Large Deformation Behavior Research Articles

A new adaptive peridynamic framework for modeling large deformation and fracture behavior of hyperelastic materials

Accurate prediction of deformation and fracture behaviors of hyperelastic materials is crucial in engineering applications and industry. The paper presents a new three-dimensional computational model to simulate large deformations and fractures in hyperelastic materials using the peridynamic method. The main innovation of the proposed three-dimensional hyperelastic peridynamic (3D-HPD) model lies in its incorporation of the stress–strain relationship of hyperelastic materials into the peridynamic framework. Therefore, the peridynamic parameters, such as bond stiffness and strength, are dynamically updated based on the instantaneous value of Young's modulus derived from the stress–strain relation of hyperelastic materials. The 3D-HPD model highlights the following novelties: 1) The 3D-HPD model directly employs the stress–strain relation for each peridynamic bond. Thus, the large deformations and fractures in hyperelastic materials are accurately captured in three dimensions by integrating the responses in all peridynamic bonds; 2) Unlike other models that may require specific hyperelastic formulations, the 3D-HPD model offers a more straightforward application, enhancing usability and reducing complexity; 3) The 3D-HPD model is capable of simulating the response of hyperelastic materials under various loading conditions, including tensile, torsional, and lateral loadings. We confirm the validity of the 3D-HPD model by evaluating it against experimental measurements and observations. For the first time, the model examines hyperelastic materials' fracture and deformation behaviors under combined loading conditions. The new findings of the mechanical performance of hyperelastic materials under multi-axial stresses provide new insights to enhance their design and usage.

Modeling via peridynamics for damage and failure of hyperelastic composites

Modeling damage and failure behaviors of hyperelastic composites under large deformations is pivotal for advancing the design of cutting-edge elastomers used in biomedical engineering and soft robotics. However, existing methods struggle with capturing the non-linearities and singularities in the displacement field under such conditions. To address these difficulties, we propose a novel bond-based peridynamics (PD) framework with multiple advancements. First, we develop a PD bond strain model grounded in the nonlinear Piola-Kirchhoff stress-stretch relationship, precisely capturing hyperelasticity and ensuring full compliance with thermodynamic laws and kinematics in large deformation scenarios. Second, our framework employs a particle discretization technique that not only sidesteps the mesh distortion issues commonly encountered in grid-based methods subjected to large deformation but also significantly lowers the computational complexity due to the ease of numerical implementation of random inclusion distributions. Third, we propose, for the first time, a refined 3D hyperelastic model within the PD framework that enables a more comprehensive and accurate prediction of material responses to external loads, surpassing the limitations of conventional 2D simulations. Validation against experimental data demonstrates that our model accurately captures key physical phenomena in hyperelastic composites, such as spontaneous crack initiation and propagation, interface debonding, crack coalescence, and the formation of non-smooth crack surfaces. Crucially, this framework is versatile and adaptable to a wide range of engineered composite systems with different inclusions and matrices, making it a powerful tool for predicting and analyzing large deformation behaviors in various advanced applications.

Sensor-Enhanced Thick Laminated Composite Beams: Manufacturing, Testing, and Numerical Analysis.

This study investigates the manufacturing, testing, and analysis of ultra-thick laminated polymer matrix composite (PMC) beams with the aim of developing high-performance PMC leaf springs for automotive applications. An innovative aspect of this study is the integration of Fiber Bragg Grating (FBG) sensors and thermocouples (TCs) to monitor residual strain and exothermic reactions in composite structures during curing and post-curing manufacturing cycles. Additionally, the Calibration Coefficients (CCs) are calculated using Strain Gauge measurement results under static three-point bending tests. A major part of the study focuses on developing a properly correlated Finite Element (FE) model with large deflection (LD) effects using geometrical nonlinear analysis (GNA) to understand the deformation behavior of ultra thick composite beam (ComBeam) samples, advancing the understanding of large deformation behavior and filling critical research gaps in composite materials. This model will help assess the internal strain distribution, which is verified by correlating data from FBG sensors, Strain Gauges (SGs), and FE analysis. In addition, this research focuses on the application of FBG sensors in structural health monitoring (SHM) in fatigue tests under three-point bending with the support of load-deflection sensors: a new approach for composites at this scale. This study revealed that the fatigue performance of ComBeam samples drastically decreased with increasing displacement ranges, even at the same maximum level, underscoring the potential of FBG sensors to enhance SHM capabilities linked to smart maintenance.

