Proposed Continuum Model Research Articles

Numerical analysis of non-proportional biaxial reverse experiments with a two-surface anisotropic cyclic plasticity-damage approach

This paper deals with the numerical analysis of ductile damage and fracture behavior under non-proportional biaxial reverse loading conditions. A two-surface anisotropic cyclic elastic–plastic-damage continuum model is adequately presented, which takes into account the Bauschinger effect, the stress-differential effect, and the change of hardening rate after reverse loading. An efficient Euler explicit numerical integration algorithm, based on the inelastic (plastic or plastic-damage) predictor-elastic corrector approach, is utilized to analyze the stress and finite strain loading histories. Detailed discussions are provided on different numerical integration-related consistent tangent operators that achieve convergence within the global Newton–Raphson scheme. The proposed continuum model is implemented into the commercial software Ansys as a user-defined subroutine (UMAT). Furthermore, the novel non-proportional biaxial tensile reverse experiments are performed to validate the proposed continuum model. The associated numerical simulations investigate the stability and accuracy of the proposed algorithm and material model.

Multiscale nanoindentation modelling of concentrated solid solutions: A continuum plasticity model

Recently developed single-phase concentrated solid-solution alloys (CSAs) contain multiple elemental species in high concentrations with different elements randomly arranged on a crystalline lattice. These chemically disordered materials present excellent physical properties, including high-temperature thermal stability and hardness, with promising applications to industries at extreme operating environments. The aim of this paper is to present a continuum plasticity model accounting for the first time for the behaviour of a equiatomic five-element CSA, that forms a face-centred cubic lattice. The inherent disorder associated with the lattice distortions caused by an almost equiatomic distribution of atoms, is captured by a single parameter α that quantifies the relative importance of an isotropic plastic contribution to the model. This results in multiple plasticity mechanisms that go beyond crystallographic symmetry-based ones, common in the case of conventional single element metals. We perform molecular dynamics simulations of equiatomic CSAs: NiFe, NiFeCr, NiFeCrCo, and Cantor alloys to validate the proposed continuum model which is implemented in the finite element method and applied to model nanoindentation tests for three different crystallographic orientations. We obtain the representative volume element model by tracking the combined model yield surface.

A discrete-to-continuum model of weakly interacting incommensurate two-dimensional lattices: The hexagonal case

In this paper, we extend the discrete-to-continuum procedure we developed in Español et al. (2018) to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing elastic terms and a weak interaction term that could utilize either a Lennard-Jones potential or a Kolmogorov–Crespi potential. To validate our modeling, we perform numerical simulations to compare the predictions of the original discrete model and the proposed continuum model, which also show an agreement with experimental findings for, e.g., twisted bilayer graphene.

Modeling of affective-negative content in the course of schizophrenia

IntroductionThe world literature presents ambiguous results regarding the conjugation of negative and depressive syndromes, due to an incomplete understanding of the main symptoms of depression in schizophrenia.ObjectivesTo analyze the variants of the conjugation of depressive and negative symptoms at different stages of schizophrenia.MethodsWe used the data of our own observations (238 patients with a diagnosis of schizophrenia and no more than 5 years of experience of the disease) and compared them with the previously published results of studies. As a hypothesis, we analyze the variants of the conjugacy of affect and the negative domain within the framework of a single discrete field of schizophrenia.ResultsThe analysis shows that with the apparent heterogeneity of the psychopathological structure, some depressive features, such as apathy, anhedonia and social autism (characteristic of negative symptoms), tend to the abulia factor, whereas low mood, suicidal thoughts, pessimism, show affinity for the cluster of impoverishment of expression, that is, they represent an attenuated type of negative symptoms tending to the affective spectrum.ConclusionsThe conjugacy of depressive and negative disorders in schizophrenia, taking into account their phenomenological similarity, allows us to formulate a hypothesis about their existence within the framework of a single continuum model. The proposed continuum model can be used to understand the processes underlying pathogenesis and formulate the principles of personalized treatment and can be used as a starting point for research on the underlying biological processes and personalized treatment.DisclosureNo significant relationships.

