Nonlinear Deformation Research Articles

Fatigue Strength Analysis of Rail Fastening Baseplate

Superstructural elements of a railway track experience dynamic loads varying over time. As a consequence, this is accompanied by the initiation and accumulation of fatigue damages. Defects in intermediate rail fastening are quite difficult to identify using flaw detection methods, and some can be destructed. In particular, rail fastening baseplates often fail due to insufficient fatigue strength.Purpose: To investigate the fatigue strength of rail fastening baseplate.Methodology: Development of the mathematical model of deformation based on the finite element method (FEM). Strength analysis of the baseplate using the model of a variable-thickness slab resting on a nonlinear elastic foundation. The latter is modeled by a set of rods with nonlinear deformation and parameters determined by compression tests of the baseplate. A mathematical model developed in COSMOS software for the FE analysis of the stress-strain state of the baseplate at a time-varying load from rolling equipment and assembly forces from attaching the baseplate to the sleeper and rail.Research findings: The cyclic loading parameters are obtained at dangerous points of the baseplate and its durability is analyzed at different loads with respect to unevenness of track settlement and failure of bolt connections of rail fasteners. The influence of these factors on actual loads on the rail fastener is determined. It is found that the service life of the baseplate mainly depends on the dynamic load.

New Methodology for Assessing Seismic Ground Vulnerability Based on Microtremor and Taiwan Seismic Intensity Scale

ABSTRACT The Taiwan Ground Deformation Index (TGDI) is proposed to quantify site vulnerability using a non-linear soil deformation model, PGA parameters from the Taiwan seismic intensity scale, and microtremor analysis. Site vulnerability is graded into four levels: low (TGDI < 2.4), moderate (2.4 ≤ TGDI < 4.2), high (4.2 ≤ TGDI < 7.4), and very high (TGDI ≥ 7.4), based on susceptibility to seismic damage. Validating TGDI with 13 disaster events in Tainan during the 2016 Meinong earthquake showed 12 cases of moderate-to-high vulnerability. Since weak ground and strong amplification properties favor TGDI increases, this index serves as an early warning parameter for disasters.

Study on the Stress Distribution Characteristics of Rock in the Bottomhole and the Influence Laws of Various Parameters Under the Impact of a Liquid Nitrogen Jet

This study presents research on the stress distribution characteristics of rock in the bottomhole and the influence laws of various parameters under the impact of liquid nitrogen jet. A multi-field coupled numerical model considering transient flow field, conjugate heat transfer, and nonlinear solid deformation was established to investigate the damage-induced fracturing mechanism of rock under liquid nitrogen jet. The study compares the impact effects of liquid nitrogen jet and water jet on rock and analyzes the variations in the stress field under different parameters. Due to its extremely low temperature, the liquid nitrogen jet creates a strong thermal stress gradient in a short time, significantly increasing the maximum principal stress and Mises stress in the rock compared to a water jet. Solid parameters, particularly the confining pressure and elastic modulus of the rock, have a more significant impact on stress distribution, while fluid parameters such as outlet pressure and fluid temperature have a smaller and more volatile effect. An increase in confining pressure inhibits tensile failure in the rock, while a higher elastic modulus enhances both tensile and shear failure. The initial rock temperature significantly affects the stress distribution, with optimal tensile failure observed at intermediate temperatures. The liquid nitrogen jet achieves a higher maximum velocity and overflow velocity than the water jet, contributing to more effective rock fracturing. The results provide a theoretical basis for the optimization of liquid nitrogen jet drilling parameters, which can help improve drilling efficiency.

Kirigami-Inspired Three-Dimensional Metamaterials with Programmable Isotropic and Orthotropic Thermal Expansion.

