Nonlinear Mechanical Behavior Research Articles

Damage Mechanism on Different Joint Types of Plain Concrete under Uniaxial Compression

Excavation of tunnels or chambers causes crack initiation, propagation and coalescence, resulting in the instability and destruction of underground projects. Understanding the damage mechanism of joint rock-like materials is important for maintaining the stability of concrete construction. Based on the Mohr–Coulomb criterion and Lemaitre strain equivalence hypothesis, the coupling-damage constitutive model of rock masses was improved for application to plain concrete. Parameters including the mesoscopic and macro-meso coupling damage variables, as well as the fractal dimension, were calculated to realize the non-linear mechanical behaviour during damage evolution. The rationality of the model was verified by comparing experimental and theoretical parameters. Results revealed that the coupled-damage constitutive model of rock masses has a good applicability to plain concrete. Furthermore, two main factors affected the damage deformation: the number of joints and the inclination angle. As the number of joints increased, the early damage accumulation increased and the inflection point of the damage rate occurred in advance. The damage deformation varied significantly when the inclination angle was changed. The cumulative damage curve of the plain-concrete specimens is shown as the evolution law of an S-type curve. Both peak strength and elastic modulus were positively correlated with the damage variable. Moreover, a smaller peak strength resulted in a larger fractal dimension and coupling-damage variable. KEYWORDS: Rock mass, Joint inclination angle, Mesoscopic, Macroscopic, Fractal dimension, Coupling-damage constitutive model.

Modeling for strain-softening rocks with lateral damage based on statistical physics.

Statistical physics is widely used to study the nonlinear mechanical behaviors of rock. For the limitations of existing statistical damage models and Weibull distribution, a new statistical damage with lateral damage is established. In addition, by introducing the maximum entropy distribution function and the strict constraint on damage variable, a expression of the damage variable matching the proposed model is obtained. Through comparing with the experimental results and the other two statistical damage models, the rationality of the maximum entropy statistical damage model is confirmed. The proposed model can better reflect the strain-softening behavior for rocks and respond to the residual strength, which provides a theoretical reference for practical engineering construction and design.

Modeling progressive failure and crack evolution in a randomly distributed fiber system via a coupled phase-field cohesive model

Despite the high microstructural heterogeneity of fiber-reinforced composites, few modeling framework provides a comprehensive and detailed understanding of the failure mechanisms of these materials. The aim of this work is to present a coupled phase-field cohesive-modeling framework that can precisely capture the progressive failure and damage behaviors of multiphasic microstructures and multifiber systems. Here, the phase-field method captures crack evolution in the matrix, and a coupled cohesive-zone model is introduced to characterize interfacial debonding. The novel model framework comprises the following novel aspects. (1) A newly developed scalar indicator that directly extracts inelastic strain from the total strain field and couples the cohesive traction-separation law with the phase-field model to determine the regularized interfacial displacement jump. (2) The periodic boundary conditions in the coupled phase-field cohesive framework are incorporated to characterize crack evolution in random fiber systems. (3) A complete set of failure modes, namely crack initiation, propagation, kinking, and coalescence are characterized in highly heterogeneous solids. Parametric studies of the novel framework yield numerical results that are highly consistent with experimental findings and reveal the effects of fiber distributions, fiber volume fractions, and boundary conditions on the nonlinear mechanical behaviors of fiber-reinforced composites. The results demonstrate the excellent potential of the novel numerical framework to evaluate the mechanical performances of composite materials in engineering applications.

