Papers by Savvas Triantafyllou
Intelligent Systems, Control and Automation: Science and Engineering, 2018
This review chapter outlines the outcomes of a combined experimentalnumerical investigation on th... more This review chapter outlines the outcomes of a combined experimentalnumerical investigation on the retrofitting of masonry structures by means of polymeric textile reinforcement. Masonry systems comprise a significant portion of cultural heritage structures, particularly within European borders. Several of these systems are faced with progressive ageing effects and are exposed to extreme events, as for instance intense seismicity levels for structures in the center of Italy. As a result, the attention of the engineering community and infrastructure operators has turned to the development, testing, and eventual implementation of effective strengthening and protection solutions. This work overviews such a candidate, identified as a full-coverage reinforcement in the form of a polymeric multi-axial textile. This investigation is motivated by the EU-funded projects Polytect and Polymast, in the context of which this protection solution was developed. This chapter is primarily concerned with the adequate simulation and verification of the retrofitted system, in ways that are computationally affordable yet robust in terms of simulation accuracy. To this end, finite element based mesoscopic and multiscale representations are here overviewed and discussed within the context of characterization, identification and performance assessment.
In this work we propose a general theoretic framework for the derivation of constitutive equation... more In this work we propose a general theoretic framework for the derivation of constitutive equations for dual-phase steels, undergoing continuum finite deformation. The proposed framework is based on the generalized plasticity theory and comprises the following three basic characteristics: 1.A multiplicative decomposition of the deformation gradient into elastic and plastic parts. 2.A hyperelastic constitutive equation 3.A general formulation of the theory which prescribes only the number and the nature of the internal variables, while it leaves their evolution laws unspecified. Due to this generality several different loading functions, flow rules and hardening laws can be analyzed within the proposed framework by leaving its basic structure essentially unaltered. As an application, a rather simple material model, which comprises a von-Mises loading function, an associative flow rule and a non-linear kinematic hardening law, is proposed. The ability of the model in simulating simplif...
Computer Methods in Applied Mechanics and Engineering, 2019
A novel phase field material point method is introduced for robust simulation of dynamic fracture... more A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly defined crack density functional. The particular case of impact driven fracture is treated by employing a discrete field approach within the material point method setting. In this, the equations of motion and phase field governing equations are solved independently for each discrete field using a predictor-corrector algorithm. Contact at the interface is resolved through frictional contact conditions. The proposed method is verified using analytical predictions. The influence of surface energy anisotropy and loading conditions on the resulting crack paths is assessed through a set of benchmark problems. Comparisons are made with the standard Phase Field Finite Element Method and experimental observations.
Applied Sciences, 2019
Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), ... more Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.
Archive of Applied Mechanics, 2017
A blocked Hamiltonian Schur decomposition is herein proposed for the solution process of the Scal... more A blocked Hamiltonian Schur decomposition is herein proposed for the solution process of the Scaled Boundary Finite Element Method (SBFEM), which is demonstrated to comprise a robust simulation tool for Linear Elastic Fracture Mechanics (LEFM) problems. By maintaining Hamiltonian symmetry increased accuracy is achieved, resulting in higher rates of convergence and reduced computational toll, while the former need for adoption of a stabilizing parameter and, inevitably user-supervision, is alleviated. The method is further enhanced via adoption of superconvergent patch recovery theory in the formulation of the stress intensity factors. It is shown that in doing so, superconvergence, and in select cases ultraconvergence, is succeeded in the Stress Intensity Factors (SIFs) calculation. Based on these findings, a novel error estimator for the stress intensity factors within the context of SBFEM is proposed. To investigate and assess the performance of SBFEM in the context of linear elastic fracture mechanics, the method is contrasted against the Finite Element Method (FEM) and the eXtended Finite Element Method (XFEM) variants. The comparison, carried out in terms of computational toll and accuracy for a number of applications, reveals SBFEM as a highly performant method.
Archive of Applied Mechanics, 2017
A novel phase field formulation implemented within a material point method setting is developed t... more A novel phase field formulation implemented within a material point method setting is developed to address brittle fracture simulation in anisotropic media. The case of strong anisotropy in the crack surface energy is treated by considering an appropriate variational, i.e., phase field approach. Material point method is utilized to efficiently treat the resulting coupled governing equations. The brittle fracture governing equations are defined at a set of Lagrangian material points and subsequently interpolated at the nodes of a fixed Eulerian mesh where solution is performed. As a result, the quality of the solution does not depend on the quality of the underlying finite element mesh and is relieved from mesh-distortion errors. The efficiency and validity of the proposed method is assessed through a set of benchmark problems.
