Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner, Computer Methods in Applied Mechanics and Engineering, vol.290, pp.156-182, 2015. ,
DOI : 10.1016/j.cma.2015.02.028
Topology optimization for minimum stress design with the homogenization method. Structural and Multidisciplinary Optimization, pp.87-98, 2004. ,
Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004. ,
DOI : 10.1016/j.jcp.2003.09.032
Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials. Structural and Multidisciplinary Optimization, pp.695-705, 2014. ,
Efficient topology optimization in matlab using 88 lines of code. Structural and Multidisciplinary Optimization, pp.1-16, 2011. ,
Design of manufacturable 3D extremal elastic microstructure, Mechanics of Materials, vol.69, issue.1, pp.1-10, 2014. ,
DOI : 10.1016/j.mechmat.2013.09.018
Matlab tensor toolbox version 2.4, 2010. ,
Topology optimization with implicit functions and regularization, International Journal for Numerical Methods in Engineering, vol.130, issue.8, pp.1177-1196, 2003. ,
DOI : 10.1002/nme.824
Optimal shape design as a material distribution problem, Structural Optimization, vol.23, issue.4, pp.193-202, 1989. ,
DOI : 10.1007/BF01650949
Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988. ,
DOI : 10.1016/0045-7825(88)90086-2
Material interpolation schemes in topology optimization, Archive of Applied Mechanics (Ingenieur Archiv), vol.69, issue.9-10, pp.635-654, 1999. ,
DOI : 10.1007/s004190050248
Topology optimization: theory, methods and applications, 2003. ,
Optimal design of material properties and material distribution for multiple loading conditions, International Journal for Numerical Methods in Engineering, vol.20, issue.7, pp.1149-1170, 1995. ,
DOI : 10.1002/nme.1620380705
Optimization of structure and material properties for solids composed of softening material, International Journal of Solids and Structures, vol.33, issue.12, pp.1799-1813, 1996. ,
DOI : 10.1016/0020-7683(95)00121-2
Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling, International Journal for Numerical Methods in Engineering, vol.190, issue.2, pp.1578-1597, 2012. ,
DOI : 10.1002/nme.4253
Design-dependent loads in topology optimization. ESAIM -Control, Optimisation and Calculus of Variations, pp.19-48, 2003. ,
Consistency approach and diffuse derivation in element free methods based on moving least squares approximation, Computer Assisted Mechanics and Engineering Sciences, vol.5, issue.4, pp.479-501, 1998. ,
Integration constraint in diffuse element method, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.12-14, pp.12-141203, 2004. ,
DOI : 10.1016/j.cma.2003.12.014
Topology optimization for minimum weight with compliance and stress constraints. Structural and Multidisciplinary Optimization, pp.369-384, 2012. ,
An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms, International Journal for Numerical Methods in Engineering, vol.13, issue.4950, pp.1413-1430, 2003. ,
DOI : 10.1002/nme.783
Stiffness design of geometrically nonlinear structures using topology optimization. Structural and Multidisciplinary Optimization, pp.93-104, 2000. ,
Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol.194, issue.1, pp.344-362, 2004. ,
DOI : 10.1016/j.jcp.2003.09.033
On design of multi-functional microstructural materials, Journal of Materials Science, vol.5, issue.656, pp.51-66, 2013. ,
DOI : 10.1007/s10853-012-6643-4
Stress constrained topology optimization with free-form design domains, Computer Methods in Applied Mechanics and Engineering, vol.289, pp.267-290, 2015. ,
DOI : 10.1016/j.cma.2015.02.012
Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.361-387, 2014. ,
DOI : 10.1016/j.cma.2014.06.007
Analysis of individual differences in multidimensional scaling via an n-way generalization of ???Eckart-Young??? decomposition, Psychometrika, vol.12, issue.3, pp.283-319, 1970. ,
DOI : 10.1007/BF02310791
A discrete level-set topology optimization code written in matlab. Structural and Multidisciplinary Optimization, pp.453-464, 2010. ,
Design of three dimensional isotropic microstructures for maximized stiffness and conductivity, International Journal of Solids and Structures, vol.45, issue.14-15, pp.14-154130, 2008. ,
DOI : 10.1016/j.ijsolstr.2008.02.025
Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization, International Journal of Solids and Structures, vol.49, issue.23-24, pp.23-243397, 2012. ,
DOI : 10.1016/j.ijsolstr.2012.07.019
Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus. Structural and Multidisciplinary Optimization, pp.287-296, 2014. ,
