Security and defence of mobile systems under impact

The Group “Dynamics and Fracture of Structural Elements” offers its experience in Solid Mechanics analysis for the study of the impact protection of vehicles, aircrafts and persons. The Group activities have a strong research component, in which numerical simulation tools as well as sophisticated experimental techniques are employed. This technological offer could be of interest to automobile companies (impact and collision security), aeronautical companies (impact of external body on fuselage, attack, and fragments o ice) and defence companies (special armours for mobile systems and persons).Contrato Programa de Comercialización e Internacionalización. Sistema Regional de Investigación Científica e Innovación Tecnológica. (Comunidad de Madrid; Universidad Carlos III de Madrid

Analytical modelling of normal and oblique ballistic impact on ceramic/metal lightweight armours

This paper presents a new analytical model developed to simulate ballistic impact of projectiles on ceramic/metal add-on armours. The model is based on Tate and Alekseevskii’s equation for the projectile penetration into the ceramic tile, whilst the response of the metallic backing is modelled following the ideas of Woodward’s and den Reijer’s models. The result is a fully new analytical model that has been checked with data of residual mass and residual velocity of real fire tests of medium caliber projectiles on ceramic/metal add-on armours. Agreement observed between experimental and analytical results confirmed the validity of the model. Therefore, the model developed can be a useful tool for optimisation of ceramic/metal armour design.The authors are indebted to the Research & Development Department of Empresa Nacional Santa Bárbara (Spain) for the performance of the ballistic tests and the X-ray shadowgraphs. This work is part of the EUCLID RTP 3.2 project, supported by the Ministries of Defence of Spain, Denmark, Holland and Italy. The above project has been developed with the collaboration of several companies and research centres of the aforementioned countries.Publicad

An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations

19 pages, 4 figures.The so-called viscoplastic consistency model, proposed by Wang, Sluys and de Borst, is extended here to the integration of a thermoviscoplastic constitutive equation for J2 plasticity and adiabatic conditions. The consistency condition in this case includes not only strain rate but also the effect of temperature on the yield function. Using the backward Euler integration scheme to integrate the constitutive equations, an implicit algorithm is proposed, leading to generalized expressions of the classical return mapping algorithm for J2 plasticity, both for the iterative calculation of the plastic multiplier increment and for the consistent tangent operator when strain rate and temperature are considered also as state variables of the hardening equation. The model was implemented in a commercial finite element code and its performance is demonstrated with the numerical simulation of four Taylor impact tests.This research was done with the financial support of the Comunidad Autónoma de Madrid under Project 07N/0040/2002.Publicad

A new tool based on artificial neural networks for the design of lightweight ceramic–metal armour against high-velocity impact of solids

15 pages, 10 figures.-- MSC2000 codes: 74K99, 74M20, 74S05.Zbl#: Zbl 1168.74396A new tool based on artificial neural networks (ANNs) has been developed for the design of lightweight ceramic–metal armours against high-velocity impact of solids. The tool developed predicts, in real-time, the response of the armour: impacting body arrest or target perforation are determined and, in the latter case, the residual mass and velocity of the impacting body are determined. A large set of impact cases has been generated, by FEM numerical simulation, in order to train and test the ANN. The impact cases consider different impacting body and target geometries, materials and impact velocities, all these parameters varying in a wide range that covers most common impact situations. The behaviour of the ceramic material under impact was simulated using a modified version of the model developed by Cortés et al. The ANN developed has a remarkable prediction ability and therefore it constitutes a complementary methodology to the conventional design techniques.The authors are indebted to the Comunidad Autónoma de Madrid and to the University Carlos III of Madrid for the financial support of this work (CCG07-UC3M/DPI-3395).Publicad

Dynamic analysis and non-standard continualization of a Timoshenko beam lattice

In this paper, a Timoshenko beam lattice, made up of a chain of masses and straight segments, is proposed, considering bending and shear deformation by means of linear rotational and transverse springs, respectively. Different standard and non-standard continualization methods are applied to it, highlighting here for the first time the suitability of taking the coupled discrete governing equations as a starting point for deriving new continuum models. Several novel low order non-classical continuum models are obtained, with the aim of reliably capturing size-effects and reflecting the dispersive behaviour of the discrete system. Low order governing equations prevents the need for extra boundary conditions when finite (bounded) solids are treated. An extensive analysis of the transition frequency, which initiates the shear propagation spectrum, has been carried out, examining its influence for the discrete and non-standard continuum models. The natural frequencies of a finite solid with two different boundary conditions are obtained through an edge treatment applied here for the first time to this kind of lattices, thus making it possible to solve the clamped-free edges configuration. The reliability of these approaches is evaluated by comparing their dynamic behaviours with that of the discrete system (taken as a reference), through both dispersion and vibration analyses, some of the new proposed continuum models successfully capturing the behaviour of the discrete one, even for high wavenumbers. Moreover, the appearance of physical inconsistencies is examined.The authors acknowledge support from MCIN/ AEI /10.13039/501100011033 under Grants numbers PGC2018-098218-B-I00 and PRE2019-088002. FEDER: A way to make Europe. ESF invests in your future