Study on synthesis and mechanical properties of Eu3+‐π/covalent hybrid crosslinked silicone rubber

AbstractSilicone rubber is widely used in industry, dairy products, medical, defense support, and other fields due to its excellent comprehensive properties, which have become one of the most important research objects of high‐performance elastomer. Cationic‐π dynamic noncovalent bond has attracted more and more attention from material researchers due to its dynamic reversibility and design flexibility and has been applied to different material systems, giving new characteristics to traditional materials. Cationic‐π/covalently crosslinked silicone rubber was prepared by one‐step method with glycidol propyl terminated polydimethylsiloxane (DMS‐E21) as basic polymer, epoxy indole monomer (IN) as crosslinking structure modifier, Europium ion (Eu3+) as cation donor and triethylenetetramine (TETA) as a crosslinking agent. The influence of the reversibility of Eu3+‐π interaction on the static and dynamic mechanical behaviors of silicone rubber was studied. The results show that the elongation at break of cationic‐π/covalent hybrid crosslinked silicone rubber increases by more than 60% compared with pure covalent crosslinked silicone rubber when the breaking energy reaches the maximum, while the tensile strength increases by more than 100% and the introduction of Eu3+‐π dynamic bond can weaken the Mullins effect and the Payne effect on the high temperature of silicone rubber with obvious creep resistance. It shows an excellent mechanical strengthening effect with the characteristic of strengthening and toughening simultaneously and attractive nonlinear mechanical behavior on elastomers.

Experimental Behavior and Modelling of Steel Bolted T-Stub Connections

The paper comprehensively investigates the tension performance of Q355 steel T-stubs, whose nonlinear mechanical behavior is modelled by spring-slider elements. First, tension tests were conducted on seven specimens to explore the tension performance of Q355 steel T-stubs. T-stub connections were discussed in terms of their tension characteristics. Second, a numerical simulation was performed to analyze the stress distribution of T-stub components during deformation. Finally, on the basis of the tension characteristics of the T-stub connections, we constructed the constitutive model’s density function. The constitutive model’s force–displacement relationship was derived mathematically. A method for determining parameters was also developed. With the proposed model, the entire tensile behavior of T-stub connections can be described accurately while reducing the degrees of freedom at the contact interfaces, resulting in more efficient computing. Four parameters are defined physically in the model, and their values can be determined directly by macroscopic experiments.

A Strain Hardening and Softening Constitutive Model for Hard Brittle Rocks

To study the strain hardening and softening mechanism for hard brittle rocks, a strain hardening and softening constitutive model for hard brittle rocks is developed. First, the normalised hardening and softening factors are defined, which characterise the yield state of rock at the stages of pre-peak hardening and post-peak softening, respectively. Then, a unified strength parameter evolution model is established that can describe the nonlinear characteristics of cohesion and the internal friction angle under different confining pressures. Based on the Mohr–Coulomb criterion, a strain hardening and softening constitutive model is proposed. Finally, the proposed model was implemented in FLAC3D, and triaxial compression numerical tests of granite and diabase were conducted. The results show that the constitutive model can characterise the nonlinear mechanical behaviour of the pre-peak hardening stage and post-peak softening stage of hard brittle rock. The model was also able to satisfactorily capture the transition from brittle failure to plastic failure for hard brittle rock under high confining pressures.

Nonlinear responses of longitudinally coupled slab tracks exposed to extreme heat waves

Structural responses of longitudinally coupled slab tracks (LCSTs) under extreme heat waves (EHWs) and the adaptability of track reinforcement measures to cope with EHWs-related issues have been unprecedentedly investigated in this study. A novel finite element model (FEM) to assess nonlinear mechanical behaviours of LCSTs exposed to temperature rise has been established. The nonlinearities of material constitutional properties, interfacial behaviours and temperature distribution are taken into account, and the FEM has been fully validated by experimental data. This paper is the world's first to highlight nonlinear structural responses of LCSTs such as slab arching and interface failure under EHWs and under normal temperature rises (NTRs). More importantly, effectiveness of track reinforcement measures (such as post-installed anchors and interface adhesives) in mitigating track damage under EHWs are demonstrated to determine whether those measures are capable of making LCSTs adapt to EHWs. The new findings reveal that: (1) vertical buckling of LCST can be caused by atmospheric temperature rises; (2) the interface area between the mortar layer and the track slab adjacent to the joint with initial defect can fail under NTRs, while the interface delamination incurs under EHWs; (3) vertical displacements of track slabs under EHWs can be reduced by 97.3 % when post-installed anchors are introduced; and (4) the bond strength of interface adhesives should be larger than 0.02 MPa and 0.048 MPa to retain the vertical displacements within the threshold of level III interfacial gaps under NTRs and under EHWs, respectively.