Design sensitivity analysis and topology optimization of displacement???loaded non-linear structures, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.22-24, pp.22-232539, 2003. ,
DOI : 10.1016/S0045-7825(03)00274-3
Computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis, International Journal for Numerical Methods in Engineering, vol.23, issue.4, pp.91799-824, 2012. ,
DOI : 10.1002/nme.4293
Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials, Computer Methods in Applied Mechanics and Engineering, vol.254, pp.61-82, 2013. ,
DOI : 10.1016/j.cma.2012.10.016
A hierarchical model for concurrent material and topology optimisation of three-dimensional structures. Structural and Multidisciplinary Optimization, pp.107-115, 2008. ,
Multiscale topology optimization of bi-material laminated composite structures, Composite Structures, vol.132, pp.495-505, 2015. ,
DOI : 10.1016/j.compstruct.2015.05.059
Multi-scale continuous???discontinuous framework for computational-homogenization???localization, Journal of the Mechanics and Physics of Solids, vol.60, issue.8, pp.1486-1507, 2012. ,
DOI : 10.1016/j.jmps.2012.04.002
A PGD-based homogenization technique for the resolution of nonlinear multiscale problems, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.275-292, 2013. ,
DOI : 10.1016/j.cma.2013.08.009
URL : https://hal.archives-ouvertes.fr/hal-01403834
A survey of structural and multidisciplinary continuum topology optimization: post 2000. Structural and Multidisciplinary Optimization, pp.1-38, 2014. ,
Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material. Structural and Multidisciplinary Optimization, pp.583-597, 2013. ,
Constitutive potentials for dilutely voided nonlinear materials, Mechanics of Materials, vol.3, issue.1, pp.41-54, 1984. ,
DOI : 10.1016/0167-6636(84)90013-9
Topology optimization of continuum structures with local stress constraints, International Journal for Numerical Methods in Engineering, vol.10, issue.8, pp.1453-1478, 1998. ,
DOI : 10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2
On Transformation Strains and Uniform Fields in Multiphase Elastic Media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.437, issue.1900, pp.291-310, 1992. ,
DOI : 10.1098/rspa.1992.0062
The modeling of inelastic composite materials with the transformation field analysis, Modelling and Simulation in Materials Science and Engineering, vol.2, issue.3A, pp.571-586, 1994. ,
DOI : 10.1088/0965-0393/2/3A/011
FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition, Computer Methods in Applied Mechanics and Engineering, vol.257, pp.183-202, 2013. ,
DOI : 10.1016/j.cma.2013.01.011
Bubble method for topology and shape optimization of structures, Structural Optimization, vol.24, issue.2, pp.42-51, 1994. ,
DOI : 10.1007/BF01742933
FE 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, pp.3-4309, 2000. ,
Recent advances in surrogate-based optimization, Progress in Aerospace Sciences, pp.50-79, 2009. ,
DOI : 10.1016/j.paerosci.2008.11.001
Three-dimensional finite element implementation of the nonuniform transformation field analysis, International Journal for Numerical Methods in Engineering, vol.426, issue.4-5, pp.803-829, 2010. ,
DOI : 10.1002/nme.2920
Nonuniform transformation field analysis of materials with morphological anisotropy, Composites Science and Technology, vol.71, issue.4, pp.433-442, 2011. ,
DOI : 10.1016/j.compscitech.2010.12.013
URL : https://hal.archives-ouvertes.fr/hal-00723639
Reduced basis homogenization of viscoelastic composites, Composites Science and Technology, vol.76, pp.84-91, 2013. ,
DOI : 10.1016/j.compscitech.2012.12.012
The finite element square reduced (fe 2R ) method with gpu acceleration: towards three-dimensional two-scale simulations, International Journal for Numerical Methods in Engineering, 2015. ,
Reduced basis hybrid computational homogenization based on a mixed incremental formulation, Computer Methods in Applied Mechanics and Engineering, vol.260, pp.143-154, 2013. ,
DOI : 10.1016/j.cma.2013.03.007
GPU accelerated computational homogenization based on a variational approach in a reduced basis framework, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.186-217, 2014. ,
DOI : 10.1016/j.cma.2014.05.006
Topology optimization of multiscale elastoviscoplastic structures, International Journal for Numerical Methods in Engineering, vol.2, issue.2, 2015. ,
DOI : 10.1002/nme.5122
Composite material design of two-dimensional structures using the homogenization design method, International Journal for Numerical Methods in Engineering, vol.10, issue.9, pp.2031-2051, 2001. ,
