Inelastic Model Research Articles

Surface erosion of BaF2 thin films under SHI irradiation: Angular distribution and role of different substrates

In the present report, the surface erosion of the thin films of barium fluoride (BaF2) deposited on different substrates (Glass, Silicon, and Aluminum) using the electron beam evaporation method, has been investigated under swift heavy ions irradiation employing experimental and theoretical aspects. The experiments have been carried out at room temperature using normally incident 100 MeV Au+28 ions. Rutherford backscattering spectrometry has been employed to estimate the sputtering yield and angular distribution of sputtering yield has been obtained using the unique catcher technique approach. The variation of sputtering yield at different angles shows an isotropic distribution superimposed with enhanced sputtering at surface normal. The sputtering studies in the thin films on different substrates show that the maximum sputtering takes place for glass (insulator) substrate while minimum sputtering occurs for the aluminum (metal) substrate. Simulations based on the inelastic thermal spike model have been performed to compare the observed experimental findings. The temperature spike generated in Al will smear out more efficiently and quickly because of its high thermal conductivity as compared to Si and glass substrates resulting in less contribution to the temperature spike generated in the film and thus causing lower sputtering yield for Al substrate.

A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains

Maxwellian-type rheological models of inelastic effects of creep type at large strains are revisited in relation to inelastic strain gradient theories. In particular, we observe that a dependence of the stored energy density on inelastic strain gradients may lead to spurious hardening effects, preventing the model from accommodating large inelastic slips. The main result of this paper is an alternative inelastic model of creep type, where a higher-order energy contribution is provided by the gradients of the elastic strain and of the plastic strain rate, thus preventing the onset of spurious hardening under large slips. The combination of Kelvin–Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model. The existence of weak solutions is proved by way of a Faedo–Galerkin approximation.

Seismic barriers filled with granular metamaterials: Mathematical models for granular metamaterials

The problem of seismic protection from the main types of surface acoustic waves and shear–pressure (SP) evanescent waves emanating from vicinity of an epicenter of an earthquake is discussed. Herein, SP waves represent a kind of the evanescent waves arising at critical angles of incident of bulk shear waves. The proposed seismic protection method utilizes vertical trenches (vertical barriers) filled with the specially constructed granular metamaterials. Some of nonlinear hyperelastic models along with nonlinear and inelastic models are analyzed for applications using granular metamaterials in case of cyclic dynamic loadings that correspond to arrival of the large intensity surface acoustic and evanescent waves. The main attention is paid to arrival of the large intensity Rayleigh, Rayleigh–Lamb and SP waves, as the most frequent waves and the most dangerous waves for engineering structures. Some of the new constitutive equations for metamaterials exhibiting different elastic moduli at tension and compression phases are proposed and discussed.

Dark matter models for the 511 keV galactic line predict keV electron recoils on Earth

We propose models of Dark Matter that account for the 511 keV photon emission from the Galactic Centre, compatibly with experimental constraints and theoretical consistency, and where the relic abundance is achieved via p-wave annihilations or, in inelastic models, via co-annihilations. Due to the Dark Matter component that is inevitably upscattered by the Sun, these models generically predict keV electron recoils at detectors on Earth, and could naturally explain the excess recently reported by the XENON1T collaboration. The very small number of free parameters make these ideas testable by detectors like XENONnT and Panda-X, by accelerators like NA64 and LDMX, and by cosmological surveys like the Simons observatory and CMB-S4. As a byproduct of our study, we recast NA64 limits on invisibly decaying dark photons to other particles.