A computational investigation of applicability of nonlinear fracture mechanics in nano-scale fracture of graphene

One of the main concerns for large-scale applications of graphene is unwanted fracture due to its low fracture toughness, close to that of an ideally brittle solid. However, graphene fracture properties and criteria have not been fully understood yet and the related understanding at the continuum-mechanics level is mostly limited to the linear elastic fracture mechanics (LEFM) investigations. In this paper, the applicability of nonlinear fracture mechanics (NLFM) to describe the fracture behavior of graphene is investigated through modeling the graphene sheets, including a center crack along the armchair and zigzag directions under mode I and mode II loading. A hyperelastic high-order continuum description is developed to be used in the nonlinear finite element simulations at the continuum level, by expanding the elastic strain energy in terms of the Lagrangian strains up to the seventh-order terms. The proposed continuum model is parameterized using the molecular dynamics (MD) simulation results to accurately reproduce the nonlinear mechanical behavior of graphene in uniaxial strain, equi-biaxial strain, and simple shear deformations. Finally, the applicability of NLFM, compared to LEFM, is investigated for graphene fracture through the continuum mechanics and MD fracture simulations. © 2001 Elsevier Science. All rights reserved

Exact strain gradient modelling of prestressed nonlocal diatomic lattice metamaterials

In this article, an exact strain gradient (SG) continuum model to capture the broadband bandgap characteristics of the prestressed diatomic lattice (PDL) with local/nonlocal interactions has been proposed. By considering the periodicity of wave motion, the wavelength-dependent Taylor expansion is established, leading to a desirable prediction when the wavelength is close to the lattice scale. For PDL, the dispersion curves of the proposed continuum model are always consistent with those of discrete model in the first Brillouin zone. The proposed SG continuum model is used to investigate the effects of structural parameters, orders of SG continua and various nonlocal interactions on bandgap properties of PDL. Highlights Continuum modelling of prestressed acoustic diatomic lattices. Perfect agreements achieved between dispersion diagrams by discrete and proposed continuum models. Effects of prestress, nonlocal interactions, mass and stiffness ratios on band gap structures analyzed. Proper strain gradient (SG) orders determined to guarantee a satisfactory accuracy.

High-frequency voltage-driven vibrations in dielectric elastomer membranes

This article deals with modelling and experimental characterisation of the continuum dynamic response of dielectric elastomer actuators (DEAs) subject to high-frequency voltage excitation.DEAs are capable of large deformations in response to an electrostatic stimulus, and they show large operating bandwidths of up to a few kilohertz. Although DEA systems normally make use of simple deformation patterns and a well-defined main actuation mode, they show complex structural dynamics and mode shapes if subject to high frequency voltage inputs. Taking advantage of these complex structural dynamics potentially allows developing multi-function actuators, audio devices and vibration isolators capable to perform different tasks using different vibration regimes.We first present a multi-domain model for the structural dynamics of DEAs, accounting for the contribution of the air pressure loads generated the DEA membrane vibrations, which play a relevant role in the DEA dynamics.We then present an extensive experimental characterisation of DEA samples’ structural dynamics based on laser Doppler vibrometer measurements. In particular, we measure the complex structural mode shapes and the velocity spectra generated through a broadband excitation in correspondence of a wide set of different design and control parameters (namely, the DEA geometric layout, the mechanical-preload and the applied voltage bias).Based on the experimental results, we validate the proposed continuum model, and we demonstrate that the forced response of the DEA can be efficiently described using a lumped-parameter computationally efficient reduced reformulation.

Numerical Analysis of Experiments on Damage and Fracture Behavior of Differently Preloaded Aluminum Alloy Specimens

A large amount of experimental studies have shown significant dependence of strength of ductile metals on stress state and stress history. These effects have to be taken into account in constitutive models and corresponding numerical analysis to be able to predict safety and lifetime of engineering structures in a realistic manner. In this context, the present paper deals with numerical analysis of the influence of the load path on damage and fracture behavior of aluminum alloys. A continuum damage model is discussed taking into account the effect of stress state and loading history on damage criteria and on evolution equations of damage strains. Experiments with the biaxially loaded H-specimen have been performed and different preloading histories have been taken into account. Evolution of strain fields is monitored by digital image correlation, and fracture modes are visualized by scanning electron microscopy (SEM). In addition, numerically predicted stress states are used to explain occurrence of different stress-state- and preloading-path-dependent localization behavior in critical specimens areas, as well as damage and fracture modes, revealed by SEM. The experiments with newly developed biaxially loaded specimens and corresponding numerical simulations show that the preloading history remarkably affects the occurrence of width and orientation of localized strain fields, as well as evolution of damage mechanisms and fracture modes. Therefore, characterization of materials must be based on an enhanced experimental program including biaxial tests with different loading histories. The observed damage and failure behavior can be predicted by the proposed continuum model taking into account stress-state-dependent damage criteria and damage strains.