Quasi - static and impact performance study of a three-dimensional negative Poisson's ratio structure with adjustable mechanical properties

The mechanical properties of most materials with a negative Poisson's ratio (NPR) cannot be flexibly adjusted after being designed to meet complex engineering requirements. To ensure the changes of those materials’ relative density are minimal when overcoming these limitations, this study proposes a novel method that adjusts the mechanical performance by grooving the structure and adjusting the angle of the diagonal support rod. Unlike traditional methods that involve adding 'ribs' to the structure for adjustability, this approach focuses on the design of the structure itself. To analyze the large deformation behavior of unit-cell lattices, we established a theoretical model based on plastic deformation theory and derive the relationship between the number of unit-cell lattices and the relative density of multi-cell lattices. Experimental samples were fabricated by using selective laser melting (SLM). Meanwhile, the accuracy of the finite element results was verified by quasi-static compression experiments and impact experiments. Then the validated finite element model is then utilized to discuss the influence of structural parameters on mechanical properties. In addition, we also studied the influence of medium and low-speed impact loads on the deformation characteristics, mechanical properties, and energy absorption (EA) of the structures. The results demonstrate the reliability of the design method, showcasing its potential to achieve on-demand adjustability of stress, stiffness, and strength to meet complex engineering requirements. Notably, the adjustment range of peak load is from 24.55 MPa at the lower limit α = 60° to 48.29 MPa at the upper limit α = 90°, with an adjustment range of 23.74 MPa. The adjustment range of the average platform stress is from 10.8 MPa at the lower limit of α = 60° to 24.34 MPa at the upper limit of α = 80°, and the adjustment range reaches 13.54 MPa. This study provides new insights on intelligent protection engineering and the adjustable mechanical properties of metamaterials.

A 3D coupled Material Point Method study on hydro-mechanical collapse mechanism of the tunnel face in shields with a partially filled chamber

The deterioration of groundwater seepage on the tunnel face stability is a principal risk for tunnelling through watery ground, and a thorough understanding of soil–water coupled large deformation behaviors is essential for effective disaster prevention. This study employs a three-dimensional (3D) coupled Material Point Method (MPM) to analyze the hydro-dynamical collapse characteristics of the tunnel face, particularly focusing on tunnel shields with partially filled chambers where the air pressure is utilized to support the upper portion of the tunnel face. Initially, the validity of the 3D coupled MPM is verified through comparing numerical and analytical results of a 1D consolidation problem, covering from small to large deformation analyses. Subsequently, the evolutionary characteristics of the tunnel face collapse and ground response are investigated through a series of large-scale simulations. Special attention is given to differentiate failure responses between saturated and dry sand, emphasizing the weakening effect of seepage flow on tunnel faces. Furthermore, the influence of different combinations of construction conditions and soil properties on the collapse process is also investigated. Numerical results validate the efficacy of the 3D coupled MPM in addressing hydro-dynamical tunnel face collapse issues, with goals of providing insights into associated disaster prevention and post-failure behavior prediction.

Analysis of sensitive clay landslide mechanism and impact pipeline bearing characteristics considering spatial variability

Landslides caused by the progressive failure of sensitive clay slopes may cause substantial economic losses and environmental pollution to pipelines. This study utilizes the Karhunen-Loève (K-L) expansion method, the coupled Eulerian-Lagrangian (CEL) method, and the Monte Carlo method to model the large deformation behaviour of slopes with spatial variability. The proposed RCEL-MC framework for joint analysis of extensive deformation-probability statistics of landslide impact on pipelines confirms that the spatial variability clay slope instability failure mechanism, considering the soil softening effect under earthquake action, aligns more closely with real-world scenarios. Furthermore, based on the statistical failure probability of pipelines impacted by landslides, a sensitive clay slope pipeline safety design method is suggested. The research highlights that the random field parameters significantly influence the load-bearing characteristics of pipelines affected by spatially variable slope progressive failure landslides. The uncertainty surrounding the maximum impact force on pipelines notably increases with the rise of the horizontal correlation length and variability coefficient. When accounting for spatial variability, the maximum impact force on landslide pipelines surpasses the deterministic model analysis results by 28-69 %. It is emphasized that the deterministic model analysis, which neglects the spatial variability of soil and the soil softening effect, may seriously underestimate landslide risk. Based on the criteria for pipeline buckling failure and yield failure, it is advised that the safe design parameters for pipelines in practical projects should fall within the intersection of the secure regions defined by the two failure criteria.