Mechanical metamaterials with specifically designed cells can provide unusual thermal expansion properties for diverse applications. Limited by very few available cell topologies and complicated non-linear structural deformation, most existing thermal expansion metamaterials can only achieve orthogonally isotropic negative/zero/positive thermal expansion (NTE/ZTE/PTE) within a mild range, especially the 3D ones. Here, based on one-degree-of-freedom kirigami polyhedrons proposed with a kinematic design strategy, a family of 3D isotropic and orthotropic metamaterials capable of programmable NTE, PTE, and even ZTE over ultra-wide range is developed. Incorporating bi-material strips as creases for isotropic polyhedrons, NTE and PTE metamaterials with coefficients of thermal expansion (CTEs) ranging from -2354.3 to 3006.7ppm/°C are designed and programmed by the theoretical model. Meanwhile, isotropic ZTE metamaterials are constructed by either homogeneous tessellation of ZTE cells or hybrid tessellation of NTE and PTE cells. Furthermore, by allowing distinct geometric parameters in the three orthogonal directions of the kirigami polyhedrons while preserving the kinematic motion, orthotropic metamaterials, in which each of the three directions can be assigned with an independently programmed NTE, ZTE, or PTE, are also achieved. This study paves a novel pathway for the development of thermal expansion metamaterials with potential applications for space optical systems, MEMS, and so on.

A new semi-analytical approach for nonlinear dynamic responses of functionally graded porous graphene platelet-reinforced circular plates and spherical shells

This paper presents the semi-analytical approach for nonlinear dynamic responses of porous graphene platelet-reinforced circular plates (CiPs) and spherical shells (SpSs) resting on the Pasternak foundation in thermal environment. The graphene platelets (GPLs) are distributed in the functionally graded (FG) distribution patterns and uniform distribution pattern through the CiP and SpS thickness direction. The governing equations of the GPL-reinforced structures subjected to time-dependent external pressure respected to the harmonic and linear functions of time are established based on the geometrically nonlinear higher-order shear deformation theory. A simple and effective semi-analytical solution for the considered problem is established using the Euler-Lagrange equations, and the damping viscosity of the foundation can be counted using the Rayleigh dispassion function. The Runge-Kutta method is employed to determine the dynamic responses of the GPL-reinforced structures, while the fundamental frequencies of free and linear vibration, and frequency-amplitude curves are obtained in explicit form. The numerical results obtained reveal that the GPL and porous distributions, geometrical and material properties can significantly affect the frequency-amplitude curves, and dynamic responses of harmonically loaded and linearly loaded structures, specially, the dynamic buckling phenomenon is clearly observable with the SpSs but not with the CiPs.

A Gram-Charlier Analysis of Scattering to Describe Nonideal Polymer Conformations.

Theories of interpreting polymer physics and rheology at the molecular level from experiments, including small-angle scattering, typically rely on the assumption that polymer chains possess a Gaussian configuration distribution. This assumption frequently fails to describe features of real polymer molecules both at equilibrium (when polymers have nonlinear topology or heterogeneous chemistry) and out of equilibrium (when they are subjected to nonlinear deformations). To better describe non-Gaussian polymer conformation distributions, we propose a moments analysis based on the Gram-Charlier expansion as a natural framework for describing structure and scattering from non-Gaussian polymers. The expansion describes the conformation distribution in terms of cumulants (equivalent to moments of the distribution) of the underlying segment density distribution function, providing low-dimensional descriptors that can be inferred directly from measured scattering in a way that is agnostic to a polymer's topology, chemistry, or state of deformation. We use this framework to show that cumulants can be used to "fingerprint" non-Gaussian conformation distributions of polymers either at equilibrium (applied to sequence-defined heteropolymers) or out of equilibrium (applied to polymers experiencing nonlinear deformation due to flow). We anticipate that this new analysis method will provide a general framework for examining nonideal polymer configurations and the properties that arise from them.