Force-based seismic design of steel haunch retrofit for RC frames

The paper presents a simplified force-based seismic design procedure for the preliminary design of steel haunch retrofitting for the seismic upgrade of deficient RC frames. The procedure involved constructing a site-specific seismic design spectrum for the site, which is transformed into seismic base shear coefficient demand, using an applicable response modification factor, that defines base shear force for seismic analysis of the structure. Recent experimental campaign; involving shake table testing of ten (10), and quasi-static cyclic testing of two (02), 1:3 reduced scale RC frame models, carried out for the seismic performance assessment of both deficient and retrofitted structures has provided the basis to calculate retrofit-specific response modification factor Rretrofitted. The haunch retrofitting technique enhanced the structural stiffness, strength, and ductility, hence, increased the structural response modification factor, which is mainly dependent on the applied retrofit scheme. An additional retrofit effectiveness factor (ΩR) is proposed for the deficient structure's response modification factor Rdeficient, representing the retrofit effectiveness (ΩR=Rretrofitted /Rdeficient), to calculate components' moment and shear demands for the retrofitted structure. The experimental campaign revealed that regardless of the deficient structures' characteristics, the ΩR factor remains fairly the unchanged, which is encouraging to generalize the design procedure. Haunch configuration is finalized that avoid brittle hinging of beam-column joints and ensure ductile beam yielding. Example case study for the seismic retrofit designs of RC frames are presented, which were validated through equivalent lateral load analysis using elastic model and response history analysis of finite-element based inelastic model, showing reasonable performance of the proposed design procedure. The proposed design has the advantage to provide a seismic zone-specific design solution, and also, to suggest if any additional measure is required to enhance the strength/deformability of beams and columns.

Nonlinear pile-head macro-element for the seismic analysis of structures on flexible piles

Performance-based design (PBD) procedures require accurate estimates of both maximum and residual displacements in structural systems. Macro-element models are already proven tools for designing structures on shallow foundations according to PBD, since they represent a very cost-effective solution in terms of balance between physical behaviour, simulation accuracy and computational cost. This work extends the macro-element approach to the analysis of laterally loaded pile-shafts and soil-pile-structure interaction. The lateral response of the entire soil-pile system to seismic actions is thus condensed at the pile-head, being represented by a zero-length element located at the base of the columns and subjected to the foundation input motion. The macro-element model is presented, based on the three fundamental features of the response of laterally loaded piles: initial elastic behaviour, gap opening/closure effects and failure conditions. These three characteristic behaviours are all made compatible by using an inelastic model which accounts for the evolution from initial nonlinear elastic behaviour to full plastic flow at failure. Such inelastic model is based on a bounding surface plasticity theory formulation that ensures a smooth transition from the initial elastic pile-head response up to nonlinear behaviour and plastic mechanism formation. In order to validate the macro-element, its response is favourably compared with numerical results from advanced simulations of pile lateral behaviour and with load tests on real piles.

Comparison of second-order serendipity and Lagrange tetrahedral elements for nonlinear explicit methods

This paper evaluates the performances of second-order finite elements for nodal lumped-mass explicit methods in nonlinear solid dynamics, with a particular emphasis on 10-node “serendipity” and 15-node “Lagrange” tetrahedral elements. Historically, many nonlinear explicit finite element codes have exclusively used first-order elements, until a fairly recent flurry of activity that has resulted in higher-order elements becoming available in explicit codes including the authors' in-house one, ParaAble, and the production software EPIC, IMPETUS, LS-DYNA, and Abaqus. A major attractiveness of tetrahedrons is their ease in meshing and higher-order elements can facilitate the avoidance of severe volumetric locking with unstructured C0 meshes, which are generally used with these codes for the discontinuities of inelasticity, contact, etc. They also can improve modeling of flexure and curved shapes as well as eliminate spurious modes without artificial stabilization. The inclusion of face and body centroid nodes with Lagrange interpolants, including the 15-node tetrahedron, has proven to provide robust overall performance with lumped-mass explicit methods and with contact. Nevertheless, versions of the 10-node tetrahedron have also emerged in lumped-mass explicit software. In contrast to hexahedrons, an important observation about tetrahedrons is that the 10-node serendipity version uses about four times fewer quadrature points and a larger time increment than their 15-node Lagrange counterpart, which could result in tremendous computational differences. Serendipity elements, however, notoriously do not nodal mass lump well and tetrahedron versions have not been rigorously evaluated/documented for their effectiveness, as will be done herein with comparisons of those using 15-node tetrahedrons. Using row-summation lumping for Lagrange elements and the ad hoc HRZ scheme for serendipity ones, performances are assessed in common benchmark problems and practical applications using various elastic and inelastic material models and involving large strains/deformations/rotations and severe distortions. Whereas the 10-node tetrahedrons were found to perform much better than their 20-node serendipity hexahedral counterparts, specifically with substantial computational reductions and reasonable predictions, they are not generally quite as accurate or robust as the 15-node tetrahedral elements. The results thus indicate benefits of including both 10- and 15-node tetrahedrons in an explicit code's element library.

