Elastoplastic Model Research Articles

An Elastoplastic Damage Model for Sandstone Considering the Compaction Effect and Freeze–Thaw Action

An Elastoplastic Damage Model for Sandstone Considering the Compaction Effect and Freeze–Thaw Action

Johnson–Cook yield functions for cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) derived from single crystal plasticity models

High-fidelity constitutive models are critical for accurate meso-scale continuum modeling and prediction of shock initiation of crystalline energetic materials (EMs). While empirically calibrated or atomistic-guided anisotropic elastoplastic models of EM such as cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) capture important micromechanical phenomena (such as dislocation evolution, slip-resistance, and anisotropic elasticity), the computational cost of using anisotropic single-crystal plasticity models can become prohibitive for meso-scale computations of void-collapse and hotspot formation in microstructures. Thermo-mechanically representative, isotropic, pressure, temperature, and rate-dependent material constitutive models are practical alternatives for meso-scale simulations of the shock response of microstructures. To this end, this work constructs physically consistent isotropic plasticity from anisotropic single-crystal plasticity models for HMX and RDX. State-of-the-art crystal plasticity models for HMX and RDX are used to compute the stress states in single crystals oriented in three different directions relative to shocks generated by impact at velocities ranging from 100 to 1000 m/s. Post-shock von Mises stress fields for the three orientations are then used to calibrate the strain-rate hardening coefficient and the reference strain rate for a rate-dependent Johnson–Cook (JC) yield surface model. We compare the pressures and the post-shock von Mises stresses between the JC and the anisotropic models to show that the isotropic computations closely approximate the averaged deformation response of the three different crystal orientations. We then model the interaction of a shock generated by a 500 m/s impact with a 0.5 μm void and show that the pressures and the deviatoric stresses obtained using the isotropic model closely match those computed from anisotropic models for both HMX and RDX. The resulting isotropic J2 plastic flow model for HMX and RDX can be employed to perform meso-scale simulations for energy localization due to shear bands and void collapse in the two materials.

Force in Cable of Pretensioner Tube—A Possibility of Car Accident Reconstruction

The reconstruction of traffic accidents has grown as an interdisciplinary field, encompassing bodies of research from automotive engineering, traffic and transport engineering, biomechanics, and forensic sciences. In this work, a method is proposed by which the value of the force in the safety belt buckle can be determined provided the belt buckle is equipped with a pretensioning system with a pyrotechnic trigger in the pretensioner tube, PBP—Pyrotechnical Buckle Pretensioner, or PLP—Pyrotechnical Lap Pretensioner type. The anti-return system of the pretensioner mechanism, which prevents the passenger’s body from moving forward, contains a set of balls that block the movement of the piston in the pretensioner tube after its activation. When limiting the movement, the force the human body exerts on the safety belt webbing is transformed into the deformation of the pretensioner tube by the balls of the anti-return system. Depending on the magnitude of the force, the marks left by the balls differ. This is an alternative method for determining the force that occurs in a seatbelt and causes injury to the occupants of a vehicle. The advantage of this method is that the force in the seatbelt buckle cable can be determined relatively quickly and accurately by analyzing the deformations in the pretensioner tube, without a need for expensive laboratory equipment. The limitation of the model resides in the consideration of a static system with rigid bodies. The correlation between the normal force causing the deformation of the tube and the force in the belt buckle cable is obtained by means of a mechanical model that explains the operation of the anti-return system. By comparing the values of the normal force given by the proposed model and the elastoplastic model, a good correlation is found. Finally, a regression curve is determined to help the expert in approximating the force in the buckle cable depending on the deformation size in the pretensioner tube. The value of this force also enables biomechanical or medical specialists to correlate the degree of injury to occupants of a vehicle depending on the force in the seatbelt.