3D printed negative stiffness meta-structures with superior energy absorption and super-elastic shape-recovery features

The aim of this paper is to create novel 3D cubic negative stiffness (NS) structures (NSSs) with superior mechanical performances such as high energy absorption, shape recovery, super-elasticity, and reversibility. The conceptual design is based on an understanding of geometrical influences, non-linear buckling-type instability, snap-through mechanism, elasto-plastic deformation growth and plastic hinges. A finite element (FE) based computational model with an elasto-plastic material behavior is developed to design and analyze NSSs, saving time, material, and energy consumption. Material samples and meta-structures are 3D printed by selective laser sintering printing method. Material properties are determined via mechanical testing revealing that the printing process does not introduce much anisotropy into the fabricated parts. Experimental tests are then conducted to study the behavior of novel designs under loading–unloading cycles verifying the accuracy of the computational model. A good correlation is observed between experimental and numerical data revealing the high accuracy of the FE modeling. The structural model is then implemented to digitally design and test NSSs. Effects of the geometrical parameters of the negative stiffness members under three cyclic loading are investigated, and their implications on the non-linear mechanical behavior of NSSs under cyclic loading are put into evidence, and pertinent conclusions are outlined. In addition, the dissipated energy and loss factor values of the designed structures are studied and the proposed unit cell is presented for the energy absorbing systems. The results show that the structural and geometry of energy absorbers are key parameters to improve the energy absorption capability of the designed structures. This paper is likely to fill a gap in the state-of-the-art NS meta-structures and provide guidelines that would be instrumental in the design of NSS with superior energy absorption, super-elasticity and reversibility features.

Influence of oblique incidence of P-waves on seismic response of prefabricated utility tunnels considering joints

The dynamic performance of prefabricated utility tunnels under seismic excitation is a topic that deserves careful study, especially when considering the oblique incidence of P-waves. Instead of ignoring the effect of axial forces on the stiffness of joints in prefabricated utility tunnels and assuming the stiffness to be constant values, this paper carefully investigated the nonlinear mechanical behavior of joints in all directions by numerical and theoretical methods at first. After the data processing work, the nonlinear behavior was introduced into the 3D real-site numerical model, and the seismic responses of prefabricated utility tunnels with different incident angles of P-waves were simulated. The results showed that the axial forces play an important role in the nonlinear mechanical behavior of joints, the forces and deformations of joints in different directions reached their peaks with different incident angles. Based on the study, it is recommended that the effects of the non-linearity of joint stiffness and the incident direction of earthquake waves should be taken into consideration during the seismic design of prefabricated utility tunnels.

A hybrid algorithm to solve a nonlinear inverse problem of boundary conditions and damage identification

In this communication we present a method exploiting displacement data measured at accessible parts of solid’s boundary, for the solution of boundary conditions and damage identification problems encountered in mechanics. Targeted applications are made of materials presenting a nonlinear mechanical behavior with damage-based approaches. A hybrid algorithm has been developed in order to identify the missing data by minimizing a gap-functional. It takes into account the incremental mechanical behavior of the material and the damage evolution inside the solid via the concept of piloting. An application on a solid made of mortar with synthetic measurements is presented to illustrate the efficiency and robustness of the algorithm.