Mathematical modeling of dynamic related processes based on the finite element techniques

In the process of investigation the functioning of information systems with the help of mathematical modeling, problems can arise that are solved using finite element techniques. For example, In the present work we solved the axially symmetric dynamic problem of related phenomena under microscale thermal loading. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The nonlinear behavior of a material is described by the unified model of flow. The problem is solved numerically by the time step integration method, iterative method and finite element method. Equations of the evolution for the inelastic flow model are integrated by the second-order Euler implicit method with the use of the rule of «middle point». The system of nonlinear transcendental equations obtained in each time step is solved by the method of simple iteration. To accelerate convergence, we apply the Stephensen – Aitken procedure. The equations of motion are integrated by the Newmark method, whereas the heat-conduction equation is integrated by the first-order implicit method. The problem of heat-conduction is linearized by finding the temperature-dependent thermal characteristics according to the temperature distribution in the previous time step or previous iteration. The main results obtained in the work are the following: quantitative estimations of temperature effects of thermostructural-mechanical coupling, which are caused by volumetric thermoelastic effect, dissipation of mechanical energy and hidden heat are obtained.

Порівняльний аналіз лінійного та нелінійного правил сумішей при моделюванні напруженого стану півпростору

In the present work we solve the axially symmetric problem of a half-space under thermal loading. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The thermomechanical behavior of an isotropic material is described by the Bodner–Partom unified model of flow generalized in the case of microstructure influence on inelastic characteristics of steel. To determine the parameters of the model corresponded to yield stress and yield strength the mixture rule is utilized. The problem is solved with using the finite element technique. The numerical realization of our problem is performed with the help of step-by-step time integration. Equations of the evolution for the inelastic flow model are integrated by the second-order Euler implicit method. The equations of motion are integrated by the Newmark method, whereas the heat-conduction equation is integrated by the first-order implicit method. We use quadrangular isoparametric elements. The parameters of a fine grid are chosen with the help of the criterion of practical convergence of the solutions. The stress state taking into account linear and nonlinear rules of mixtures is described.

Dark Matter production in association with dilepton resonance from heavy Z’ decay using Monte Carlo simulation

In the present work, we search for Dark Matter candidates generated in association with the Z 0 boson, in events with large missing transverse momentum produced in proton-proton collisions at the Large Hadron Collider, using Monte Carlo simulation, at total integrated luminosity of 136.2 f b −1 and center-of-mass energy of 13 TeV. The signal is evaluated from three new physics scenarios beyond standard model of dark matter with Z' boson as a final-state radiation, and they are: Dark Higgs model, Light vector model and the light Z' with inelastic effective field theory coupling model. The three models assume that the Z' is coupled to new dark sector states, which might be a candidate or decaying to a candidate suitable to be the dark matter. The dark matter candidate is supposed to have mass of order GeV to few TeV. The Z’ boson is considered to decay leptonically. The dileptons invariant mass and the missing transverse momentum distributions are studied before and after selection conditions of the resonance event. The significances of the three models will be tested.

Learning data-driven reduced elastic and inelastic models of spot-welded patches

Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.

Investigating the effects of inelastic soil–foundation interface response on the seismic demand of soil–structure systems

The effect of inelastic response of the soil–foundation interface is explored on the seismic demand of structures attached on top of shallow foundations. An ensemble of 20 strong ground motions recorded on National Earthquake Hazards Reduction Program site class D was employed for analyzing soil–structure systems with the Winkler foundation model and an equivalent single-degree-of-freedom system as the superstructure. Results show that there are key parameters that control the amount of difference between the elastic and inelastic modeling of the soil at the soil–foundation interface. Depending on the structural aspect ratio, the elastic modeling leads to an overestimated result for the total lateral displacement demands. Also, more than 50% reduction in the superstructure demands is desired when nonlinear soil modeling is considered and foundation sliding is allowed. The benefits from the “shrinking-dominated rocking motion” can be acquired with inelastic soil material that limits the transferred inertial force into the superstructure.