Large-deformation elastic hardening of a structured graphene kirigami nano-spring with re-entrant honeycombs

The programmable nature of graphene kirigami enables it highly applicable in the development of stretchable nanodevices. In this study, we employed molecular dynamics simulations to investigate the large deformation behavior of a structured graphene kirigami nano-spring (GKNS) with re-entrant honeycombs. During a uniaxial test, the elastic deformation can be categorized into two stages based on the applied load level. Stage I exhibits a maximal strain (εYstart) exceeding 50 % under low loading conditions, while stage II demonstrates a strain (εYend) surpassing 70 % at a high hardening rate. Both εYstart and εYend are greater than those observed in GKNS with transversal periodic boundary conditions. Furthermore, increasing the length or decreasing the width of bars within GKNS with cells of identical shape leads to an increase in both εYstart and εYend values. Ambient temperature has minimal impact on εYstart and εYend however, higher temperatures result in lower hardening rates due to weakened carbon–carbon bonds within GKNS structures. Additionally, variations in cell/void arrangement within structured GKNS affect both εYstart and εYend values, whereas widening the GKNS structure leads to reduced hardening rates. The findings presented herein provide valuable insights for designing nanodevices that necessitate significant deformations.

Thermo‐hydro‐mechanical coupled material point method for modeling freezing and thawing of porous media

AbstractClimate warming accelerates permafrost thawing, causing warming‐driven disasters like ground collapse and retrogressive thaw slump (RTS). These phenomena, involving intricate multiphysics interactions, phase transitions, nonlinear mechanical responses, and fluid‐like deformations, and pose increasing risks to geo‐infrastructures in cold regions. This study develops a thermo‐hydro‐mechanical (THM) coupled single‐point three‐phase material point method (MPM) to simulate the time‐dependent phase transition and large deformation behavior arising from the thawing or freezing of ice/water in porous media. The mathematical framework is established based on the multiphase mixture theory in which the ice phase is treated as a solid constituent playing the role of skeleton together with soil grains. The additional strength due to ice cementation is characterized via an ice saturation‐dependent Mohr–Coulomb model. The coupled formulations are solved using a fractional‐step‐based semi‐implicit integration algorithm, which can offer both satisfactory numerical stability and computational efficiency when dealing with nearly incompressible fluids and extremely low permeability conditions in frozen porous media. Two hydro‐thermal coupling cases, that is, frozen inclusion thaw and Talik closure/opening, are first benchmarked to show the method can correctly simulate both conduction‐ and convection‐dominated thermal regimes in frozen porous systems. The fully THM responses are further validated by simulating a 1D thaw consolidation and a 2D rock freezing example. Good agreements with experimental results are achieved, and the impact of hydro‐thermal variations on the mechanical responses, including thaw settlement and frost heave, are successfully captured. Finally, the predictive capability of the multiphysics MPM framework in simulating thawing‐triggered large deformation and failure is demonstrated by modeling an RTS and the settlement of a strip footing on thawing ground.

A hyperelastic strain energy function for isotropic rubberlike materials

A three parameter novel hyperelastic strain energy function is introduced in this paper for soft and rubber-like materials. The function integrates a non-separable exponential component with a single term Ogden-type polynomial-like function, resulting in an exponential-polynomial based strain energy function. This helps in capturing both small and large deformation (stretch) behaviours of hyperelastic materials. The structure of the model is simple and validated against several experimental datasets including rubbers, hydrogel, and soft tissues. The model is reported to capture key material behaviors, including strain stiffening and various deformation paths. Through comparative studies with well-known models like the Ogden (six parameters) and Yeoh (three parameters), the model’s effectiveness is established. Furthermore, the model successfully addresses pressure-inflation instability in thin spherical balloons. It’s applicability extends to biological materials, as evidenced by its effectiveness in characterizing porcine brain tissue and a monkey’s bladder.