A Constitutive Model for Stud Connection in Composite Structures

The complexity of finite element analysis for composite structures can be significantly reduced by representing the connector and adjacent concrete as a macroscopic element. Nevertheless, the prevailing macroscopic models for shear connections predominantly employ nonlinear elastic theory. This approach introduces inaccuracies in estimating structural stiffness and load-bearing capabilities, primarily due to its inability to precisely capture the cumulative effects of plastic damage. In response, this study introduces a novel macroscopic elastoplastic model grounded in plasticity theory, aimed at accurately characterizing the nonlinear behavior of stud connections subjected to concurrent shear and tensile forces. This paper meticulously delineates the implementation of the elastoplastic constitutive model using the backward Euler method for numerical integration. It further articulates the derivation of the consistent tangent stiffness, which aligns with the convergence efficiency of the Newton–Raphson iterative approach. The computation of the element stiffness matrix for a two-node element is executed via the governing equation inherent to the finite element method. An exemplar macroelement test conducted in ABAQUS affirms the implicit backward Euler scheme’s stability and consistency across varying tolerances. Validation of the elastoplastic model against empirical test outcomes corroborates its efficacy, demonstrating the model’s precision in predicting the load–displacement behavior of stud connections under the influence of shear and tensile forces.

Mean-field analysis of the glassy dynamics of an elastoplastic model of super-cooled liquids

Abstract We present a mean-field theory of a coarse-grained model of a super-cooled liquid in which relaxation occurs via local plastic rearrangements. Local relaxation can be induced by thermal fluctuations or by the long-range elastic consequences of other rearrangements. We extract the temperature dependence of both the relaxation time and the lengthscale of dynamical correlations. We find two dynamical regimes. First, a regime in which the characteristic time and length scales diverge as a power law at a critical temperature $T_c$. This regime is found by an approximation that neglects activated relaxation channels, which can be interpreted as akin to the one found by the mode-coupling transition of glasses. In reality, only a cross-over takes place at $T_c$. The residual plastic activity leads to a second regime characterised by an Arrhenius law below $T_c$. In this case, we show that the lengthscale governing dynamical correlations diverges as a power law as $T\to 0$, and is logarithmically related to the relaxation time.

A Unified Particle-Based Solver for Non-Newtonian Behaviors Simulation.

In this article, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.

Modeling of time-dependent mechanical behavior of oleic acid nanocomposites using nanoindentation

Supercrystalline nanocomposites are a burgeoning class of hybrid inorganic-organic materials. Studies showed that self-assembly of iron oxide particles surface-functionalized with organic (e.g. oleic acid) ligands produces a supercrystalline nanocomposite with exceptional mechanical properties. Consequently, significant research has been conducted on these materials to experimentally characterize the mechanical properties of such materials. However, so far all modeling studies used time and rate independent elastoplastic material models. In the light of new experimental results, we propose to extent this view and use time-dependent models to capture viscoelastic behavior. To this end, we quantified this behavior using nanoindentation creep experiments and modelled it using a rheological network model with several parallel Maxwell branches and an additional elasto-plastic branch. We demonstrate how the parameters of such a model can be found using inverse analysis. With the calibrated material model, a good agreement of the time dependent behavior between simulation and experimental results is achieved. Thus, a method is provided to model time dependent behavior using complex non-classical experiments like nanoindentation.

Solidified water at room temperature hosting tailored fluidic channels by using highly anisotropic cellulose nanofibrils

Highly anisotropic cellulose nanofibrils can solidify liquid water, creating self-supporting structures by incorporating a tiny number of fibrils. These fibrillar hydrogels can contain as much as 99.99 wt% water. The structure and mechanical properties of fibrillar networks have so far not been completely understood, nor how they solidify the bulk water at such low particle concentrations. In this work, the mechanical properties of cellulose fibrillar hydrogels in the dilute regime from a wt% perspective have been studied, and an elastoplastic model describing the network structure and its mechanics is presented. A significant insight from this work is that the ability of the fibrils to solidify water is very dependent on particle stiffness and the number of contact points it can form in the network structure. The comparison between the experimental results and the theoretical model shows that the fibrillar networks in the dilute regime form via a non-stochastic process since the fibrils have the time and freedom to find contact points during network formation by translational and rotational diffusion. The formed, dilute fibrillar network deforms by sliding fibril contacts upon straining the network beyond its elastic limit. Our results also show that before macroscopic failure, the fibril contacts are restored once the load is released. The exceptional properties of this solidified water are exploited to host fluidic channels, allowing directed fluid transportation in water. Finally, the microfluidic channels formed in the hydrogels are tailored by the layer-by-layer technique to be interactive against external stimuli, a characteristic envisioned to be useful in biomedical applications.