Bifurcation of magnetorheological film–substrate elastomers subjected to biaxial pre-compression and transverse magnetic fields

This work investigates the primary sinusoidal bifurcation wrinkling response of single- and multi-layered magnetorheological elastomer (MRE) film–substrate systems subjected to combined transverse applied magnetic fields and in-plane biaxial pre-compression. A recently proposed continuum model that includes the volume fraction of soft-magnetic particles is employed to analyze the effect of the magnetic properties upon the bifurcation response of the system. The analysis is built in a highly versatile manner using a finite-element discretization approach along the direction of the applied magnetic field and Fourier expansions along the infinite in-plane layer directions. This allows for a seamless investigation of various multi-layered structures. First, we analyze the effect of biaxial pre-compression upon the critical magnetic field for a film–substrate system and for various mechanical stiffness ratios. We observe a kink in the critical magnetic curves and a reflection in the corresponding wave numbers as they cross the equi-biaxial pre-compression regime. Subsequently, we consider a MRE film bonded to a MRE substrate and study the effect of the particle volume fraction ratios in those two parts. As a result, we obtain sharp pattern transitions, i.e., long-to-short wavelength changes with only minor perturbations of the applied pre-compression. The presence of a magnetic substrate changes qualitatively and quantitatively the bifurcation response of the film–substrate system. Finally, we carry out a data-mining exercise to minimize the critical magnetic field at bifurcation by using three different topologies, i.e., a monolayer, a bilayer and a sandwich film. We find that the topologies resembling closely the monolayer one lead to the lowest critical magnetic fields for a given biaxial pre-compression.

Dynamics of growth and collapse of nanopores in copper

Variation of pore size is relevant for both the growth of voids during fracture and the compaction of pores at compression of a porous medium. In this work we examine the previously proposed continuum model of dislocation-stimulated growth of nanovoids in Al to the case of Cu for both tension and compression of the sample with a previously cut pore. Results of continuum model are verified and parameters are fitted using the molecular dynamics(MD) simulations. Dependencies of surface tension and energy of dislocation formation on temperature are obtained from fitting procedure. Continuum model allows one to adequately describe the evolution of pressure, pore radius and dislocation density with time during both tension and compression in the MD system.

Modelling of supply voltage frequency effect on partial discharge repetition rate and charge amplitude from AC to DC at room temperature

This paper has the purpose to derive an analytical model (continuum model) able to describe the behavior of partial discharge (PD) repetition rate and amplitude, occurring in a cavity embedded in polymeric insulation, as a function of the frequency of the supply voltage, going from AC power supply frequency, 50–60 Hz, to DC. In the range between DC and 50–60 Hz focus is made on data coming from tests under AC sinewave with very low frequency (VLF) such as 0.1 Hz and 0.01 Hz, which are commonly used for cable testing. It is shown that the proposed continuum model can provide reasonably good fit to the experimental results obtained in the range DC to 60 Hz, regarding PD repetition rate and amplitude. To reach such result, the equivalent circuit is modified from that commonly used and made by fully-capacitive or resistive components, in order to take into account the change of polarization mechanisms which, depending on dielectric material, may play a non-negligible role to establish the repetition rate from low frequency to DC power supply. In addition, the residual voltage after a PD event has to vary with frequency to reach good fitting. Also, it is shown that PD amplitude under DC and VLF can be lower than under AC 50–60 Hz due to the delay time of the firing electron, thus experimental PD amplitude varies with frequency depending on material and defect typology and location.