An effective nonlinear dynamic formulation to analyze grasping capability of soft pneumatic robotic gripper

ABSTRACT Soft pneumatic robotic grippers have found extensive applications across various engineering domains, which prompts active research due to their splendid compliance, high flexibility, and safe human-robot interaction over conventional stiff counterparts. Previously simplified rod-based models principally focused on clarifying overall large deformation and bending postures of soft grippers from static or quasi-static perspectives, whereas it is challenging to elaborate grasping characteristics of soft grippers without considering contact interaction and nonlinear large deformation behaviors. To address this, based on absolute nodal coordinate formulation (ANCF), comprehensively allowing for structural complexity, geometric, material and boundary nonlinearities, and incorporating Coulomb’ friction law with a multiple-point contact method, we put forward an effective nonlinear dynamic modeling approach for exploring grasping capability of soft gripper. Moreover, we solved the established dynamic equations using Generalized-α scheme, and conducted thorough numerical simulation analysis on a three-jaw soft pneumatic gripper (SPG) in terms of grasping configurations, displacements and contact forces. The proposed dynamic approach can accurately both describe complicated deformed configurations along with stress distribution and provide a feasible solution to simulate grasping targets, whose effectiveness and precision were analyzed theoretically and verified experimentally, which may shed new light on devising and optimizing other multifunctional SPGs.

A non-linear stress–strain relationship for soil and rock

While many employ a hyperbolic stress–strain relationship for soils, it is known that such a relationship is accurate over the small-strain range as encountered in earthquake and soil dynamics problems. For large strains, a relationship with different input parameters is needed, as is required for finite-element analyses of large-deformation behaviour. These separate characterisations do not carry over into the other application. Here, a proposed power relationship is presented that was developed to characterise the triaxial test stress–strain behaviour of cohesionless material from lubricated or ‘frictionless’ cap and base tests (144 tests) covering a range in the natural variation in particle size, particle shape and surface roughness, over low to high confining pressure. This relationship covers the strain range from 10−6 to soil failure. To date, it has been successfully used in laterally loaded pile response characterisation (the strain wedge model) and shallow-foundation load–settlement–bearing capacity response. Most recently, it has been extended to assess the behaviour of rock-like material (caliche). The relationship and its comparison with the hyperbolic relationship for large strain and the shear modulus reduction curve for seismic behaviour are presented.

Density dependent constitutive model for Bi-2212 powder compression deformation

Bi-2212 HTS materials are fabricated into multi-filamentary wires via powder-in-tube (PIT) method followed by proper heat treatment to obtain superconductivity, but how to predict the large compression deformation behaviors of the Bi-2212 powder is critical to design the processing of the Bi-2212 HTS wire. Drucker Prager/Cap (DPC) model was the most commonly used model for powders including Bi-2212 with soil-like mechanical behavior to consider its shear failure as well as hydrostatic compression. However, the parameters for DPC Cap evolve with densities change and the original model is inadequate to precisely describe the densification process of Bi-2212 powder with large strain. In this study, the modified DPC model with density dependent parameters was introduced for Bi-2212 powder compressions by measuring the failure strength and hydrostatic compressive behavior under different density states. The DPC yield surface was plotted with an evolution trend of non-linear outward expansion with density increased. FEM model of uniaxial compression based on the as-introduced model was built with subroutine VUSDFLD applied. The distribution of Mises stress and relative density were analyzed. The axial stress-density curve for FEM and experimental results were normalized and quantitively evaluated by Mean Square Error (MSE). The introduced model shows good convergence and could match the experimental results well with normalized MSE of 0.000207 and Root Mean Square Error (RMSE) of 0.0144, indicating the mean error percentage of 1.44%. The model introduced in this article provides supports toward large strain deformation simulation of Bi-2212 powder.