DOI : 10.1002/nme.105
Microstructure sensitive design for performance optimization, Progress in Materials Science, vol.55, issue.6, pp.477-562, 2010. ,
DOI : 10.1016/j.pmatsci.2009.08.002
Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method, Journal of Computational Physics, vol.226, issue.1, pp.326-353, 2007. ,
DOI : 10.1016/j.jcp.2007.04.009
A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate, International Journal for Numerical Methods in Engineering, vol.8, issue.2, pp.98-114, 2012. ,
DOI : 10.1002/nme.4270
Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Structural and Multidisciplinary Optimization, pp.1075-1088, 2013. ,
Topology optimization of structures with geometrical nonlinearities, Computers & Structures, vol.79, issue.20-21, pp.20-211977, 2001. ,
DOI : 10.1016/S0045-7949(01)00117-1
Multi-scale computational homogenization: Trends and challenges, Journal of Computational and Applied Mathematics, vol.234, issue.7, pp.2175-2182, 2010. ,
DOI : 10.1016/j.cam.2009.08.077
A multi-level computational model for multi-scale damage analysis in composite and porous materials, International Journal of Solids and Structures, vol.38, issue.14, pp.2335-2385, 2001. ,
DOI : 10.1016/S0020-7683(00)00167-0
Multiphase composites with extremal bulk modulus, Journal of the Mechanics and Physics of Solids, vol.48, issue.3, pp.461-498, 2000. ,
DOI : 10.1016/S0022-5096(99)00043-5
The lattice structure configuration design for stereolithography investment casting pattern using topology optimization, Rapid Prototyping Journal, vol.18, issue.5, pp.353-361, 2012. ,
DOI : 10.1108/13552541211250355
Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Computer Methods in Applied Mechanics and Engineering, vol.83, issue.2, pp.143-198, 1990. ,
DOI : 10.1016/0045-7825(90)90148-F
Relating cellular structure of open solid food foams to their Young???s modulus: Finite element calculation, International Journal of Solids and Structures, vol.45, issue.10, pp.452881-2896, 2008. ,
DOI : 10.1016/j.ijsolstr.2008.01.007
Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability, International Journal of Solids and Structures, vol.43, issue.22-23, pp.22-237028, 2006. ,
DOI : 10.1016/j.ijsolstr.2006.03.001
Design of maximum permeability material structures, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.4-61006, 2007. ,
DOI : 10.1016/j.cma.2006.08.006
Stress-related topology optimization via level set approach, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.47-48, pp.47-483439, 2011. ,
DOI : 10.1016/j.cma.2011.08.016
Multi-scale robust design and optimization considering load uncertainties, Computer Methods in Applied Mechanics and Engineering, vol.283, pp.994-1009, 2015. ,
DOI : 10.1016/j.cma.2014.10.014
Sur les matériaux standards generalisés, Journal de Mécanique, vol.14, issue.1, pp.39-63, 1975. ,
A review of homogenization and topology optimization I???homogenization theory for media with periodic structure, Computers & Structures, vol.69, issue.6, pp.707-717, 1998. ,
DOI : 10.1016/S0045-7949(98)00131-X
A review of homogenization and topology opimization II???analytical and numerical solution of homogenization equations, Computers & Structures, vol.69, issue.6, pp.719-738, 1998. ,
DOI : 10.1016/S0045-7949(98)00132-1
High-performance model reduction techniques in computational multiscale homogenization, Computer Methods in Applied Mechanics and Engineering, vol.276, pp.149-189, 2014. ,
DOI : 10.1016/j.cma.2014.03.011
The Elastic Behaviour of a Crystalline Aggregate, Proceedings of the Physical Society. Section A, vol.65, issue.5, pp.349-354, 1952. ,
DOI : 10.1088/0370-1298/65/5/307
Elastic properties of reinforced solids: Some theoretical principles, Journal of the Mechanics and Physics of Solids, vol.11, issue.5, pp.357-372, 1963. ,
DOI : 10.1016/0022-5096(63)90036-X
Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials, Computational Mechanics, vol.45, issue.1, pp.393-401, 2009. ,
DOI : 10.1007/s00466-008-0312-0
A further review of eso type methods for topology optimization . Structural and Multidisciplinary Optimization, pp.671-683, 2010. ,
Topology Optimization of Continuum Structures: Methods and Applications, 2010. ,
DOI : 10.1002/9780470689486
Convergent and mesh-independent solutions for the bidirectional evolutionary structural optimization method. Finite Elements in Analysis and Design, pp.1039-1049, 2007. ,
Topology optimization of nonlinear structures under displacement loading, Engineering Structures, vol.30, issue.7, pp.2057-2068, 2008. ,