Investigation of the nonlinear dynamics of thin sandwich shells composed of functionally graded materials with double curvature in thermal environments

Double curvature structures play a crucial role as load-bearing components across various engineering fields. Functionally graded materials, blending metals and ceramics, boast superior material characteristics, fueling their expanding applications. This study pioneers the non-linear dynamic analysis of sandwich shells that feature functional gradient compositions in thermal settings. We assume that both the upper and lower shells of these double curvature structures are crafted from functionally graded materials, with a ceramic core. This variation in material exhibits a ceramic layer on the inner surface and a metallic layer on the outer surface, showing properties that vary along the shell thickness in a power-law gradient. Non-linear dynamic equations are derived using third-order shear theory, encompassing geometric non-linearity and shear deformation. Employing the Galerkin method, we discretize the equations of motion into a non-linear dynamic system with five degrees of freedom, and subsequently give an analytical expression for the nonlinear naturalfrequency by means of multiscale analysis. Our discussion examines the impacts of structural parameters, porosity volume fraction, volume fraction index, and temperature differences on the non-linear/linear frequency ratio of doubly curved sandwich shells. Calculations reveal a sharp rise followed by a rapid decline in the non-linear/linear frequency ratio with increasing structural aspect ratio b/a. Conversely, it decreases with increasing thickness-to-length and radius-to-length ratios, with temperature differences initially reducing and later increasing it. These findings offer practical insights for designing functional gradient double curvature sandwich shells.

Kineto-static analysis of a hybrid manipulator consisting of rigid and flexible limbs with locking function for planar shape morphing

The incorporation of lockable passive backbones into active compliant morphing systems efficiently results in lightweight, high-load, and large deformation systems. However, there exist challenges in kineto-static analysis due to the interaction between rigid reconfigurable kinematic constraints and the nonlinear deformation of actuated flexible limbs. This paper addresses these issues by developing a kineto-static method to analyze the motion in a novel planar 3-DOF shape-morphing manipulator. The manipulator features two actuated flexible limbs with a lockable variable geometry truss (LVGT). In this study, two isostatic topologies are selected for reconfigurable motion control under external tip loads. A multi-step sequential control strategy is proposed to maneuver the manipulator's platform for desired poses. Then, a constrained-trajectory-based kinematic model is proposed for an inverse kinematic solution considering motion planning. Subsequently, a kineto-static model is introduced, considering constraints from rigid and flexible limbs, aiming to distribute distributing redundant actuation forces. Finally, nonlinear finite element analysis (FEA) and experiments are carried out to validate the effectiveness of the proposed method.

Nonlinear Dynamics Research of Ground Undulatory Fin Robot with Flexible Deformation and Frictional Contact.

The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

Study on Bionic Design and Tissue Manipulation of Breast Interventional Robot.

Minimally invasive interventional surgery is commonly used for diagnosing and treating breast cancer, but the high fluidity and deformability of breast tissue reduce intervention accuracy. This study proposes a bionic breast interventional robot that mimics the scorpion's predation process, actively manipulating tissue deformation to control target displacement and enhance accuracy. The robot's structure is designed using a modular method, and its kinematics and workspace are analyzed and solved. To address the nonlinear breast tissue deformation problem, a hierarchical tissue method is proposed to simplify the three-dimensional problem into a two-dimensional one. A two-dimensional tissue deformation solver is established based on the minimum energy method for quick resolution. The problem is treated as quasi-static, deriving the displacement relationship between external manipulation points and internal tissue targets. The method of active manipulation of tissue deformation is simulated using MATLAB (2019-b) software to verify the feasibility of the method. Results show maximum errors of 1.7 mm for prostheses and 2.5 mm for in vitro tissues in the X and Y directions. This method improves intervention accuracy in breast surgery and offers a new solution for breast cancer diagnosis and treatment.