Mechanical Systems and Signal Processing, 2017
Problems that result into locally non-differentiable and hence non-smooth state-space equations a... more Problems that result into locally non-differentiable and hence non-smooth state-space equations are often encountered in engineering. Examples include problems involving material laws pertaining to plasticity, impact and highly non-linear phenomena. Estimating the parameters of such systems poses a challenge, particularly since the majority of system identification algorithms are formulated on the basis of smooth systems under the assumption of observability, identifiability and time invariance. For a smooth system, an observable state remains observable throughout the system evolution with the exception of few selected realizations of the state vector. However, for a non-smooth system the observable set of states and parameters may vary during the evolution of the system throughout a dynamic analysis. This may cause standard identification (ID) methods, such as the Extended Kalman Filter, to temporarily diverge and ultimately fail in accurately identifying the parameters of the system. In this work, the influence of observability of non-smooth systems to the performance of the Extended and Unscented Kalman Filters is discussed and a novel algorithm particularly suited for this purpose, termed the Discontinuous Extended Kalman Filter (DEKF), is proposed.
International Journal for Numerical Methods in Engineering, 2017
SummaryThe material point method for the analysis of deformable bodies is revisited and originall... more SummaryThe material point method for the analysis of deformable bodies is revisited and originally upgraded to simulate crack propagation in brittle media. In this setting, phase‐field modelling is introduced to resolve the crack path geometry. Following a particle in cell approach, the coupled continuum/phase‐field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, ie, non‐evolving, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying finite element mesh and relieved from corresponding mesh‐distortion errors. A staggered incremental procedure is implemented for the solution of the discrete coupled governing equations of the phase‐field brittle fracture problem. The proposed method is verified through a series of benchmark tests while comparisons are made between the proposed scheme, the corresponding finite element implementation, and experimental results.
Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures, 2016
In this work, a study of computational and implementational efficiency is presented, on the treat... more In this work, a study of computational and implementational efficiency is presented, on the treatment of Linear Elastic Fracture Mechanics (LEFM) problems. To this end, the Scaled Boundary Finite Element Method (SBFEM), is compared against the popular eXtended Finite Element Method (XFEM) and the standard FEM approach for efficient calculation of Stress Intensity Factors (SIFs). The aim is to examine SBFEM's potential for inclusion within a multiscale fracture mechanics framework. The above features will be exploited to solve a series of benchmarks in LEFM comparing XFEM, SBFEM and commercial FEM software to analytical solutions. The extent to which the SBFEM lends itself for inclusion within a multiscale framework will further be assessed.
The Journal of Strain Analysis for Engineering Design, 2015
A framework for the development of accurate yet computationally efficient numerical models is pro... more A framework for the development of accurate yet computationally efficient numerical models is proposed in this work, within the context of computational model validation. The accelerated computation achieved herein relies on the implementation of a recently derived multiscale finite element formulation, able to alternate between scales of different complexity. In such a scheme, the micro-scale is modeled using a hysteretic finite element formulation. In the micro-level, nonlinearity is captured via a set of additional hysteretic degrees of freedom compactly described by an appropriate hysteric law, which gravely simplifies the dynamic analysis task. The computational efficiency of the scheme is rooted in the interaction between the micro- and a macro-mesh level, defined through suitable interpolation fields that map the finer mesh displacement field to the coarser mesh displacement field. Furthermore, damage-related phenomena that are manifested at the micro-level are accounted for,...
Computational Methods in Applied Sciences, 2015
In this work, a three dimensional multiscale formulation is presented for the analysis of masonry... more In this work, a three dimensional multiscale formulation is presented for the analysis of masonry structures based on the multiscale finite element formulation. The method is developed within the framework of the Enhanced Multiscale Finite Element Method. Through this approach, two discretization schemes are considered, namely a fine mesh that accounts for the micro-structure and a coarse mesh that encapsulates the former. Through a numerically derived mapping, the fine scale information is propagated to the coarse mesh where the numerical solution of the governing equations is performed. Inelasticity is introduced at the fine mesh by considering a set of internal variables corresponding to the plastic deformation accumulating at the Gauss points of each fine-scale element. These additional quantities evolve according to properly defined smooth evolution equations. The proposed formalism results in a nonlinear dynamic analysis method where the micro-level state matrices need only be evaluated once at the beginning of the analysis procedure. The accuracy and computational efficiency of the proposed scheme is verified through an illustrative example.
Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures, 2014
In this work, a multiscale finite element scheme is proposed for the nonlinear dynamic analysis o... more In this work, a multiscale finite element scheme is proposed for the nonlinear dynamic analysis of structures based on the hysteretic finite element method. Through this approach, an advanced non-linear multiscale formulation is derived where the state matrices, namely the mass and stiffness matrix of the microstructures, need to be evaluated only once at the beginning of the analysis and remain constant throughout the analysis procedure. Nonlinearity is accounted for at the microlevel by defining additional hysteretic degrees of freedom that evolve according to properly defined evolution equations such as the Bouc-Wen model or the Preisach model of hysteresis. Since the nature of composite materials comes with significant uncertainties as to the properties of the individual constituents the validity of the model is confirmed through a Monte Carlo simulation, comparing the sensitivity of the proposed hysteretic scheme to that of a detailed fine mesh FE simulation, with regard to the coefficients of variation of the elastic properties of the constituents. The latter is of great importance considering the stochasticity involved in defining the properties of such complex materials.
Vulnerability, Uncertainty, and Risk, 2014
Composite materials are being implemented in numerous engineering applications including, though ... more Composite materials are being implemented in numerous engineering applications including, though not limited to, the aerospace, auto-mobile and wind turbine industries. Advancements in manufacturing processes enable the production of composites whose macroscopically observed properties are elaborately determined at the microscale. Composites are therefore inherently multiscale materials. Consequently, the reliability of structural systems being comprised of composites heavily depends on the micro-mechanical properties of the latter. In this work, a methodology is presented for the evaluation of failure probabilities of composite structures. The hysteretic multiscale finite element method (HMsFEM) is implemented for the modelling of composites while the subset simulation method is used to evaluate the corresponding probabilities of failure. In the HMsFE method, the nonlinear behaviour of the constituents is accurately modelled in the fine scale, while global solution of the structure is performed in a macro-scale thus significantly reducing the computational cost of the reliability analysis procedure.
In this work, an alternative rod element formulation is proposed for the nonlinear dynamic analys... more In this work, an alternative rod element formulation is proposed for the nonlinear dynamic analysis of trusses. The classical, geometrically nonlinear elastic rod element formulation is extended by implicitly defining new, hysteretic, degrees of freedom, subjected to an evolution equation of the Bouc Wen type with kinematic hardening. An interpolation field is proposed for the new degrees of freedom, which are regarded as hysteretic strains. By means of the principle of virtual work a geometrically nonlinear elastoplastic stiffness matrix is derived. This stiffness matrix together with the hysteretic evolution equations fully describes the constitutive behavior of the element. Solutions are obtained by simultaneously solving the three sets of governing equations of the structure, namely the global equilibrium equations, global compatibility equations and local constitutive equations. A Livermore solver for stiff differential equations is implemented. Following this approach, the linearization of the constitutive relations is avoided, contrary to the usual step-by-step solution approaches. Furthermore, stability problems can be studied as a dynamic phenomenon. The efficiency of the proposed method is demonstrated with a characteristic example.
Computational Mechanics, 2014
A new multiscale finite element formulation is presented for nonlinear dynamic analysis of hetero... more A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments.
Proceedings of the Ninth International Conference on Computational Structures Technology
In this paper, a new framework of form finding and structural optimizations for tensile domes was... more In this paper, a new framework of form finding and structural optimizations for tensile domes was developed using a cutting-edge parametric modelling tool Grasshopper in Rhino. The detailed exploration of this new techniques is presented. It is found that the use of this parametric tool allows a more intuitive, rapid and flexible design. Structural optimisation of the member sizes, topology and surface can be explored easily at an initial design stage in a project. Therefore, the proposed new framework provides a more effective and efficient way for form finding and structural optimization. Based on the new method, a prototype Tensile dome which is to replicate the existing Tensile Dome Georgia dome is designed and analyzed. The structural behavior of the cable domes is investigated. Using this new framework, two ellipse shape Tensile domes with new geometrical configuration are developed. They exhibit enhanced load bearing capacity, therefore can be used the future long span structure projects.
Solid Mechanics and its Applications, 2006
... By combining such elements one assembles multi-storey plane frames, which are linked ... stre... more ... By combining such elements one assembles multi-storey plane frames, which are linked ... stress redistribution which occurs due to the non linear behaviour of the ... Diploma Thesis, (2004), «Inelastic analysis of multistory buildings with a Bouc-Wen type hysteretic model», NTUA. ...