DOI : 10.1016/j.engstruct.2008.01.009
Topology optimization of energy-absorbing structures, International Journal of Crashworthiness, vol.44, issue.6, pp.663-675, 2007. ,
DOI : 10.1299/jsmec.49.1091
Topological design of microstructures of cellular materials for maximum bulk or shear modulus, Computational Materials Science, vol.50, issue.6, pp.1861-1870, 2011. ,
DOI : 10.1016/j.commatsci.2011.01.030
Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity. Structural and Multidisciplinary Optimization, pp.385-398, 2012. ,
Topology optimization of microstructures of cellular materials and composites for macrostructures, Computational Materials Science, vol.67, pp.397-407, 2013. ,
DOI : 10.1016/j.commatsci.2012.09.018
Topology optimization for microstructures of viscoelastic composite materials, Computer Methods in Applied Mechanics and Engineering, vol.283, pp.503-516, 2015. ,
DOI : 10.1016/j.cma.2014.10.007
Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.28-303089, 2003. ,
DOI : 10.1016/S0045-7825(03)00342-6
Multi-scale models and mathematical aspects in solid and fluid mechanics, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.199-220, 2010. ,
DOI : 10.1016/j.cma.2010.01.012
Topology optimization of nonlinear structures. Finite Elements in Analysis and Design, pp.1417-1427, 2004. ,
Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis. Structural and Multidisciplinary Optimization, pp.595-608, 2014. ,
Analytical sensitivity in topology optimization for elastoplastic composites. Structural and Multidisciplinary Optimization, 2015. ,
Towards a standardized notation and terminology in multiway analysis, Journal of Chemometrics, vol.56, issue.3, pp.105-122, 2010. ,
DOI : 10.1002/1099-128X(200005/06)14:3<105::AID-CEM582>3.0.CO;2-I
Optimal design and relaxation of variational problems (part i) ,
Optimal design and relaxation of variational problems (part i) ,
Optimal design and relaxation of variational problems (part i) ,
An approach to micro-macro modeling of heterogeneous materials, Computational Mechanics, vol.27, issue.1, pp.37-48, 2001. ,
DOI : 10.1007/s004660000212
Routes for Efficient Computational Homogenization of??Nonlinear Materials Using the??Proper Generalized Decompositions, Archives of Computational Methods in Engineering, vol.198, issue.33???36, pp.373-391, 2010. ,
DOI : 10.1007/s11831-010-9051-4
Surfaces generated by moving least squares methods, Mathematics of Computation, vol.37, issue.155, pp.141-158, 1981. ,
DOI : 10.1090/S0025-5718-1981-0616367-1
Computational homogenization of nonlinear elastic materials using neural networks, International Journal for Numerical Methods in Engineering, vol.172, issue.1, 2015. ,
DOI : 10.1002/nme.4953
URL : https://hal.archives-ouvertes.fr/hal-01165987
Stress-based topology optimization for continua. Structural and Multidisciplinary Optimization, pp.605-620, 2010. ,
A simple checkerboard suppression algorithm for evolutionary structural optimization. Structural and Multidisciplinary Optimization, pp.230-239, 2001. ,
A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters, Composite Structures, vol.94, issue.12, pp.943529-3537, 2012. ,
DOI : 10.1016/j.compstruct.2012.06.014
A semi-implicit level set method for structural shape and topology optimization, Journal of Computational Physics, vol.227, issue.11, pp.5561-5581, 2008. ,
DOI : 10.1016/j.jcp.2008.02.003
Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique, Computer Methods in Applied Mechanics and Engineering, vol.286, pp.422-441, 2015. ,
DOI : 10.1016/j.cma.2014.12.023
Shape and topology optimization for closed liquid cell materials using extended multiscale finite element method. Structural and Multidisciplinary Optimization, pp.367-385, 2014. ,
Adaptive topology optimization of elastoplastic structures, Structural Optimization, vol.10, issue.2, pp.81-91, 1998. ,
DOI : 10.1007/BF01278493
Nonuniform transformation field analysis, International Journal of Solids and Structures, vol.40, issue.25, pp.6937-6955, 2003. ,
DOI : 10.1016/S0020-7683(03)00346-9
URL : https://hal.archives-ouvertes.fr/hal-00088331
Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.48-51, pp.5477-5502, 2004. ,
DOI : 10.1016/j.cma.2003.12.071
URL : https://hal.archives-ouvertes.fr/hal-00088245
Effective properties of composite materials with periodic microstructure: a computational approach, Computer Methods in Applied Mechanics and Engineering, vol.172, issue.1-4, pp.1-4109, 1999. ,
DOI : 10.1016/S0045-7825(98)00227-8
Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation, International Journal for Numerical Methods in Engineering, vol.7, issue.11, pp.1285-1322, 2002. ,
DOI : 10.1002/nme.515
Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials, Computer Methods in Applied Mechanics and Engineering, vol.171, issue.3-4, pp.3-4387, 1999. ,
DOI : 10.1016/S0045-7825(98)00218-7
A priori hyper-reduction method for coupled viscoelastic???viscoplastic composites, Computers & Structures, vol.119, pp.95-103, 2013. ,
DOI : 10.1016/j.compstruc.2012.11.017
URL : https://hal.archives-ouvertes.fr/hal-00790175
Hierarchically parallel coupled finite strain multiscale solver for modeling heterogeneous layers, International Journal for Numerical Methods in Engineering, vol.85, issue.2, pp.3-4748, 2014. ,
DOI : 10.1002/nme.4755
Nonlinear structural design using multiscale topology optimization. Part I: Static formulation, Computer Methods in Applied Mechanics and Engineering, vol.261, issue.262, pp.261-262167, 2013. ,
DOI : 10.1016/j.cma.2012.12.018
Generalizing the finite element method: Diffuse approximation and diffuse elements, Computational Mechanics, vol.313, issue.5, pp.307-318, 1992. ,
DOI : 10.1007/BF00364252
Optimal design of periodic linear elastic microstructures, Computers & Structures, vol.76, issue.1-3, pp.421-429, 2000. ,
DOI : 10.1016/S0045-7949(99)00172-8
Topology optimization of periodic microstructures with a penalization of highly localized buckling modes, International Journal for Numerical Methods in Engineering, vol.83, issue.4, pp.809-834, 2002. ,
DOI : 10.1002/nme.449
Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency. Structural and Multidisciplinary Optimization, pp.115-132, 2009. ,
Indentation size effects in crystalline materials: A law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, vol.46, issue.3, pp.411-425, 1998. ,
DOI : 10.1016/S0022-5096(97)00086-0
Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.7, pp.1216-1243, 2007. ,
DOI : 10.1016/j.cma.2006.08.015
Topology synthesis of large-displacement compliant mechanisms, International Journal for Numerical Methods in Engineering, vol.76, issue.2, pp.2683-2705, 2001. ,
DOI : 10.1002/nme.148
Surrogate-based analysis and optimization, Progress in Aerospace Sciences, pp.1-28, 2005. ,
DOI : 10.1016/j.paerosci.2005.02.001
Computational efficiency and validation of bi-directional evolutionary structural optimisation, Computer Methods in Applied Mechanics and Engineering, vol.189, issue.2, pp.559-573, 2000. ,
DOI : 10.1016/S0045-7825(99)00309-6
Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design, Computer Methods in Applied Mechanics and Engineering, vol.265, issue.1, pp.174-185, 2013. ,
DOI : 10.1016/j.cma.2013.06.010
URL : https://hal.archives-ouvertes.fr/hal-00977903
Hierarchical optimization of material and structure. Structural and Multidisciplinary Optimization, pp.1-10, 2002. ,
Aims, scope, methods, history and unified terminology of computeraided topology optimization in structural mechanics. Structural and Multidisciplinary Optimization, pp.90-108, 2001. ,
Topology and shape optimization for elastoplastic structural response, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.15-17, pp.15-172135, 2001. ,
DOI : 10.1016/S0045-7825(00)00227-9
Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, issue.2, pp.489-528, 2000. ,
DOI : 10.1006/jcph.2000.6581
Combined topology and fiber path design of composite layers using cellular automata. Structural and Multidisciplinary Optimization, pp.413-421, 2005. ,
Design of variable???stiffness laminates using lamination parameters, Composites Part B: Engineering, vol.37, issue.4-5, pp.4-5301, 2006. ,
DOI : 10.1016/j.compositesb.2005.12.001
Materials with prescribed constitutive parameters: An inverse homogenization problem, International Journal of Solids and Structures, vol.31, issue.17, pp.312313-2329, 1994. ,
DOI : 10.1016/0020-7683(94)90154-6
A new class of extremal composites, Journal of the Mechanics and Physics of Solids, vol.48, issue.2, pp.397-428, 2000. ,
DOI : 10.1016/S0022-5096(99)00034-4
A 99 line topology optimization code written in matlab. Structural and Multidisciplinary Optimization, pp.120-127, 2001. ,
Topology optimization approaches -a comparative review. Structural and Multidisciplinary Optimization, pp.1031-1055, 2013. ,
Design of materials with extreme thermal expansion using a three-phase topology optimization method, Journal of the Mechanics and Physics of Solids, vol.45, issue.6, pp.1037-1067, 1997. ,
DOI : 10.1016/S0022-5096(96)00114-7
Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1-2, pp.181-192, 1998. ,