A theoretical framework for multi-physics modeling of poro-visco-hyperelasticity-induced time-dependent fracture of blood clots

Fracture resistance of blood clots plays a crucial role in physiological hemostasis and pathological thromboembolism. Although recent experimental and computational studies uncovered the poro-viscoelastic property of blood clots and its connection to the time-dependent deformation behavior, the effect of these physical processes on clot fracture and the underlying fracture mechanisms are not well understood. This work aims to formulate a thermodynamically consistent, multi-physics theoretical framework for describing the time-dependent deformation and fracture of blood clots. This theory concurrently couples fluid transport through porous fibrin networks, non-linear visco-hyperelastic deformation of the solid skeleton, solid-fluid interactions, mechanical degradation of tissues, gradient enhancement of energy, and protein unfolding of fibrin molecules. The constitutive relations of tissue constituents and the governing equation of fluid transport are derived within the framework of porous media theory by extending non-linear continuum thermodynamics at large strains. A physics-based, compressible network model is developed for the fibrin network of blood clots to describe its mechanical response. The kinetic equations of the internal variables, introduced for describing the non-linear viscoelastic deformation, non-local damage driving force and protein unfolding, are formulated according to the thermodynamics principles by incorporating a non-equilibrium energy of fibrin networks, a gradient-enhanced energy, and a stretch-induced energy of fibrin molecules, respectively, into the total free energy density function. An energy-based damage model is developed to predict the damage and fracture of blood clots, and an evolving regularization parameter is proposed to limit the damage zone bandwidth. The proposed model is implemented into finite element code by writing subroutines and is experimentally validated using single-edge cracked clot specimens with different constituents. The fracture of blood clots subject to different loading conditions is simulated, and the mechanisms of clot fracture are systematically analyzed. Computational results show that this model can accurately capture the experimentally measured deformation and fracture. The viscoelasticity and fluid transport play essential roles in the fracture of blood clots under physiological loading.

The impact of effective fractured rock mass properties on development of flow channeling in enhanced geothermal systems

Controlling the distribution of working fluid in an Enhanced Geothermal System (EGS) is crucial to prevent early thermal breakthrough and sustain the initial heat drainage area. Over time, working fluid flow may localize to a small area if fracture permeability increases non-uniformly, and efforts are not made to control the flow distribution. This scenario can potentially lead to mechanical reopening of hydraulic fractures, flow channeling, and thermal short-circuiting. However, current models neglect the nonlinear and inelastic deformation of fractured rock masses on EGS coupled thermo-mechanical response. The objective of this work is to estimate and predict the likelihood of thermal short-circuiting by flow-channeling in an EGS reservoir composed of rock and compliant natural fractures. We utilize three dimensional numerical solutions with reservoir properties based on effective medium theory of fractured rocks to achieve this objective. The results show that presence of natural fractures considerably changes the EGS response to thermal destressing, compared to linear poroelastic models. Flow channeling and short-circuiting, resulting in early thermal breakthrough, are more likely to occur in sparsely fractured reservoirs with stiff and strong natural fractures. Conversely, short-circuiting is unlikely in densely fractured reservoirs where thermal strains are absorbed by natural fracture opening and shear sliding rather than by rock matrix contraction. Estimation of natural fracture density is crucial in long-term forecasting and prediction of EGS power output. Accurate fracture characterization could decisively impact the fate of a project.

Harnessing centrifugal and Euler forces for tunable buckling of a rotating elastica

We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent ‘fictitious’ (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an angular acceleration around a fixed axis, we demonstrate that dynamically coupled centrifugal and Euler forces can produce tunable structural deformations. Specifically, by systematically varying the acceleration ramp in a highly automated experimental setup, we show how the buckling onset of a cantilevered beam can be precisely tuned and its deformation direction selected. In a second configuration, we demonstrate that Euler forces can cause a pre-arched beam to snap-through, on demand, between its two stable states. We also formulate a theoretical model rooted in Euler’s elastica that rationalizes the problem and provides predictions in excellent quantitative agreement with the experimental data. Our findings demonstrate an innovative approach to the programmable actuation of slender rotating structures, where complex loading fields can be produced by controlling a single input parameter, the angular position of a rotating system. The ability to predict and control the buckling behaviors under such non-trivial loading conditions opens avenues for designing devices based on rotational fictitious forces.

