the pre-peak and post-peak nonlinear mechanical behaviors of geological materials such as rocks and concrete. Compared with the HJC model, the damage pattern of the modified HJC model is closer to the real damage pattern. For the strain rate effect, the modified HJC model can reflect the real compressive strain rate effect and improve the sensitivity of tensile strength to strain rate. The results of the numerical simulation of the blasting funnel illustrate that: the modified HJC model can simulate explosive tensile cracking well and can explain the formation mechanism of blasting funnel due to the distinction between tensile and compressive meridian surfaces and the addition of tensile damage. The modified HJC model is more applicable to the numerical simulation of engineering blasting.

Theory-inspired machine learning for stress–strain curve prediction of short fiber-reinforced composites with unseen design space

Computational analysis of composites is well established; however, the process is time-consuming, owing to the disparate length scales and nonlinearities involved. Therefore, the use of machine learning models to predict the mechanical properties of short fiber-reinforced composites (SFRCs) is promising when large amounts of data are lacking. However, predicting data for an unseen design space remains challenging. The use of existing theoretical models for training is a viable solution to address this issue. This paper proposes a theory-guided machine learning (TGML) framework through training deep neural networks, based on the finite element analysis dataset that considers the cohesive effect of the interface, to predict the nonlinear mechanical responses of SFRCs. Our results demonstrate that incorporating the Halpin-Tsai theory with machine learning improves the predictive performance of the model in an unseen design space. Moreover, inspired by this theory, we propose a theory-inspired two-phase machine learning (TPML) approach to further improve predictive performance. Our results indicate that TGML and TPML capture more information from the data and thus enhance predictive performance. The proposed method can be adapted to the analyses of other composites with nonlinear mechanical behaviors.