DOI : 10.1016/S0045-7825(97)00139-4
On the Topological Derivative in Shape Optimization, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1251-1272, 1999. ,
DOI : 10.1137/S0363012997323230
Size-dependent optimal microstructure design based on couple-stress theory. Structural and Multidisciplinary Optimization, pp.243-254, 2010. ,
A homogenization method for shape and topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.93, issue.3, pp.291-318, 1991. ,
DOI : 10.1016/0045-7825(91)90245-2
Polytop: a matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Structural and Multidisciplinary Optimization, pp.329-357, 2012. ,
The evolutionary structural optimization method: theoretical aspects, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.47-48, pp.47-485485, 2002. ,
DOI : 10.1016/S0045-7825(02)00464-4
An adaptive method for homogenization in orthotropic nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.35-36, pp.35-363409, 2007. ,
DOI : 10.1016/j.cma.2007.03.017
A numerical method for homogenization in non-linear elasticity, Computational Mechanics, vol.190, issue.6, pp.281-298, 2007. ,
DOI : 10.1007/s00466-006-0097-y
Optimal material design in composites: An iterative approach based on homogenized cells, Computer Methods in Applied Mechanics and Engineering, vol.169, issue.1-2, pp.31-42, 1999. ,
DOI : 10.1016/S0045-7825(98)00174-1
A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.45-46, pp.45-46, 2011. ,
DOI : 10.1016/j.cma.2011.06.012
URL : https://hal.archives-ouvertes.fr/hal-00725389
Level-set methods for structural topology optimization: A review. Structural and Multidisciplinary Optimization, pp.437-472, 2013. ,
Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems, Computer Methods in Applied Mechanics and Engineering, vol.276, pp.453-472, 2014. ,
DOI : 10.1016/j.cma.2014.03.021
Design of materials with prescribed nonlinear properties, Journal of the Mechanics and Physics of Solids, vol.69, issue.1, pp.156-174, 2014. ,
DOI : 10.1016/j.jmps.2014.05.003
A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.1-2, pp.227-246, 2003. ,
DOI : 10.1016/S0045-7825(02)00559-5
A study on X-FEM in continuum structural optimization using a level set model, Computer-Aided Design, vol.42, issue.8, pp.42708-719, 2010. ,
DOI : 10.1016/j.cad.2009.12.001
Concurrent topology optimization design of material and structure within <mml:math altimg="si25.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>FE</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> nonlinear multiscale analysis framework, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.524-542, 2014. ,
DOI : 10.1016/j.cma.2014.05.022
A reduced multiscale model for nonlinear structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.280, pp.117-134, 2014. ,
DOI : 10.1016/j.cma.2014.07.024
Recent advances on topology optimization of multiscale nonlinear structures. submitted for publication in Archives of Computational Methods in Engineering, 2015. ,
Multiscale structural topology optimization with an approximate constitutive model for local material microstructure, Computer Methods in Applied Mechanics and Engineering, vol.286, pp.147-167, 2015. ,
DOI : 10.1016/j.cma.2014.12.018
Design of of materials using topology optimization and energy-based homogenization approach in matlab. Structural and Multidisciplinary Optimization, 2015. ,
Numerical material representation using proper orthogonal decomposition and diffuse approximation, Applied Mathematics and Computation, vol.224, pp.450-462, 2013. ,
DOI : 10.1016/j.amc.2013.08.052
URL : https://hal.archives-ouvertes.fr/hal-00984762
A unified periodical boundary conditions for representative volume elements of composites and applications, International Journal of Solids and Structures, vol.40, issue.8, pp.401907-1921, 2003. ,
DOI : 10.1016/S0020-7683(03)00024-6
On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites, International Journal of Solids and Structures, vol.43, issue.2, pp.266-278, 2006. ,
DOI : 10.1016/j.ijsolstr.2005.03.055
Model reduction by CPOD and Kriging, Structural and Multidisciplinary Optimization, vol.22, issue.3, pp.555-574, 2010. ,
DOI : 10.1007/s00158-009-0434-9
A simple evolutionary procedure for structural optimization, Computers & Structures, vol.49, issue.5, pp.885-896, 1993. ,
DOI : 10.1016/0045-7949(93)90035-C
Evolutionary Structural Optimization, 1997. ,
DOI : 10.1007/978-1-4471-0985-3
Concurrent design of composite macrostructure and cellular microstructure under random excitations, Composite Structures, vol.123, pp.65-77, 2015. ,