Feasibility analysis of deep steep riser based on co-rotational coordinate method

DSR (Deep steep riser) is a new riser structure that reduces the ultra-high-tension load caused by the riser self-weight. In this paper, the mechanical behavior of DSR under different buoyancy module configurations and different ocean currents is studied. The finite element model of DSR is established based on co-rotational coordinate method. The model is solved by arc length method. The accuracy of the numerical method is verified by Abaqus software. Then, the effects of buoyancy module length and buoyancy factor on DSR are analyzed. Finally, the influence of different current incidence angles and velocities on DSR is evaluated. The results show that the DSR model based on the co-rotational coordinate method can effectively simulate the nonlinear behavior of large deformation of DSR. The method is simple, flexible and computationally efficient. This method can quickly improve the efficiency of numerical calculation in static analysis of deepwater riser. And DSR is feasible under certain conditions.

Theoretical Analysis on Large Deformation Behaviors of Zigzag- spring Based on the Nonlinear Deformation Theory

Theoretical Analysis on Large Deformation Behaviors of Zigzag- spring Based on the Nonlinear Deformation Theory

A neural network peridynamic method for modeling rubber-like materials

Peridynamic (PD) is a powerful tool for simulating the large deformation and failure process of many types of materials. However, its use in modeling rubber-like materials is limited due to the complex constitutive nature of the material, and low efficiency and numerical oscillation caused by PD. To address this issue, a neural network (NN) non-ordinary state-based peridynamics (NOSB PD) method is developed to model the large deformation and failure behavior of rubber-like materials. This method is free of the zero-energy modes, and can significantly improve the computational efficiency. Unlike the traditional NOSB PD method that formulates the force density vector based on the deformation gradient, this method uses a deep NN to map the bond related quantities to the force density vector. The accuracy and efficiency of the proposed method are demonstrated through a series of numerical examples. Additionally, this method can be applied to various hyperelastic materials for which analytical constitutive models exist.

Dynamical analysis of a 40 m span precast posttensioned concrete girder during lifting operations

AbstractCranes are employed to lift precast concrete girders during their construction. Presently, there is no recommendation for operational velocities during girder assemblage, particularly for long elements; simultaneously, several accidents have been reported during the transitory phase of girder motion. Since this mechanical problem has been examined in technical literature using a static approach, the present research study aims to investigate the dynamical behavior of a long, prestressed concrete girder by determining critical operational velocities according to crane movements. Prestressing cables' eccentricity and lifting loop position deviation were accounted for in 3D finite element simulations of a 40 m span precast prestressed concrete girder. Transient nonlinear analyses to obtain stresses and deflections were performed, so as to account for the large deformation behavior of the motion. A frequency domain approach was employed to analyze the time history results using the girder's natural frequencies obtained by modal analysis. The finite element model was developed to simulate upward, downward, and lateral girder movements. The most significant displacements and stresses were observed in the highest girder acceleration peaks, amplified by eccentricities. Safety against cracking and subsequent failure during vertical and lateral movements was ensured for crane operating accelerations of 0.02 g (v = 20 cm/s) and 0.007 g (v = 7 cm/s), respectively. Compared with the usual static analysis, for the critical case investigated, the inertial effect intensified the tensile stresses by 27 times, increased the compressive stresses by 11%, and increased the girder deflection by 3 times.

Slope Stability Analysis Based on the Explicit Smoothed Particle Finite Element Method

A landslide is a common natural disaster that causes environmental damage, casualties and economic losses, which seriously affects the sustainable development of society. In geomechanics, it is one of the largest deformation problems. Herein, the GPU-accelerated explicit smoothed particle finite element method (eSPFEM) for large deformation analysis in geomechanics was developed on the CUDA platform based on high-performance computing using a self-designed eSPFEM program code. The eSPFEM combines the strain smoothing nodal integration techniques found in the particle finite element method (PFEM) framework, which allows for the use of low-order triangular elements without volume locking and avoids frequent information transfer and mapping errors between Gaussian points and particles in PFEM. A numerical simulation of slope instability using the eSPFEM and based on a strength reduction technique was conducted using various examples, including a cohesive homogeneous slope, a non-cohesive homogeneous slope, a non-homogeneous slope and a slope with a thin soft band. The calculation results show that the eSPFEM can be applied to slope stability analysis under different working conditions, simulating the entire process of slope instability initiation, sliding and reaccumulation, and obtaining reliable FOS values. A numerical simulation was conducted to analyse a landslide that occurred in the Zhangjiazhuang tunnel on the Lanzhou–Xinjiang high-speed railway line on 18 January 2016. A natural unsaturated soil slope, a soil slope with a high moisture content and a soil slope with a high moisture content subjected to an earthquake were analysed. The findings of this study are in good agreement with the actual slope failure conditions. The primary triggers identified for the landslide were heavy rainfall and earthquakes. The verification results indicate that the eSPFEM can effectively simulate an actual landslide case, showcasing high accuracy and applicability in simulating the large deformation behaviour of landslides.