The phase-field paradigm provides a robust damage modelling approach which is equipped with capab... more The phase-field paradigm provides a robust damage modelling approach which is equipped with capabilities of automatically predicting initiation, propagation, branching and merging of complex curvilinear crack topologies. To this point, phase-field modelling has been widely applied to study brittle fractures based on Griffith's theory, with some extensions also to ductile and cohesive fractures. Despite its immense popularity, its application to complex high-performance materials, for e.g. composites, has been limited. This is because most composites are not brittle in the Griffith's sense. Rather, they display quasi-brittle fracture characteristics wherein a crack is driven by cohesive forces present within the fracture process zone, which spans over a domain sufficiently large in comparison to the overall structure. As a result, industrial applications of phase-field method for composites using commercial software has not been much widespread, also due to its requirements o...
In this work, a Material Point Method (MPM) is employed for the analysis of rocking body dynamics... more In this work, a Material Point Method (MPM) is employed for the analysis of rocking body dynamics. MPM is effectively an Arbitrary Lagrangian Eulerian scheme where the continuum is represented by a set of material points that are moving within a fixed computational grid; solution of the governing equations is performed in this grid considering an appropriate mapping. To accurately account for the contact dynamics between the bodies, a discrete field approach is adopted whereby each deformable domain is treated independently whereas impenetrability constraints and a Coulomb friction model are introduced to account for the contact at the interface. The proposed scheme is used to simulate the rocking response of a rigid body on an elastic-half space and comparisons are made with the Inverted Pendulum and Winkler rocking models.
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Papers by Savvas Triantafyllou
frictionless guide and the other moving along a parabola. This configuration gives rise to a restoring force in the form of a cubic order polynomial of the displacement and sets the mass to a non-linear dynamic behavior described by the Duffing equation. By adding a viscous damper in the perpendicular direction, a damping force in the form of a quadratic polynomial of the displacement multiplying velocity is introduced. Finally, if instead of a parabola a symmetric curve of higher order is used, a vibro-impact type of dynamic response is observed. The proposed device is suitable for the seismic isolation of museum artifacts which are usually characterized by relatively small mass. An illustrative example is presented demonstrating the main features of the proposed isolator.
(1) It is based on a physical quantity that can be determined by experimental procedures and which does not consider neither the introduction of an “artificial” primary measure accounting for plastic deformation, nor any decomposition of the kinematic quantities into elastic and plastic parts.
(2) It can describe several internal structures which may differ vastly from the classical Euclidean one, namely directional densities, curved material structures, pre – formed materials, pre – stressed reference configurations as well as the presence of dislocation fields, which may change the internal structure from a Euclidean to a non – Euclidean one.
(3) It can be extended naturally to a covariant formulation.
As an application, the derived model is tested numerically for the solution of several problems of large scale plastic flow.
for the nonlinear dynamic analysis of frame structures. The classical Euler – Bernoulli formulation for the
elastic case is extended by implicitly defining new, hysteretic, degrees of freedom, subjected to an evolution
equation of the Bouc-Wen type with kinematic hardening. An interpolation field is proposed for these new
degrees of freedom, which are regarded as hysteretic curvatures. By means of the principle of virtual work an
elastoplastic stiffness matrix is derived. This stiffness matrix together with the hysteretic evolution equations
fully describes the constitutive behaviour of the element. In the present paper only material nonlinearities are
accounted for. Solutions are obtained by simultaneously solving the three sets of governing equations of the
structure, namely the global equilibrium equations, global compatibility equations and local constitutive
equations. A Runge-Kutta solver is implemented. In doing so, the linearization of the constitutive relations is
avoided, contrary to the usual step–by–step solution approaches. Examples are presented in order to
demonstrate the efficiency of the proposed methodology. Firstly, a single cantilever beam is examined and the
validity of the proposed formulation is established. Secondly the nonlinear vibrations of a plane frame are
examined and finally the collapse path of an example taken from the bibliography is presented.
phase and the design of the network in a single optimization problem which is solved using genetic
algorithms. In this way, the multiplicity of the form-finding procedure is removed by implicitly directing the
network towards a desired final configuration. The force-density method is used, within the genetic algorithm
scheme, to search among the different equilibrium configurations using instead of the prestressing forces, the
“force density” parameters as design variables. By augmenting the objective function, the minimum weight
design is solved by incorporating resistance constraints in the form of a penalty function. A computer code has
been developed that treats the entire problem. Apart from performing single form-finding analysis by
implementing the force-density method, the code is able of conducting static nonlinear analysis taking into
consideration geometric nonlinearities. Finally the developed program performs the size optimization of the
network using genetic algorithm. A number of different optimization schemes are implemented by changing
either the genetic algorithm procedure (Standard GA, Micro – GA, Saw – Tooth), or their individual control
parameters i.e. crossover type, selection mode and replication features to reveal the most efficient GA variant
for this type of structures.