DOI : 10.1016/j.compstruct.2014.10.037
Numerical modelling of oxidized microstructure and degraded properties of 2d c/sic composites in air oxidizing environments below 800 ? C, Materials Science and Engineering A, issue.27, pp.5287974-7982, 2011. ,
A strain energy model for the prediction of the effective coefficient of thermal expansion of composite materials, Computational Materials Science, vol.53, issue.1, pp.241-250, 2012. ,
DOI : 10.1016/j.commatsci.2011.08.013
Concurrent topology optimization of structures and their composite microstructures, Computers & Structures, vol.133, pp.103-110, 2014. ,
DOI : 10.1016/j.compstruc.2013.12.001
Design of microstructures of viscoelastic composites for optimal damping characteristics, International Journal of Solids and Structures, vol.37, issue.35, pp.4791-4810, 2000. ,
DOI : 10.1016/S0020-7683(99)00181-X
Element connectivity parameterization for topology optimization of geometrically nonlinear structures, International Journal of Solids and Structures, vol.42, issue.7, pp.1983-2009, 2005. ,
DOI : 10.1016/j.ijsolstr.2004.09.005
Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization, International Journal for Numerical Methods in Engineering, vol.24, issue.10, pp.2196-2218, 2007. ,
DOI : 10.1002/nme.1843
Multiple scale eigendeformation-based reduced order homogenization, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.21-26, pp.21-26, 2009. ,
DOI : 10.1016/j.cma.2008.12.038
Optimization of a frame structure subjected to a plastic deformation, Structural Optimization, vol.92, issue.3-4, pp.197-208, 1995. ,
DOI : 10.1007/BF01742592
Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method, Structural Optimization, vol.63, issue.610, pp.286-299, 1999. ,
DOI : 10.1007/BF01207005
The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains, Journal of Computational Physics, vol.223, issue.1, pp.341-368, 2007. ,
DOI : 10.1016/j.jcp.2006.09.019
URL : https://hal.archives-ouvertes.fr/hal-00693621
Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.33-36, pp.33-362723, 2009. ,
DOI : 10.1016/j.cma.2009.03.017
URL : https://hal.archives-ouvertes.fr/hal-00692234
COMPUTATIONAL HOMOGENIZATION METHOD AND REDUCED DATABASE MODEL FOR HYPERELASTIC HETEROGENEOUS STRUCTURES, International Journal for Multiscale Computational Engineering, vol.11, issue.3, pp.201-225, 2013. ,
DOI : 10.1615/IntJMultCompEng.2013005374
URL : https://hal.archives-ouvertes.fr/hal-00820417
Rank-One Approximation to High Order Tensors, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.2, pp.534-550, 2002. ,
DOI : 10.1137/S0895479899352045
Scale-related topology optimization of cellular materials and structures, International Journal for Numerical Methods in Engineering, vol.8, issue.9, pp.993-1011, 2006. ,
DOI : 10.1002/nme.1743
Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures, Acta Mechanica Sinica, vol.81, issue.22/23 ,
DOI : 10.1007/s10409-006-0045-2
URL : https://hal.archives-ouvertes.fr/hal-00263914
Optimal topology design of continuum structures with stress concentration alleviation via level set method, International Journal for Numerical Methods in Engineering, vol.42, issue.9, pp.942-959, 2013. ,
DOI : 10.1002/nme.4416
The COC algorithm, Part II: Topological, geometrical and generalized shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.89, issue.1-3, pp.1-3309, 1991. ,
DOI : 10.1016/0045-7825(91)90046-9
On the validity of eso type methods in topology optimization. Structural and Multidisciplinary Optimization, pp.80-83, 2001. ,
Bi-Directional Evolutionary Topology Optimization Using Element Replaceable Method, Computational Mechanics, vol.20, issue.1, pp.97-109, 2007. ,
DOI : 10.1007/s00466-006-0087-0
Topology Optimization in Aircraft and Aerospace Structures Design, Archives of Computational Methods in Engineering, vol.50, issue.4, pp.11831-11846 ,
DOI : 10.1016/j.cma.2015.03.007
Multi-scale design of composite materials and structures for maximum natural frequencies, Materials & Design, vol.51, pp.1023-1034, 2013. ,
DOI : 10.1016/j.matdes.2013.05.014
Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004. ,
DOI : 10.1016/j.jcp.2003.09.032
Layout and material gradation in topology optimization of functionally graded structures: a global???local approach, Structural and Multidisciplinary Optimization, vol.36, issue.2, pp.855-868, 2010. ,
DOI : 10.1007/s00158-010-0514-x
Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures, International Journal for Numerical Methods in Engineering, vol.78, issue.3, pp.733-756, 2010. ,