An implicit stabilized material point method for modelling coupled hydromechanical problems in two-phase geomaterials

In this study, an implicit stabilized material point method (MPM) based on the updated Lagrangian formulation has been developed to model soil-like two-phase coupled problems under undrained/drained conditions, in which the displacement of solid phase and pore water pressure are used as primary variables. Instead of using the Cauchy stress in the equilibrium equation, we employ the first Piola-Kirchhoff stress (PK1 stress) and rigorously implement the objective Jaumann stress to account for large deformations. To address numerical oscillation in (nearly) incompressible coupled problems, the finite difference method (FDM) is used to calculate the pore water pressure stored at the center of the background grid cells and the B-bar method proposed by Hughes (1980) is also incorporated into the proposed MPM to avoid the volumetric locking problem. Through simulations of various classic hydromechanical coupled problems and comparing them with analytical solutions or other numerical simulations, the reliability and robustness of the proposed implicit MPM are extensively validated. The method demonstrates its capability to accurately capture the large deformation behavior and hydromechanical interactions in geomaterials, resulting in stable and reliable simulation outcomes.

Performance of circular steel tubes infilled with rubberised concrete under cyclic loads

This paper presents a detailed numerical investigation into the inelastic cyclic performance of circular steel tubes filled with rubberised concrete materials. The study considers rubberised concrete infills with relatively high values of up to 60% volumetric rubber replacement of conventional mineral aggregates, which is lacking in existing investigations. Co-existing axial loads of up to 30% of the nominal composite cross-section capacity are also considered. Modified continuum finite element modelling procedures are proposed and employed to account for the high cumulative deformations and damage development of rubberised concrete under cyclic loading. In particular, the influence of crack opening and closure in concrete under cyclic loading is examined and discussed. In addition to full numerical cyclic analyses, idealised monotonic simulations are also proposed and verified to enable computationally efficient representation of the envelope response. Validations of the full-cyclic and envelope-monotonic models are carried out against available experimental cyclic results, indicating the suitability of the models for representing the inelastic response and degradation of confined concrete with high rubber content. Parametric assessments are then undertaken to examine the influence of key material and geometric parameters, including the rubber content, material strength and cross-section properties, on the inelastic large deformation behaviour. The results of the parametric studies are used to quantify the main response parameters, with focus on the member stiffness, moment-axial strength interaction, local buckling criteria and other ductility measures. Based on the findings, modifications are proposed to current design procedures in order to provide a reliable prediction of the inelastic cyclic response characteristics of rubberised concrete filled circular steel tubes. Apart from providing experimentally validated numerical approaches that can be used in future studies, the proposed analytical and design procedures are suitable for implementation in practical assessment and design applications.

Seepage effect on progressive failure of shield tunnel face in granular soils by coupled continuum-discrete method

Seepage induced by the difference of hydraulic head between the ground and the shield’s chamber will adversely affect the stability of tunnel face when tunnels are excavated through water-rich stratum. In order to investigate the influence of seepage on the stability of tunnel face, a 3D continuum-discrete method is proposed to simulate the failure of tunnel face. The large deformation behavior of soil is determined by the discrete element method and the fluid flow in soil phase is described by the Darcy fluid model and continuity equation. A series of simulations are carried out to obtain the failure mechanism and critical support pressure of tunnel face. Then the results under dry, undrained and seepage conditions are analyzed and the seepage effect on the stability of tunnel face with different water depth is investigated. Besides, a comparison between the simulation results and solutions in previous researches is conducted. Additionally, the micro-mechanical analysis under dry and seepage conditions are presented. The results show that the coupled method can well evaluate the stability of tunnel face considering seepage effect and provider useful guidance for practical tunnel designs.