Structural modifications of boron carbide irradiated by swift heavy ions

Boron carbide (B4C) behavior under irradiation is widely studied in order to predict the lifetime of this material in future (Generation IV) nuclear fission reactors. This paper is focused on the effects of high electronic stopping powers (Se) on B4C structure modifications. Sintered B4C samples were irradiated at room temperature with swift heavy ions (between 0.5 and 3 MeV·u − 1) corresponding to Se values in the 4.1 to 15.4 keV·nm−1 range at the sample surface. In order to investigate the structural changes as a function of depth, transmission electron microscopy and Raman mapping were performed on the irradiated samples along the path of the incident ions. For the highest Se values, damage results in the creation of large hillocks at the sample surface along with the amorphization of the bulk. These results are explained, in the frame of the inelastic thermal spike model, by local melting in latent tracks that are created only when irradiations are performed above a Se threshold evaluated at around 9 keV nm−1.

Numerical study and strength model of concrete-filled high-strength tubular flange beam under mid-span load

High-strength steels (HSS) have been increasingly used in building and bridges due to their advantages, such as lightening the self-weight and reducing the carbon emissions. However, these benefits cannot be fully utilised for long-span flexural members because of lateral–torsional buckling (LTB). For an improved buckling resistance, a new concrete-filled high-strength tubular flange beam (HS-CFTFB) is formed, and its strength is theoretically and numerically studied. Theoretical models of the HS-CFTFB are derived to estimate the full plastic strength and the elastic LTB strength. The finite-element models are then built to determine the buckling factor in the inelastic LTB strength model. The FE models are validated and found to be in good agreement experimental results. With these verified numerical models, a comprehensive parametric study is conducted to investigate the effect of geometric and material properties of HS-CFTFBs. Finally, the design formula of HS-CFTFBs and its scope of application are determined on the basis of a parametric study.

Sustainability Characteristics of Damaged Carbon Fiber Composites

Usage of composites has increased in many fields of application ranging from space to repair and rehabilitation. Damage of composites in the form of cracking or de-lamination is quite common during its life. Performance of the composites after damage with or without repair is an indicator to one of its sustainability aspects. Here in this study, the damage parameter from the point of cracking is studied beyond normal yield considerations using inelastic material model to assess its remaining life. It is observed that, based on the load quantity of damage occurrence, sustainability is measured as life cycle analysis in terms of remaining life that can change significantly if one accounts for inelastic material behaviour.

Inelastic background modelling applied to hard X-ray photoelectron spectroscopy of deeply buried layers: A comparison of synchrotron and lab-based (9.25 keV) measurements

Hard X-ray Photoelectron Spectroscopy (HAXPES) provides minimally destructive depth profiling into the bulk, extending the photoelectron sampling depth. Detection of deeply buried layers beyond the elastic limit is enabled through inelastic background analysis. To test the robustness of this technique, we present results on a thin (18 nm) layer of metal–organic complex buried up to 200 nm beneath organic material. Overlayers with thicknesses 25–140 nm were measured using photon energies ranging 6–10 keV at the I09 end station at Diamond Light Source, and a new fixed energy Ga Kα (9.25 keV) laboratory-based HAXPES spectrometer was also used to measure samples with overlayers up to 200 nm thick. The sampling depth was varied: at Diamond Light Source by changing the photon energy, and in the lab system by performing angle-resolved measurements. For all the different overlayers and sampling depths, inelastic background modelling consistently provided thicknesses which agreed, within reasonable error, with the ellipsometric thickness. Relative sensitivity factors were calculated, and these factors consistently provided reasonable agreement with the expected nominal stoichiometry, suggesting the calculation method can be extended to any element. These results demonstrate the potential for the characterisation of deeply buried layers using synchrotron and laboratory-based HAXPES.