Structural and thermal investigations of rolling tires in a flat road

Rubber is an essential component of a pneumatic tire. In general, the tire, or the rubber part, is heated by the hysteresis effects caused by the deformation of the rubber part during the operation. Besides, the tire temperature depends on many factors, such as inflation pressure, vehicle loading, car speed, road tire, environment condition, and tire geometry, etc. This study focuses on the finite element approach to compute by simulating the temperature distributions of a steady-state rolling tire. For simplicity, the tire is assumed to be composed of rubber, body-ply, wire, and rim only. The nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model, while the other parts are assumed to be a linear elastic material. The coupled effects of the inflation pressure and vehicle loading are investigated. Hysteresis energy loss is used as a bridge to link the strain energy density to the heat source in rolling tires. The steady-state thermal analysis may obtain the temperature distribution of rolling tires. On the other hand, an efficient computational process is being introduced to decrease the time for coupled 3D dynamic rolling simulation of the tire. The simulation results show that loading is the main factor in determining the temperature field

Experimental investigations on nonlinear mechanical behaviors of Kevlar tether

A Kevlar tether usually exhibits strong nonlinearity in engineering applications, bringing new challenges to the modeling of tether dynamics. The nonlinear mechanical behaviors, including creep behavior, nonlinear stiffness, hysteresis effect, and dynamical property of a Kevlar tether, are investigated through a series of experiments. The longitudinal loading experiment setup is established, from which the relationships between tether deformation, tension, and time can be obtained. The creep process of Kevlar tethers is divided into three stages, namely, linear creep stage, deceleration creep stage, and long-term creep stage. This paper studied the longitudinal nonlinear stiffness of a Kevlar tether, whose nonlinearity is fitted by the cubic function model. The hysteresis effect under single loading and unloading is fitted well by the Kawabata stress-strain model, which verifies the correctness and validity of Kawabata model. The nonlinear dynamical model, which includes the elastic force, hysteresis force, and damping force, is established to describe the general dynamical property of the Kevlar tether. The experiment results verify the correctness of the dynamical model form. To simplify the analysis, a simplified model is proposed to describe the dynamical property of the Kevlar tether, and the parameters have a good consistency. The works in this paper contribute to the accurate modeling of flexible tether and lay the foundation for the further research of tether dynamics and control.

An advanced constitutive model for transversely isotropic rock - Evaluation of two different regularization approaches

The mathematical description of the material behavior of rock is a demanding task in engineering practice. Rock is classified as a frictional cohesive material characterized by highly nonlinear mechanical behavior with irreversible deformation, strain hardening, strain softening and degradation of stiffness. In addition, depending on the origin of a particular rock type, the orientation of minerals and grains as well as the formation of stratification planes lead to inherent anisotropic behavior. Especially in stratified rock types like shales or phyllites, often the special case of transversely isotropic material behavior is encountered. In a previous work, a novel continuum-based material model for describing both, the highly nonlinear and transversely isotropic material behavior of rock, denoted as TI-RDP model, was presented. By means of the linear mapping of the Cauchy stress tensor into a fictitious isotropic configuration, an established isotropic damage plasticity model for rock was extended. In this contribution two different regularization approaches, which are well established for isotropic models, i.e., the mesh-adjusted softening modulus and the implicit gradient-enhancement, are adopted for the TI-RDP model. Based on uniaxial tension and triaxial compression tests considering different orientations of the principal material directions with respect to the direction of axial loading, their capabilities are assessed in terms of predicting the direction-dependent mechanical behavior in a mesh-insensitive manner.

Stretch-Induced Uncrimping of Equatorial Sclera Collagen Bundles.