Anisotropic elastoplasticity and fracture of SCFR-PEEK composites in complex biaxial loading: Experiments and modelling

This research aims to gain insight into the anisotropic deformation and fracture behaviours of short carbon fibre reinforced polyether-ether ketone composites (SCFR-PEEK) under complex loading using experimental and modelling approaches. Novel biaxial tensile experiments using optimised cruciform specimens are designed and performed to study the anisotropic elastoplasticity and fracture behaviours of SCFR-PEEK in various stress states. An advanced anisotropic constitutive model was developed, experimentally calibrated, numerically implemented, and successfully verified by mechanical responses of biaxial tension with various stress ratios. Furthermore, using a hybrid experimental-numerical approach, the biaxial failure stress at crack initiation sites captured by a high-speed camera in biaxial tension was obtained. Employing experimental failure stresses at various uniaxial and biaxial stress states, a maximum stress based failure criterion was developed, which is coupled with the anisotropic elastoplastic model, thus enabling the description the anisotropic elastoplastic and failure behaviours under complex loading. The prediction of the failure of SCFR-PEEK in complex biaxial stress states using the coupled model is in good agreement with biaxial tensile experimental results using circular-notched specimens. Therefore, the developed model is verified to be capable of describing both elastoplastic deformation and fracture failure behaviours of SCFR-PEEK composites in complex loading.

An elastoplastic model with egg-shaped yield surface for coastal soft clay

A novel elastoplastic constitutive model with an egg-shaped yield surface (ESE model) is proposed herein to elucidate the strength-deformation characteristics of marine soft clay. One of the key improvements offered by this model is its ability to address the singularity associated with plastic strain increments at yield surface corners—a limitation commonly encountered in traditional elastoplastic models. Additionally, the proposed model demonstrates flexibility, as it can transform into various forms under different conditions. Subsequently, to evaluate the efficacy of this egg-shaped elastoplastic model, numerical simulations are performed within the finite element software ABAQUS using an implicit integration algorithm through the user material subroutine interface (UMAT). The simulations encompass standard triaxial consolidation tests involving saturated soft clay sourced from the Itsukaichi marine clay as well as two types of saturated kaolin clays. The outcomes derived from these simulations by the ESE model are compared with both empirical data and numerical simulations originating from the widely employed Modified Cam-Clay (MCC) model. The simulations of the ESE model for three conventional triaxial tests on clay demonstrate superior concordance with experimental measurements in comparison to the MCC model. This underscores the efficacy of the proposed ESE model in predicting the strength and deformation characteristics manifested by coastal soft clays under undrained conditions. Finally, the predictions for deformation in an adjacent tunnel according to the ESE model closely align with experimental measurements and prior to the simulations conducted using the MCC model and advanced models such as the bounding surface model and the unified model, thereby affirming its practical utility in engineering applications.

Investigation of local soil resistance on suction caissons at capacity in undrained clay under combined loading

Winkler modelling offers a flexible and computationally efficient framework for estimating suction caisson capacity. However, there is a limited understanding of the local soil resistance acting on caissons at capacity under combined six degrees-of-freedom (6DoF) loading, which is essential for accurately estimating caisson failure envelopes. Furthermore, existing simplified design models for caissons cannot assess capacity under non-planar lateral and moment loading, which is common in offshore wind applications. To address these limitations, this paper presents a comprehensive three-dimensional (3D) finite element analysis (FEA) study, which investigates the local soil resistance acting on the caisson at capacity in undrained clay under combined 6DoF loading. The paper introduces the concept of ‘soil reaction failure envelopes’ to characterise the interactions between soil reactions at capacity. Closed-form formulations are derived to approximate these soil reaction failure envelopes. An elastoplastic Winkler model is then developed, incorporating linear elastic perfectly plastic soil reactions based on these formulations. The results demonstrate that the Winkler model can provide efficient and reasonably accurate estimations of caisson capacity under combined 6DoF loading, even for irregular soil profiles that pose much uncertainty and challenges to existing macro-element models.

Experimental and model investigation on hydro-mechanical behaviour of sandy mudstone

The hydro-mechanical behaviour and the constitutive model of sandy mudstone were investigated in this article. Two groups of hydro-mechanical triaxial compression tests were conducted. The results indicated that the inelastic deformation, damage, permeability and failure of the sandy mudstone were affected by the pore pressure and confining pressure. The hydro-mechanical behaviour was characterised by the coupled elastoplastic damage model. This model was based on the effective stress principle and numerical return mapping algorithms. Sensitivity analysis was also performed to examine the effects of four key parameters on the modelling of elastoplastic and damage behaviour. This study can provide a foundation for physical understanding and mathematical modelling of sandy mudstone under coupled loads.