Inelastic Dark Matter and the SABRE experiment

We present here the sensitivity of the SABRE (Sodium iodide with Active Background REjection) experiment to benchmark proton-philic, spin dependent, Inelastic Dark Matter models previously proposed due to their lowered tension with existing experimental results. We perform fits to cross section, mass, and mass splitting values to find the best fit to DAMA/LIBRA data for these models. In this analysis, we consider the Standard Halo Model (SHM), as well as an interesting extension upon it, the SHM+Stream distribution, to investigate the influence of the Dark Matter velocity distribution upon experimental sensitivity and whether or not its consideration may be able to help relieve the present experimental tension. Based on our analysis, SABRE should be sensitive to all the three benchmark models within 3–5 years of data taking.

Commutative-symmetrical elastic–plastic stretch-tensor products and their rates

The commutative-symmetrical elastic–plastic stretch-tensor product and the multiplicative Bilby-Kröner-Lee decomposition of a deformation gradient are compared to one another in particular with respect to the corresponding time derivatives and tensor rates. It turns out that these multiplicative deformation-tensor models differ with respect to the elastic response just for a Lagrangean point of view and coincide for an Eulerian perspective. The uniqueness of the constitutive equations requires symmetric plastic-flow rules for commutative-symmetrical elastic–plastic stretch-tensor products and non-symmetric plastic-flow rules for multiplicative Bilby-Kröner-Lee formulations. Further, the author discusses whether a plastic rotation tensor—implied from a non-symmetric plastic-flow rule—is appropriate for a proper finite-plasticity formulation of polycrystalline metals and whether at all a plastic rotation is a material-dependent property in this context. A proper elasto-plasticity/-inelasticity model may be constituted for a symmetric plastic-flow rule in conjunction with a commutative-symmetrical elastic–plastic stretch-tensor product, which inherently includes even the simultaneous modeling of finite-elastic and finite-plastic/-inelastic orthotropy.

A thermal–hydromechanical coupled model for poro-viscoplastic saturated freezing soil

Most existing thermal–hydromechanical (THM) models used to describe the process of frost heave assumed the freezing soil to be elastic. However, an inelastic constitutive model capable of reflecting the viscous constitutive behaviour of freezing soils should be considered. Based on the existing mathematical model, this study presented an improved mathematical model of coupled water, heat, and stress for saturated freezing soil, in which the soil was assumed to be elastic-viscoplastic and its viscoplasticity was modelled by means of a simple (linear) Norton–Hoff’s law. In addition, solid–fluid interface energy was considered to formulate the effective water and ice pressures and liquid–crystal equilibrium condition which can be used to explain the micro-cryosuction mechanism was adopted to replace Clapyron equation which were used in most existing models. To solve the nonlinear governing equations, numerical simulations were performed using COMSOL software. Finally, the improved model was validated by comparing its simulation results with reference model and the distribution curves of frost heave, temperature, water content and flux rate were discussed.

The impact of inelastic self-interacting dark matter on the dark matter structure of a Milky Way halo

Abstract We study the effects of inelastic dark matter self-interactions on the internal structure of a simulated Milky Way (MW)-size halo. Self-interacting dark matter (SIDM) is an alternative to collisionless cold dark matter (CDM) which offers a unique solution to the problems encountered with CDM on sub-galactic scales. Although previous SIDM simulations have mainly considered elastic collisions, theoretical considerations motivate the existence of multi-state dark matter where transitions from the excited to the ground state are exothermic. In this work, we consider a self-interacting, two-state dark matter model with inelastic collisions, implemented in the Arepo code. We find that energy injection from inelastic self-interactions reduces the central density of the MW halo in a shorter timescale relative to the elastic scale, resulting in a larger core size. Inelastic collisions also isotropize the orbits, resulting in an overall lower velocity anisotropy for the inelastic MW halo. In the inner halo, the inelastic SIDM case (minor-to-major axis ratio s ≡ c/a ≈ 0.65) is more spherical than the CDM (s ≈ 0.4), but less spherical than the elastic SIDM case (s ≈ 0.75). The speed distribution f(v) of dark matter particles at the location of the Sun in the inelastic SIDM model shows a significant departure from the CDM model, with f(v) falling more steeply at high speeds. In addition, the velocity kicks imparted during inelastic collisions produce unbound high-speed particles with velocities up to 500 km s−1 throughout the halo. This implies that inelastic SIDM can potentially leave distinct signatures in direct detection experiments, relative to elastic SIDM and CDM.