Nano-thick surface-modified layer governs bending deformation of micrographite

This study aimed to investigate the impact of surface-modified layer (SML) on the bending deformation of van der Waals (vdW)-stacked materials. Bending tests were conducted on micrographite (highly oriented pyrolytic graphite, HOPG) cantilevers with controlled SML thickness using various ion beam irradiation conditions. Irradiation of the HOPG surface with ion beams at accelerating voltages of 30, 5 and 0.1 kV resulted in the formation of SMLs with thicknesses of approximately 10, 5 and less than 3 nm, respectively. Microcantilever-beam specimens with SML thicknesses of less than 3 nm and approximately 5 nm exhibited shear deformation with localized interlayer slip. In contrast, specimens with a thickness of approximately 10 nm showed no interlayer slip, with bending deformation dominating. This transition was attributed to the increase in SML thickness. The nominal shear modulus increased by a factor of approximately 1.58 and 2.23 for specimens with SML thicknesses of approximately 5 and 10 nm, respectively, compared with those with thicknesses of less than 3 nm. The resistance to subsequent nonlinear deformation also increased with thicker SML. These results indicate that the presence of SMLs of only a few nanometers to 10 nm suppressed interlayer slip and significantly enhanced the deformation resistance of micro-HOPGs.

Prediction of permanent deformation of subgrade soils under F-T cycles using SABO-optimized CNN-BiLSTM network

Accurately predicting the permanent deformation of subgrade soils under combined loading and seasonal freeze-thaw (F-T) effects is crucial for optimizing pavement design and maintenance planning in cold regions. However, existing empirical models have limitations in capturing the non-linear deformation behavior influenced by interacting factors. This study developed a deep learning framework, specifically a convolutional neural network-bidirectional long short-term memory (CNN-BiLSTM), for time-series prediction of subgrade strains. Laboratory tests established a comprehensive database to examine soil response across various conditions. Regression analysis revealed the constraints of traditional models. The optimized hybrid architecture directly learned patterns from experimental data, outperforming regression by 29−71 % based on error metrics. Sensitivity analysis confirmed that the model identified primary governing inputs consistent with theory. Hyperparameter tuning with the Subtraction-Average-Based Optimizer further enhanced performance. This data-driven methodology demonstrated the potential of advanced machine learning in simulating complex subsurface deformation behavior under compounding factors in seasonal frozen environments.

Systematization of the application of polymer composite materials in the design of bridge structures

Background. This study systematizes the principles of using polymer composite materials in bridge structure design, outlining the fundamental principles for calculating load-bearing structures of bridge spans featuring these materials. Aim. The goal is to enhance the strength and durability of bridge spans during construction and maintenance, while optimizing costs through the use of polymer composite materials. Materials and Methods. The research employs a modern approach to bridge structure design, utilizing mathematical statistics for experimental data analysis and numerical methods for calculating bridge structures using nonlinear deformation models of anisotropic materials. Results. Developed principles for designing bridge spans with polymer composite elements include methods for strengthening and reinforcing concrete bridge structures. These methods account for operational factors such as long-term constant and temporary loads, low and elevated temperatures, as well as methods for designing all-composite spans pedestrian and road bridges Conclusion. The principles of designing bridge spans with elements made of polymer composite materials have been introduced into the practice of transport construction in the Russian Federation. The technical and economic efficiency of using polymer composite materials in bridge structures of transport infrastructure has been confirmed.

