Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures. Part II: identification from tests under heterogeneous stress field

In Part I of this paper we have presented a simple model capable of describing the localized failure of a massive structure. In this part, we discuss the identification of the model parameters from two kinds of experiments: a uniaxial tensile test and a three-point bending test. The former is used only for illustration of material parameter response dependence, and we focus mostly upon the latter, discussing the inverse optimization problem for which the specimen is subjected to a heterogeneous stress field.Comment: 18 pages, 12 figures, 6 table

Structural seismic fragility analysis of RC frame with a new family of Rayleigh damping models

International audienceStructural seismic vulnerability assessment is one of the key steps in a seismic risk management process. Structural vulnerability can be assessed using the concept of fragility. Structural fragility is the probability for a structure to sustain a given damage level for a given input ground motion intensity, which is represented by so-called fragility curves or surfaces. In this work, we consider a moment-resisting reinforced concrete frame struc- ture in the area of the Cascadia subduction zone, that is in the South-West of Canada and the North-West of the USA. According to shaking table tests, we first validate the capability of an inelastic fiber beam/column element, using a recently developed concrete constitutive law, for representing the seismic behavior of the tested frame coupled to either a commonly used Rayleigh damping model or a proposed new model. Then, for each of these two damping models, we proceed to a structural fragility analysis and in- vestigate the amount of uncertainty to be induced by damping models

Adaptive modelling in atomistic-to-continuum multiscale methods

International audienceDue to the lack of computational power to perform a fully atomistic simulation of practical, engineering systems, a number of concurrent multiscale methods is developed to limit atomic model to a small cluster of atoms near the hot spot. In this paper the overview of salient features of the main multiscale families is given. The special attention is drawn towards the role of model adaptivity, that is, which part of the problem domain to model by the atomic scale (the hot spot) and which by coarse scale model, as well as where to place the interface of the two models to control the accuracy. Taking Quasicontinuum method as a reference, review of the evolution of the Bridging domain/Arlequin method is given, which parallels the development of a posteriori modeling error estimation

DISCRETE LATTICE ELEMENT APPROACH FOR ROCK FAILURE MODELING

This paper presents the ‘discrete lattice model’, or, simply, the ‘lattice model’, developed for rock failure modeling. The main difficulties in numerical modeling, namely, those related to complex crack initiations and multiple crack propagations, their coalescence under the influence of natural disorder, and heterogeneities, are overcome using the approach presented in this paper. The lattice model is constructed as an assembly of Timoshenko beams, representing the cohesive links between the grains of the material, which are described by Voronoi polygons. The kinematics of the Timoshenko beams are enhanced by the embedded strong discontinuities in their axial and transversal directions so as to provide failure modes I, II, and III. The model presented is suitable for meso-scale rock simulations. The representative numerical simulations, in both 2D and 3D settings, are provided in order to illustrate the model’s capabilities

Partitioned solution to fluid-structure interaction problems in application to free-surface flows

International audienceIn this work we discuss a way to compute the impact of free-surface flow on nonlinear structures. The approach chosen rely on a partitioned strategy that allows to solve strongly coupled fluid-structure interaction problem. It is then possible to re-use existing and validated strategy for each sub-problem. The structure is formulated in a Lagrangian way and solved by the finite element method. The free-surface flow approach considers a Volume-Of-Fluid (VOF) strategy formulated in an Arbitrary Lagrangian-Eulerian (ALE) framework, and the finite volume are used to discrete and solve this problem. The software coupling is ensured in an efficient way using the Communication Template Library (CTL). Numerical examples presented herein concern 2D validations case but also 3D problems with a large number of equations to be solved

Hasar-Plastisite Çifti Modeli İle Çevrimsel Elastik Olmayan Davranışların İncelenmesi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Bu çalışmada, iki temel inelastik davranış plastisite ve hasar mekanizmalarının çift olarak çalıştığı bir fenomenolojik bünye modeli pekleşme davranışları dikkate alarak iki boyutlu yapı elemanı için oluşturulmuştur. Çeşitli tekrarlı yüklemeler altında bu yapı elemanın çevrimsel davranışları incelenmiş, gerilme şekil değiştirme diyagramları ile gösterilmiştir. Sayısal çözüm yöntemi olarak hibrid sonlu eleman modeli kullarak literatürde yer alan araştırmalarla doğrulanmıştır

Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

The final publication is available at link.springer.com[EN] In this paper we propose different multi-field variational formulations for electrostatics and magnetostatics, which can provide optimal discrete approximation of any particular vector field. The proposed formulations are constructed by appealing to mechanics point of view amenable to using general constitutive equations, which is quite different from electrostatics and magnetostatics formulations typical of physics and electrical engineering focusing on the corresponding global form suitable only for linear case. In particular, the formulations we propose can be combined with mixed discrete approximations that can ensure the continuity of tangential component of electric ormagnetic field and normal component of electric displacement and magnetic flux even for low order interpolations. The choice of this kind is quite different from currently favorite choice of high order finite element interpolations used for coupling electromagnetism with mechanics. The discrete approximation is based upon Whitney's interpolations representing the vector fields in terms of corresponding differential forms, with electric and magnetic fields as one-form and electric displacement and magnetic flux as two-form. The implementation of interpolations of this kind is made for 3D tetrahedron elements with non-standard approximation parameters defined not only at vertices (for zero-form), but at edges (for one-form) and at facets (for two-form). The results of several numerical simulations are presented to illustrate the performance of different formulations proposed herein.This work was supported jointly by Haut-deFrance Region (CR Picardie) (120-2015-RDISTRUCT-000010 and RDISTRUCT-000010) and EU funding (FEDER) for Chaire-deMecanique (120-2015-RDISTRUCTF-000010 and RDISTRUCTI000004). AI was also supported by IUF.Moreno-Navarro, P.; Ibrahimbegovic, A.; Ospina, A. (2020). Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics. Computational Mechanics. 65(1):41-59. https://doi.org/10.1007/s00466-019-01751-xS4159651Albanese R, Rubinacci G (1997) Finite element methods for the solution of 3d eddy current problems. In: Advances in imaging and electron physics, vol 102, pp 1–86. ElsevierAlotto P, Freschi F, Repetto M, Rosso C (2013) The cell method for electrical engineering and multiphysics problems: an introduction, vol 230. Springer, BerlinAngoshtari A, Shojaei MF, Yavari A (2017) Compatible-strain mixed finite element methods for 2d compressible nonlinear elasticity. Comput Methods Appl Mech Eng 313:596–631Arnold DN, Falk RS, Winther R (2006) Finite element exterior calculus, homological techniques, and applications. Acta Numerica 15:1–155Balanis CA (1999) Advanced engineering electromagnetics. Wiley, HobokenBamberg P, Sternberg S (1991) A course in mathematics for students of physics, vol 2. Cambridge University Press, CambridgeBochev PB, Robinson AC (2002) Matching algorithms with physics: exact sequences of finite element spaces. Collected Lectures on Preservation of Stability Under Discretization, pp 145–166Bossavit A (1988) A rationale for ‘edge-elements’ in 3-d fields computations. IEEE Trans Magn 24(1):74–79Bossavit A (1988) Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism. IEE Proc 135(8):493–500Bossavit A (2010) Discrete magneto-elasticity: a geometrical approach. IEEE Trans Magn 46(8):3485–3491Desbrun M, Kanso E, Tong Y (2008) Discrete differential forms for computational modeling. In: Discrete differential geometry, pp 287–324. SpringerDular P, Geuzaine C (1997) Getdp: a general environment for the treatment of discrete problemsDular P, Hody J-Y, Nicolet A, Genon A, Legros W (1994) Mixed finite elements associated with a collection of tetrahedra, hexahedra and prisms. IEEE Trans Magn 30(5):2980–2983Felippa CA, Park KC, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Methods Appl Mech Eng 190(24–25):3247–3270Gil AJ, Ortigosa R (2016) A new framework for large strain electromechanics based on convex multi-variable strain energies: variational formulation and material characterisation. Comput Methods Appl Mech Eng 302:293–328Golias NA, Tsiboukis TD, Bossavit A (1994) Constitutive inconsistency: rigorous solution of maxwell equations based on a dual approach. IEEE Trans Magn 30(5):3586–3589Gradinaru V, Hiptmair R (1999) Whitney elements on pyramids. Electron Trans Numer Anal 8:154–168Hale HW (1961) A logic for identifying the trees of a graph. Trans Am Inst Electr Eng Part III Power Apparatus Syst 80(3):195–197Hammond P (2013) Electromagnetism for engineers: an introductory course. Elsevier, AmsterdamHammond P, Penman J (1976) Calculation of inductance and capacitance by means of dual energy principles. In: Proceedings of the Institution of Electrical Engineers, vol 123, pp 554–559. IETHammond P, Tsiboukis TD (1983) Dual finite-element calculations for static electric and magnetic fields. IEE Proc A (Phys Sci Measurement Instrum Manag Educ Rev) 130(3):105–111Ibrahimbegovic A (2009) Nonlinear solid mechanics: theoretical formulations and finite element solution methods, vol 160. Springer, DordrechtJackson JD (1999) Classical electrodynamics. Wiley, New YorkKameari A (1989) Three dimensional eddy current calculation using edge elements for magnetic vector potential. In: Applied electromagnetics in materials, pp 225–236. ElsevierKassiotis C, Ibrahimbegovic A, Niekamp R, Matthies HG (2011) Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples. Comput Mech 47(3):305–323Kassiotis C, Ibrahimbegovic A, Niekamp R, Matthies HG (2011) Nonlinear fluid–structure interaction problem. Part II: space discretization, implementation aspects, nested parallelization and application examples. Comput Mech 47(3):335–357Keip Marc-André, Steinmann Paul, Schröder Jörg (2014) Two-scale computational homogenization of electro-elasticity at finite strains. Comput Methods Appl Mech Eng 278:62–79Ladevèze P, Pelle J-P (2005) Mastering calculations in linear and nonlinear mechanics, vol 171. Springer, New YorkMacneal RH, Harder Robert L (1985) A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1(1):3–20Manges J, Cendes Z (1996) Generation of tangential vector finite elements. Int Compumag Soc Newsl 3(1):4–10Mitchell BS (2004) An introduction to materials engineering and science for chemical and materials engineers. Wiley, HobokenMoreno-Navarro P, Ibrahimbegovic A, Pérez-Aparicio JL (2017) Plasticity coupled with thermo-electric fields: thermodynamics framework and finite element method computations. Comput Methods Appl Mech Eng 315:50–72Moreno-Navarro P, Ibrahimbegovic A, Pérez-Aparicio JL (2018) Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields. Coupled Syst Mech 7(1):5–25Nédélec J-C (1980) Mixed finite elements in $$\mathbb{R}^3$$. Numer Math 35(3):315–341Penman J, Fraser J (1982) Complementary and dual energy finite element principles in magnetostatics. IEEE Trans Magn 18(2):319–324Razek A (1995) Computation of 3d electrostatic local fields and forces using complementarity of dual formulations. Application for capacitance and torque calculations in micromotorsRen Z (1995) A 3d vector potential formulation using edge element for electrostatic field computation. IEEE Trans Magn 31(3):1520–1523Ren Z (2009) On the complementarity of dual formulations on dual meshes. IEEE Trans Magn 45(3):1284–1287Repetto M, Trevisan F (2004) Global formulation of 3d magnetostatics using flux and gauged potentials. Int J Numer Meth Eng 60(4):755–772Schröder J, Keip M-A (2012) Two-scale homogenization of electromechanically coupled boundary value problems. Comput Mech 50(2):229–244Stark S, Semenov AS, Balke H (2015) On the boundary conditions for the vector potential formulation in electrostatics. Int J Numer Meth Eng 102(11):1704–1732Taylor RL (2012) Feap–a finite element analysis program. Version 8.4 Theory ManualTonti E (2013) The mathematical structure of classical and relativistic physics. Springer, New YorkVogel F, Bustamante R, Steinmann P (2012) On some mixed variational principles in electro-elastostatics. Int J Nonlinear Mech 47(2):341–354Wang J-S, Ida N (1993) Curvilinear and higher order ‘edge’ finite elements in electromagnetic field computation. IEEE Trans Magn 29(2):1491–1494Webb JP, Forgahani B (1993) Hierarchal scalar and vector tetrahedra. IEEE Trans Magn 29(2):1495–1498Yioultsis TV, Tsiboukis TD (1996) The mystery and magic of Whitney elements—an insight in their properties and construction. ICS Newsl 3:1389–1392Zienkiewicz OC, Taylor RL (1977) The finite element method, vol 36. McGraw-Hill, Londo

Nonlinear fluid-structure interaction problem. Part II: space discretization, implementation aspects, nested parallelization and application examples

International audienceThe main focus of the present article is the development of a general solution framework for coupled and/or interaction multi-physics problems based upon re-using existing codes into software products. In particular, we discuss how to build this software tool for the case of fluid-structure interaction problem, from finite element code Feap for structural and finite volume code OpenFOAM for fluid mechanics. This is achieved by using the Component Template Library (CTL) to provide the coupling between the existing codes into a single software product. The present CTL code-coupling procedure accepts not only different discretization schemes, but different languages, with the solid component written in Fortran and fluid component written in \Cpp. Moreover, the resulting CTL-based code also accepts the nested parallelization. The proposed coupling strategy is detailed for explicit and implicit fixed-point iteration solver presented in the Part I of this paper, referred to Direct Force-Motion Transfer/Block-Gauss-Seidel. However, the proposed code-coupling framework can easily accommodate other solution schemes. The selected application examples are chosen to confirm the capability of the code-coupling strategy to provide a quick development of advanced computational tools for demanding practical problems, such as 3D fluid models with free-surface flows interacting with structures