Stretch-induced collagen uncrimping underlies the nonlinear mechanical behavior of the sclera according to what is often called the process of recruitment. We recently reported experimental measurements of sclera collagen crimp and pressure-induced uncrimping. Our studies, however, were cross-sectional, providing statistical descriptions of crimp with no information on the effects of stretch on specific collagen bundles. Data on bundle-specific uncrimping is necessary to better understand the effects of macroscale input on the collagen microscale and tissue failure. Our goal in this project was to measure bundle-specific stretch-induced collagen uncrimping of sclera. Three goat eyes were cryosectioned sagittally (30 μm). Samples of equatorial sclera were isolated, mounted to a custom uni-axial stretcher and imaged with polarized light microscopy at various levels of clamp-to-clamp stretch until failure. At each stretch level, local strain was measured using image tracking techniques. The level of collagen crimping was determined from the bundle waviness, defined as the circular standard deviation of fiber orientation along a bundle. Eye-specific recruitment curves were then computed using eye-specific waviness at maximum stretch before sample failure to define fibers as recruited. Nonlinear mixed effect models were used to determine the associations of waviness to local strain and recruitment to clamp-to-clamp stretch. Waviness decreased exponentially with local strain (p < 0.001), whereas bundle recruitment followed a sigmoidal curve with clamp-to-clamp stretch (p < 0.001). Individual bundle responses to stretch varied substantially, but recruitment curves were similar across sections and eyes. In conclusion, uni-axial stretch caused measurable bundle-specific uncrimping, with the sigmoidal recruitment pattern characteristic of fiber-reinforced soft tissues.

Nonlinear static and dynamic mechanical behaviors of Nb3Sn superconducting composite wire: experiment and analysis

Nonlinear static and dynamic mechanical behaviors of Nb3Sn superconducting composite wire: experiment and analysis

Plastic Deformation of High Explosive Projectile 155 mm during Gun Launch Conditions using Finite Element Method

The structural integrity of artillery projectile 155mm high explosive Extended Range Full Bore (ERFB)boat tail designed for 155mm howitzer guns of 39, 45 and 52 calibre plays a key role inside the gun barrel. Thisprojectile comprises a shell body, a driving band, a boat tail, nubs, an explosive, and a fuze. Plastic deformationof the projectile and stripping of driving band are not permitted, when projectile is fired. An investigational study is necessitated to check the plastic deformation of the projectile subjected to maximum propellant charge pressure.The aim of this study is to check the effective plastic deformation and affirm the structural integrity. A 3-D explicit dynamic structural analysis of 155 mm HE ERFB BT during gun launch conditions is carried out by finite element method using FE code ABAQUS/Explicit. To understand the non-linear mechanical behavior of the projectile, the true stress-strain curves of the materials are considered. The plastic behavior of the projectile subjected to the time-dependent loading is studied by using the von Mises plasticity model. The results reveal that the shell body and boat tail have no plastic deformation and the most stressed component is the driving band. The investigation has affirmed the structural integrity of the projectile during gun launch conditions.

Experimental Investigation and Micromechanical Modeling of Hard Rock in Protective Seam Considering Damage–Friction Coupling Effect

The hard rock in the protective coal seam of the Pingdingshan Mine in China is a typical quasi-brittle material exhibiting complex mechanical characteristics. According to available research on the mechanical property, the inelastic deformation and development of damage are considered related with crack initiation and propagation, which are main causes of the material degradation. In the present study, an original experimental investigation on the rock sample of the Pingdingshan coal mine is firstly carried out to obtain the basic mechanical responses in a conventional triaxial compression test. Based on the homogenization method and thermodynamic theory, a damage–friction coupled model is proposed to simulate the non-linear mechanical behavior. In the framework of micromechanics, the hard rock in a protective coal seam is viewed as a heterogeneous material composed of a homogeneous solid matrix and a large number of randomly distributed microcracks, leading to a Representative Elementary Volume (REV), i.e., the matrix–cracks system. By the use of the Mori–Tanaka homogenization scheme, the effective elastic properties of cracked material are obtained within the framework of micromechanics. The expression of free energy on the characteristic unitary is derived by homogenization methods and the pairwise thermodynamic forces associated with the inelastic strain and damage variables. The local stress tensor is decomposed to hydrostatic and deviatoric parts, and the effective tangent stiffness tensor is derived by considering both the plastic yield law and a specific damage criterion. The associated generalized Coulomb friction criterion and damage criterion are introduced to describe the evolution of inelastic strain and damage, respectively. Prepeak and postpeak triaxial response analysis is carried out by coupled damage–friction analysis to obtain analytical expressions for rock strength and to clarify the basic characteristics of the damage resistance function. Finally, by the use of the returning mapping procedure, the proposed damage–friction constitutive model is applied to simulate the deformation of Pingdingshan hard rock in triaxial compression with respect to different confining pressures. It is observed that the numerical results are in good agreement with the experimental data, which can verify the accuracy and show the obvious advantages of the micromechanic-based model.