A strain rate-dependent enhanced continuum model for elastic-plastic impact response of metal-ceramic functionally graded composites

An enhanced continuum model considering the strengthening of strain rate is developed to explore the particle size-dependent responses of the metal-ceramic functionally graded composite plates subjected to a drop-weight impact. The continuum model explicitly accounts for the effects of geometrically necessary dislocations and strain rate by combining Taylor dislocation model and Johnson–Cook model. The plastic constitutive relation of metal-ceramic FGM is derived from the Tamura–Tomota–Ozowa model subjected to different strain rates. The elastic-plastic impact responses of SiC/Al functionally graded plates with the micron-scale particle sizes and compositional gradient exponents are studied under varied impact velocities. The comparison at the numerical results for the particle size effects in the SiC/Al functionally graded plates and the experimental data reported in references demonstrates validity of the proposed continuum model.

Magneto-visco-hyperelasticity for hard-magnetic soft materials: theory and numerical applications

Soft materials that can deform under external stimuli offer great opportunities for the development of new structural applications such as sensor-actuator systems, soft robots or biomedical devices. Among these materials, soft polymers filled with magnetic particles are experiencing an increasing interest from the scientific community. Apart from magnetorheological elastomers and ferrogels, a new magneto-sensitive material type has been developed recently. These so-called hard-magnetic materials allow for shape-programmability by the addition of magnetically-hard particles within a polymeric matrix. In this regard, constitutive and computational frameworks describing the magneto-mechanics of such materials are needed to provide new avenues in the development of novel applications based on hard-magnetic soft polymers. To this end, this work focuses on the mathematical modelling of the magneto-mechanics of hard-magnetic soft materials and their implementation in finite element (FE) frameworks. The proposed continuum model is formulated for large deformations and within a thermodynamically consistent framework. In addition, the model incorporates viscous contributions to account for relaxation and dissipation effects in the deformation process of these materials when subjected to external magnetic fields and/or mechanical loading. To illustrate the theory, the magneto-mechanical model is implemented within an implicit static FE framework and three numerical examples are provided to explore potential applications as well as to evaluate the influence of the external magnetic field application on the viscoelastic response of the material. Finally, the framework is implemented in an implicit dynamic FE framework to evaluate the role of inertial terms on the dynamic response of these materials.

Continuum Gating Current Models Computed with Consistent Interactions

The action potential of nerve and muscle is produced by voltage-sensitive channels that include a specialized device to sense voltage. The voltage sensor depends on the movement of charges in the changing electric field as suggested by Hodgkin and Huxley. Gating currents of the voltage sensor are now known to depend on the movements of positively charged arginines through the hydrophobic plug of a voltage sensor domain. Transient movements of these permanently charged arginines, caused by the change of transmembrane potential V, further drag the S4 segment and induce opening/closing of the ion conduction pore by moving the S4-S5 linker. This moving permanent charge induces capacitive current flow everywhere. Everything interacts with everything else in the voltage sensor and protein, and so it must also happen in its mathematical model. A Poisson-Nernst-Planck (PNP)-steric model of arginines and a mechanical model for the S4 segment are combined using energy variational methods in which all densities and movements of charge satisfy conservation laws, which are expressed as partial differential equations in space and time. The model computes gating current flowing in the baths produced by arginines moving in the voltage sensor. The model also captures the capacitive pile up of ions in the vestibules that link the bulk solution to the hydrophobic plug. Our model reproduces the signature properties of gating current: 1) equality of ON and OFF charge Q in integrals of gating current, 2) saturating voltage dependence in the Q(charge)-voltage curve, and 3) many (but not all) details of the shape of gating current as a function of voltage. Our results agree qualitatively with experiments and can be improved by adding more details of the structure and its correlated movements. The proposed continuum model is a promising tool to explore the dynamics and mechanism of the voltage sensor.

An extended continuum model incorporating the electronic throttle dynamics for traffic flow

This study develops a novel continuum model with consideration of the effect of electronic throttle (ET) dynamics to capture the behaviour of vehicles in traffic flow. In particular, the continuum model is proposed by incorporating the opening angle of ET based on the throttle-based full velocity difference model. Theoretical analyses including stability, negative velocity and shock wave are performed systematically. Numerical experiments and comparisons are conducted to verify the performance of the proposed continuum model. Results show that the steady-state performance of the proposed model is improved with respect to the stability. In addition, the proposed model is effective to rapidly dissipate the effect of external perturbation. Also, the phenomenon of negative velocity can be avoided by the proposed model.