A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models

The storage of renewable hydrogen in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. This raises concerns about the mechanical stability of salt caverns under such operational conditions. The use of appropriate constitutive models for salt mechanics is an important step in investigating this issue, therefore many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and parameter set represents the given rock, based on stress–strain data sets, remains an unsolved challenge. In this paper, for the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation data sets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is then achieved by framing the calibration process as an optimization problem, for which the global Particle Swarm Optimization algorithm is employed. To allow for dynamic data integration, a multi-step calibration strategy is developed for a situation where experiments are included one at a time, as they become available. Additionally, due to the existing mild heterogeneity in the experimental rock samples, our optimization strategy is made flexible to allow for this slight heterogeneity. The devised optimization strategy, based on the multi-physics comprehensive constitutive modeling framework, results in a single set of representative material properties of all the deformation data sets. As a rigorous mathematical analysis for the presented method and the lack of relevant experimental data sets, we consider a wide range of synthetic experimental data sets, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust. Moreover, the results become increasingly more accurate as more data sets become available.

Magnetomechanical Behaviors of Hard-Magnetic Elastomer Membranes Placed in Uniform Magnetic Field.

This paper aims to develop a theoretical model for a viscoelastic hard-magnetic elastomer membrane (HMEM) actuated by pressure and uniform magnetic field. The HMEM is initially a flat, circular film with a fixed boundary. The HMEM undergoes nonlinear large deformations in the transverse direction. The viscoelastic behaviors are characterized by using a rheological model composed of a spring in parallel with a Maxwell unit. The governing equations for magneto-visco-hyperelastic membrane under the axisymmetric large deformation are constructed. The Zeeman energy, which is related to the magnetization of the HMEM and the magnetic flux density, is employed. The governing equations are solved by the shooting method and the improved Euler method. Several numerical examples are implemented by varying the magnitude of the pre-stretch, pressure, and applied magnetic field. Under different magnetic fields, field variables such as latitudinal stress exhibit distinct curves in the radial direction. It is observed that these varying curves intersect at a point. The position of the intersection point is independent of the applied magnetic field and only controlled by pressure and pre-stretch. On the left side of the intersection point, the field variables increase as magnetic field strength increases. However, on the other side, this trend is reversed. During viscoelastic evolution, one can find that the magnetic field can be used to modulate the instability behaviors of the HMEM. These findings may provide valuable insights into the design of the hard-magnetic elastomer membrane structures and actuators.

A new shape reconstruction method for monitoring the large deformations of offshore wind turbine towers

Offshore wind turbine (OWT) upsizing has become an inevitable trend. Compared with small OWTs, large OWT rotors exert greater horizontal loads and bending moments on the tower. These factors make a large OWT tower more prone to geometric nonlinear deformations, which can affect the normal operation of a wind turbine and even lead to damage to the wind turbine tower. Therefore, monitoring the deformation of large OWT towers is necessary. Shape sensing is a technique that uses surface strains to reconstruct deformed shapes. Currently, there is a lack of effective methods for geometric nonlinearity deformation shape sensing. In addition, the tower of OWT is a variable cross-section structure. The influence of varying cross-sections further increases the difficulty of developing a large deformation reconstruction algorithm. To solve this problem, this paper proposes a new method called rotation angle approximation (RAA). This method establishes a least-squares error functional using analytic curvature and section curvature. The rotation angles of the tower axis are obtained via this function. The deformed shape is then predicted via the boundary conditions and the rotation angles along the tower axis. Numerical simulations demonstrated this method can accurately predict the large deformations of a tower under different load conditions.

Failure analyses for plate monotonic/cyclic and elbow out-of-plane cyclic loading tests using the Gurson–Tvergaard–Needleman model

In this study, an analytical approach is proposed to simulate the failure behavior of a thinned-wall pipe elbow subjected to internal pressure and out-of-plane cyclic bending loads. This approach incorporates the Gurson–Tvergaard–Needleman model, whose parameters were determined by the plate monotonic tensile test and finite element analyses. The applicability of this analytical approach for low-cycle fatigue failure was confirmed through experiments and simulations. The analytical results captured the failure behavior of the pipe elbow during the out-of-plane cyclic bending test. This finding suggests that the analytical approach can be used for nonlinear deformation evaluation and multiaxial low-cycle fatigue assessment of piping systems.