An elastoplastic phase-field model for quasi-static fracture of nickel-based super-alloys

In the present study, an elastoplastic phase-field model of quasi-static fracture in ductile materials is proposed in the variational framework for J2 plasticity with isotropic hardening, which is suitable to describe the quasi-static behavior of metals as investigated in the performed experiments. These contributions include: (1) the free energy functions for coupling elastic response, plastic yielding and damage evolution are established. (2) The new elastic and plastic energy degradation functions are constructed to quantitatively describe the relationship between energy release and phase-field evolution of elastoplastic materials. (3) Damage evolution and plastic yielding criteria are derived. (4) From a numerical point of view, we derive the governing equations and the corresponding weak forms and the overall solution procedure for the phase-field model is given via the use of a return-mapping algorithm. This phase-field model was validated by a series of tensile experiments on Inconel 718 nickel-based super-alloys standard specimens. In order to compare the simulation results with the experimental results more comprehensively, the digital image correlation (DIC) technique is applied to experimentally investigate the specimen deformation information. In addition, to verify the potential of the model to capture complex cracks, we performed Nooru-Mohamed tests. The numerical simulation results are in good agreements with the results of previous experimental work.

A hemivariational damageable elastoplastic vertex-spring model for masonry analysis

This work is an intermediate step towards the extension of a recently proposed block-based model for masonry structures, which was based on a hemivariational approach and inspired from granular micromechanics. Here, contrarily to the previous model, plastic effects will also be taken into account along with damage and elastic behaviours, and the full hemivariational derivation of the strong-form (in)equations will be detailed for the case of a lone vertex spring. The resulting model and methods shall then be used in future works to enrich the behaviours modelled by the previously mentioned masonry model.

Post-fire mechanical properties and constitutive model of Q690 high-strength structural steel

Fire hazard is one of the main threats to the integrity of steel structural buildings. Developing an accurate post-fire constitutive model for structural steel is crucial for enhancing the failure assessment of steel structures exposed to fire. In this study, the post-fire mechanical behavior of Q690 high-strength structural steel is investigated. Eighteen round bar specimens made of Q690 steel were heated with temperatures ranging from 20 °C to 900 °C. Tensile tests were conducted on these specimens to obtain the post-fire stress-strain curves and associated mechanical parameters of the material. To accurately characterize the post-fire behavior of Q690 steel, a temperature-dependent elastoplastic constitutive model combined with its numerical implementation algorithm is proposed. This model consists of four components: a temperature-dependent elasticity criterion, the von Mises yield criterion, an associated flow rule, and a temperature-dependent isotropic hardening law. The proposed constitutive model has a notable feature, i.e. the material parameters in the model can be defined as a function of temperature according to the test results. As a result, when utilizing this model for post-fire assessments of steel members, only three routine parameters, i.e. elastic modulus at room temperature, Poisson's ratio, and the temperature experienced by the material, are required in the numerical simulation to generate the material’s stress-strain relationships. To verify the proposed constitutive model, the new model was introduced into the numerical simulations of the tested round bar specimens after exposure to various temperature conditions. Both the load-displacement curves and local deformation of each round bar specimen obtained from the numerical simulations are compared with the test results to validate the accuracy of the new model. The constitutive model presented in this study provides a useful tool for assessing the post-fire behaviors of steel components.

An in-plane phase-field ductile fracture model for orthotropic paperboard material

A phase-field ductile fracture formulation for orthotropic paperboard materials is proposed, based on an anisotropic, multi-surface elastoplastic model describing the in-plane behavior of paperboard. A variational statement for the finite-step elastoplastic problem is extended to include the variational description of Griffith-type brittle fracture by a phase-field gradient term. The interaction between plastic and fracture dissipation mechanisms is modeled by introducing a scalar modulation function, assuming plasticity driven damage growth. This function depends on a scalar measure of the plastic strain components in the material orthotropy frame. It modifies the fracture activation criterion in a non-variational fashion, resulting in a direction-dependent material strength against crack propagation. The model performance is assessed by comparing numerical simulations and experimental tests conducted in a climate-controlled laboratory.