Effect of hydrogen on the collective behavior of dislocations in the case of nanoindentation

Most of the studies reported treats the effect of hydrogen on single dislocation line, while models that describe the collective interaction are missing. In this study, hydrogen-induced softening of metallic materials is studied from a perspective of collective behavior of dislocations. Building on the evolution of dislocation density, a hydrogen-informed expanding cavity model is developed for the first time to predict the dynamic evolution of load-displacement curve obtained from nanoindentation tests. Large-scale molecular dynamics simulations on the mechanical behavior of fcc Ni with and without hydrogen (H) charged are performed to calibrate the proposed continuum model. The results show that the H-induced decrease of indentation force is due to that the energy barrier for dislocation nucleation is lowered by the solute drag of the H atmosphere formed around dislocations. Envisioned as a complex non-equilibrium process, it is found that the power-law exponent of the self-organized criticality of dislocations increases due to the insertion of H atoms. Analysis also indicates that H can reduce the probability of dislocation pile-up, thus promote the delivery of dislocations to the surface of specimens during nanoindentation.

A Variational Model for Dislocations at Semi-coherent Interfaces

We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations that compensate the lattice misfit at the interface, and a far field elastic energy, spent to decrease the amount of needed dislocations. We prove that the former scales like the surface area of the interface, the latter like its diameter. The proposed continuum model is deduced from some rigorous derivation from the semi-discrete theory of dislocations. Even if we deal with finite elasticity, linearized elasticity naturally emerges in our analysis since the far field strain vanishes as the interface size increases.

Layered anisotropic liquids: deformation of structures in electric and magnetic fields

On the basis of the analysis of the free energy of a viscoelastic anisotropic layer liquid, a chiral ferroelectric liquid crystal C^∗ , located in a thin cell in a ”bookshelf“ geometry the possibility of the smectic layers periodic distortions in the external magnetic H and electric E fields applied perpendicularly and along the plates, respectively, are investigated. The polar angle θ formed by the unit vector n and the normal a to the smectic planes is fixed, and the appearing Helfrich–Yuro distortions u of the smectic layers are assumed to be small in the proposed continuum model of the liquid ferroelectrics.

A unified statistical model for the human electrocorticogram.

Extracellular field potentials (ECFs) generated in the cerebral cortex span a vast range of spatiotemporal scales. The process(es) leading to this large dynamic range remain debatable. Here we propose a novel statistical description of the amplitude spectrum of the human electrocorticogram (ECoG). Spectral analysis was performed on long-term recordings from epilepsy patients undergoing pre-surgical evaluation with intracranial electrodes. Amplitude spectra were fit with a multi-component Gaussian model on semi-logarithmic axes. The Gaussian formulation provided excellent fits to the data. It also suggested how the changes accompanying the sleep-wake cycle and certain epileptiform transitions could be understood by variation in the parameters of the model. The proposed continuum model synthesizes several previous observations regarding the statistical structure of the resting human ECoG. It offers a conceptual platform for understanding the EEG changes accompanying the sleep-wake cycle and pathologically hypersynchronous behaviour. Statistical characterisation of the spectral distribution of field potentials yield insight into the cortico-cortical interactions that underlie the summated cortical ECFs comprising the ECoG. Such insight is relevant for a synoptic understanding of major state changes in the brain that are diagnosed in clinical practice by visual inspection of the ECoG.

Regularised crack behaviour effects on continuum modelling of quasi-brittle materials under cyclic loading

A continuum model for quasi-brittle materials able to reproduce mechanical phenomena related to cyclic loading is proposed. Specific care is taken to reproduce progressive stiffness recovery and hysteresis effects caused respectively by crack closure and friction. A virtual testing approach is set up to analyse the evolution of microscopic quantities during uni-axial cyclic tests and to justify an original and efficient modelling of these phenomena. Thus, a regularised formulation of the homogenised multiple contact problem induced by the non-simultaneous closure of microscopic cracks is presented. The proposed continuum model is validated by means of member-scale simulations of reversely loaded reinforced concrete shear walls.