Structural and biomechanical characterizations of acellular porcine mitral valve scaffolds: anterior leaflets, posterior leaflets, and chordae tendineae.

Mitral valve (MV) tissue engineering is still in its early stage, and one major challenge in MV tissue engineering is to identify appropriate scaffold materials. With the potential of acellular MV scaffolds being demonstrated recently, it is important to have a full understanding of the biomechanics of the native MV components and their acellular scaffolds. In this study, we have successfully characterized the structural and mechanical properties of porcine MV components, including anterior leaflet (AL), posterior leaflet (PL), strut chordae, and basal chordae, before and after decellularization. Quantitative DNA assay showed more than 90% reduction in DNA content, and Griffonia simplicifolia (GS) lectin immunohistochemistry confirmed the complete lack of porcine α-Gal antigen in the acellular MV components. In the acellular AL and PL, the atrialis, spongiosa, and fibrosa trilayered structure, along with its ECM constitutes, i.e., collagen fibers, elastin fibers, and portion of GAGs, were preserved. Nevertheless, the ECM of both AL and PL experienced a certain degree of disruption, exhibiting a less dense, porous ECM morphology. The overall anatomical morphology of the strut and basal chordae were also maintained after decellularization, with longitudinal morphology experiencing minimum disruption, but the cross-sectional morphology exhibiting evenly-distributed porous structure. In the acellular AL and PL, the nonlinear anisotropic biaxial mechanical behavior was overall preserved; however, uniaxial tensile tests showed that the removal of cellular content and the disruption of structural ECM did result in small decreases in maximum tensile modulus, tissue extensibility, failure stress, and failure strain for both MV leaflets and chordae.

Analysis of Axially Loaded Piezoelectric Semiconductor Rods with Geometric Nonlinearity

Piezoelectric semiconductor (PS) nanostructures have a huge application potential in flexible electronic devices. We study the nonlinear multi-field coupling mechanical behaviors of axially loaded PS rods by taking the von Kármán type of nonlinear strain–displacement relations into account. The one-dimensional equations for extensional PS rods with the geometric nonlinearity are presented. The analytical solutions for an axially loaded PS rod with open-circuit and electrically isolated boundary conditions at the two ends are obtained based on the classical perturbation method. The zeroth-order perturbation solution is exactly the same as the linearized solution. The influences of the first- and second-order solutions on the multi-field coupling responses of the PS rods under different axial loads are investigated.

A fatigue constitutive model for rock masses based on cross-applications of rheological theory

In geotechnical engineering construction and underground ore mining, periodic cyclic fatigue loading is a major cause of rock mass instability and failure. With a constitutive model, the fatigue characteristics of rock masses can be studied effectively. Based on the similarities between rock mass rheology and cyclic fatigue loading, this paper applies rheological theory to study the fatigue characteristics of rock masses. Two constitutive models that describe different stages of nonlinear mechanical behaviour during the fatigue process were proposed, and a fatigue constitutive model that accurately describes the mechanical properties of rock during different fatigue stages was established after combining the two models. A sensitivity analysis showed that the model parameters EK , γ and δ can effectively reflect the deformation and damage evolution characteristics of the rock mass during the three fatigue stages. By comparing the laboratory splitting and three-point bending fatigue experiment results with the calculated model values, the rationality, reliability, and application scope of the model were verified. Moreover, based on the model parameter inversion results, the evolution mechanism of the rock mechanical properties during the different fatigue stages can be accurately understood.