Compaction elastoplastic damage constitutive model of rock under hydro-mechanical coupling: A heuristic modeling method based on internal state variables theory

Based on the internal state variables (ISV) theory, this paper employs a heuristic modeling approach to investigate the compaction elastoplastic damage constitutive model of rocks under hydro-mechanical coupling. The heuristic modeling method demonstrated herein can seamlessly integrate with existing constitutive theories, facilitating a broader spectrum of research on hydro-mechanical coupling constitutive models. Furthermore, a numerical solution was conducted in the principal axes via stress spectrum decomposition, which can well reflect the distinct characteristics of compaction deformation and the influence of water pressure on rock stress distribution. Utilizing the classic Drucker-Prager (D-P) criterion, the modeling method and numerical algorithm were implemented to derive a hydro-mechanical coupling compaction elastic–plastic damage constitutive model. This contribution expands the application domain of the classic D-P criterion within the context of hydro-mechanical coupling environments. The rationality of the model was confirmed through compression test data under various water pressures and confining pressures. Water pressure increases nonlinear compaction deformation by changing the opening degree of microcracks under low confining pressure, which has not been paid enough attention in existing research. This study thoroughly considers the influence of water pressure on compaction deformation. The developed process of “heuristic modeling method-numerical method-model application” is helpful for enriching the constitutive theory of rock under hydro-mechanical coupling.

Damage-tolerant behavior of structural epoxies with thin PEI and PVDF interlayers

This work examines the crack-arresting capability of PEI and PVDF thermoplastic interlayers in short-glass fiber modified and core–shell rubber toughened epoxy materials under mode-I fracture loading. Experimental results show that the initial crack can be effectively arrested by the thermoplastic-epoxy interface and reinitiation of this crack at the thermoplastic layer requires up to 2.5 times higher load than the crack initiation load of the pristine epoxies. The interlayered designs also exhibit a significant increase in energy absorption by up to 43 times more than their pristine counterparts. Competing damage mechanisms and failure events are captured by microscopy images, digital image correlation and high-speed photography observations. Additionally, elasto-plastic fracture mechanics models based on configurational material forces theory are developed for a preliminary crack-arresting material selection and to elucidate the material inhomogeneity effects.

Connecting microscopic and mesoscopic mechanics in model structural glasses.

We present a novel formalism to characterize elastic heterogeneities in amorphous solids. In particular, we derive high-order strain-energy expansions for pairwise energies under athermal quasistatic dynamics. We then use the presented formalism to study the statistical properties of pairwise expansion coefficients and their link with the statistics of soft, quasilocalized modes, for a wide range of formation histories in both two- and three-dimensional systems. We further exploit the presented framework to access local yield stress maps by performing a non-linear stress-strain expansion within a cavity embedded in a frozen matrix. We show that our "bond micromechanics" compare well with the original "frozen matrix" method, with the caveat of overestimating large stress activations. We additionally show how local yield rules can be used as an input for a scalar elasto-plastic model (EPM) to predict the stress response of materials ranging from ductile to brittle. Finally, we highlight some of the limits of simple mesoscale models in capturing the aging dynamics of post-yielding systems. Intriguingly, we observe subdiffusive and diffusive shear band growths for particle-based simulations and EPMs, respectively.

Elastoplastic constitutive model of gravelly soil and its validation through numerical analysis of the Kobe Port Island liquefaction

The liquefaction of gravelly soil has been demonstrated in many earthquakes, but the constitutive model to predict its liquefaction behavior is limited. The dilatancy equation plays an important role in establishing elastoplastic models of geotechnical materials. Recognizing the unique dilatancy characteristics of gravelly soil, this study introduces an improved nonlinear dilatancy equation into the generalized plasticity model. Consequently, a unified elastoplastic constitutive model is proposed, aimed at accurately predicting both the monotonic and cyclic behaviors of saturated gravelly soil under diverse drainage conditions. A series of drained and undrained triaxial tests of gravelly soil under monotonic and cyclic loadings are carried out to validate the model performance. In addition, the model performance is also examined through monotonic and liquefaction tests of gravelly soil obtained from prior publications. Furthermore, the proposed model is implemented into the nonlinear finite element program GEODYNA and applied to the numerical simulation of the Kobe Port Island liquefaction to better validate the capabilities of the proposed model. From the comprehensive analysis of triaxial tests and numerical simulations, the proposed model performs well in predicting mechanical behavior of gravelly soil and can provide a powerful tool for seismic liquefaction analysis of gravelly soil sites.