Low-order continualization of an anisotropic membrane lattice with next-nearest interactions. Enhanced prediction of its dynamic behaviour

In this paper, a novel anisotropic membrane lattice with nearest and next-nearest interactions (long-range forces) has been continualized through different standard and non-standard continualization procedures, which enables the development of new non-classical continuum models capable of accurately capturing the scale effects, present in the matter due to its discrete nature. The performance of these continuum models is assessed by means of both dispersion and natural frequencies analyses, where the discrete model is considered as a reference. In addition, the appearance of certain physical inconsistencies in some of the developed models is analysed, concluding that these only appear for those developed with continualizations based on Taylor expansion. Interestingly, the non-standard models suitably capture the dispersive behaviour of the discrete one, without both physical inconsistencies and higher-order spatial derivatives, thus avoiding the need for extra boundary conditions when finite solids are involved.The authors acknowledge support from MCIN/AEI /10.13039/501100011033 under Grants numbers PGC2018-098218-B-I00 and PRE2019-088002. FEDER: A way to make Europe. ESF invests in your future

Novel Enriched Kinetic Energy continuum model for the enhanced prediction of a 1D lattice with next-nearest interactions

In this paper, a novel Enriched Kinetic Energy model is proposed for an enhanced prediction of the dynamic behaviour of a one-dimensional lattice with next-nearest interactions playing an important role. The lattice system here considered is made up of a chain formed by particles equally spaced and connected with nearest and next-nearest neighbours, through linear springs with different stiffness. The ability of the novel model proposed in this work in capturing the dynamic behaviour of the lattice system is compared with that of others presented in the literature, concluding that it is the one that shows the best performance around the limit of the Irreducible Brillouin Zone (small wavelengths) when next-nearest interactions are relevant. For this purpose, natural frequencies provided by the continuum models for the finite solid are compared with those provided by the discrete system, considered as a reference. Moreover, the novel Enriched Kinetic Energy model does not present physical inconsistencies, nor higher-order spatial derivatives in its governing equation, so it does not need non-classical boundary conditions to be solved when finite solids are treated.The authors acknowledge MCIN/ AEI /10.13039/501100011033 for the financial support under Grants numbers PGC2018-098218-B-I00 and PRE2019-088002. FEDER: A way to make Europe. ESF invests in your future

Finite element simulation of steel ring fragmentation under radial expansion

24 pages, 25 figures.This paper presents a numerical analysis of the expansion of a mild steel ring with of 50 mm diameter, 1 mm thickness and a cross section of 1 mm2. A hardening relation which takes into account strain, strain rate and temperature is proposed to define precisely the thermoviscoplastic behaviour of the material considered in the study. As a second step, an algorithm to integrate the thermoviscoplastic constitutive equations, including the hardening law, is implemented in the commercial finite element code ABAQUS/Explicit via a user subroutine. Finally, this tool is used to simulate the problem of a ring expanding radially in a broad range of strain rates, covering both low and high initial velocities (from 1 to 370 m/s). The aim is to analyse the effect of loading velocity on the number of fragments resulting from the multiple failure of the ring and also the influence of the hardening behaviour of the material on the number of fragments and on the failure mode of the ring, considering different values of the plastic strain hardening exponent n0. A simple failure criterion was used, based on a critical value of the equivalent strain which depends on the hardening exponent. The numerical predictions, in perfect agreement with the experimental observations, are compared with several analytical or numerical models used to solve the same problem in other materials such as aluminium, steel or copper.Publicad

A proposal for a membrane model for the small deformations of a spider orb-web

Abstract In this paper we propose a continuum membrane model for the infinitesimal deformation of a spider orb-web. The model is derived in the context of axially-symmetric webs formed by radial threads connected with circumferential threads belonging to concentric circles. The continuous model inherits a specific fibrous structure from the original discrete web. In particular, a singularity arises at the centre of the membrane as a consequence of the intensification of the density of radial threads towards the centre of the web. Under suitable assumption on the tensile pre-stress acting in the referential configuration, the out-of-plane free transverse vibrations of a circular orb-web supported at the boundary are studied in detail. The accuracy of the model in describing a discrete spider web is numerically investigated

Using an analytical model of simulation in the design of light-weight armours

9 pages, 13 figures.This paper presents a model for the simulation of the impact of projectiles of high kinetic energy on lightweight ceramic/metal armours. The work was financed jointly by the Defence Ministries of Spain, Italy, Holland and Denmark as part of a project among nations for the development of tools for the design of this type of armour. The model consists of a series of differential equations incorporating the most essential phenomena of the impact process, formulated after a close study of a series of real fire tests. It features a nucleus of calculation into which the equations may in time be integrated, and may also include a user interface. This practical, preliminary design tool's efficacy is amply confirmed by test results.The authors are indebted to the Research & Development Department of Empresa Nacional Santa Bárbara (Spain) for the performance of the ballistic tests and the X-ray shadowgraphs. This work is part of the EUCLID RTP 3.2 project, supported by the Ministries of Defence of Spain, Denmark, Holland and Italy. The above project has been developed with the collaboration of several companies and research centres of the aforementioned countries.Publicad