DOI : 10.1002/nme.2922
Efficient topology optimization in MATLAB using 88 lines of code, Structural and Multidisciplinary Optimization, vol.89, issue.1???3, pp.1-16, 2011. ,
DOI : 10.1007/s00158-010-0594-7
Design of manufacturable 3D extremal elastic microstructure, Mechanics of Materials, vol.69, issue.1, pp.1-10, 2014. ,
DOI : 10.1016/j.mechmat.2013.09.018
Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988. ,
DOI : 10.1016/0045-7825(88)90086-2
Topology optimization: theory, methods and applications A discrete level-set topology optimization code written in matlab, Berlin Challis VJ Struct Multidiscip Optim, vol.41, issue.3, pp.453-464, 2003. ,
Design of three dimensional isotropic microstructures for maximized stiffness and conductivity, International Journal of Solids and Structures, vol.45, issue.14-15, pp.14-154130, 2008. ,
DOI : 10.1016/j.ijsolstr.2008.02.025
Multiphase composites with extremal bulk modulus, Journal of the Mechanics and Physics of Solids, vol.48, issue.3, pp.461-498, 2000. ,
DOI : 10.1016/S0022-5096(99)00043-5
Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Computer Methods in Applied Mechanics and Engineering, vol.83, issue.2, pp.143-198, 1990. ,
DOI : 10.1016/0045-7825(90)90148-F
Design of maximum permeability material structures, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.4-61006, 2007. ,
DOI : 10.1016/j.cma.2006.08.006
Analysis of Composite Materials???A Survey, Journal of Applied Mechanics, vol.50, issue.3, pp.481-505, 1983. ,
DOI : 10.1115/1.3167081
A review of homogenization and topology opimization II???analytical and numerical solution of homogenization equations, Computers & Structures, vol.69, issue.6, pp.719-738, 1998. ,
DOI : 10.1016/S0045-7949(98)00132-1
A further review of ESO type methods for topology optimization, Structural and Multidisciplinary Optimization, vol.21, issue.11, pp.671-683, 2010. ,
DOI : 10.1007/s00158-010-0487-9
Topological design of microstructures of cellular materials for maximum bulk or shear modulus, Computational Materials Science, vol.50, issue.6, pp.1861-1870, 2011. ,
DOI : 10.1016/j.commatsci.2011.01.030
Structure topology optimization: fully coupled level set method via FEMLAB, Structural and Multidisciplinary Optimization, vol.29, issue.6, pp.407-417, 2005. ,
DOI : 10.1007/s00158-004-0503-z
Topology optimization of 2D continua for minimum compliance using parallel computing, Structural and Multidisciplinary Optimization, vol.89, issue.2, pp.121-132, 2006. ,
DOI : 10.1007/s00158-006-0006-1
URL : https://hal.archives-ouvertes.fr/hal-00982735
Effective properties of composite materials with periodic microstructure: a computational approach, Computer Methods in Applied Mechanics and Engineering, vol.172, issue.1-4, pp.1-4109, 1999. ,
DOI : 10.1016/S0045-7825(98)00227-8
Optimal design of periodic linear elastic microstructures, Computers & Structures, vol.76, issue.1-3, pp.421-429, 2000. ,
DOI : 10.1016/S0045-7949(99)00172-8
Optimal design of periodic functionally graded composites with prescribed properties, Structural and Multidisciplinary Optimization, vol.52, issue.12, pp.469-489, 2009. ,
DOI : 10.1007/s00158-008-0300-1
Hierarchical optimization of material and structure, Structural and Multidisciplinary Optimization, vol.24, issue.1, pp.1-10, 2002. ,
DOI : 10.1007/s00158-002-0209-z
Materials with prescribed constitutive parameters: An inverse homogenization problem, International Journal of Solids and Structures, vol.31, issue.17, pp.2313-2329, 1994. ,
DOI : 10.1016/0020-7683(94)90154-6
A new class of extremal composites, Journal of the Mechanics and Physics of Solids, vol.48, issue.2, pp.397-428, 2000. ,
DOI : 10.1016/S0022-5096(99)00034-4
A 99 line topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, vol.21, issue.2, pp.120-127, 2001. ,
DOI : 10.1007/s001580050176
Morphology-based black and white filters for topology optimization, Structural and Multidisciplinary Optimization, vol.21, issue.13, pp.4-5401, 2007. ,
DOI : 10.1007/s00158-006-0087-x
Topology optimization approaches, Structural and Multidisciplinary Optimization, vol.15, issue.2, pp.1031-1055, 2013. ,
DOI : 10.1007/s00158-013-0978-6
Design of materials with extreme thermal expansion using a three-phase topology optimization method, 1997. ,
A 199-line Matlab code for Pareto-optimal tracing in topology optimization, Structural and Multidisciplinary Optimization, vol.89, issue.4, p.665, 2010. ,
DOI : 10.1007/s00158-010-0534-6
The method of moving asymptotes???a new method for structural optimization, International Journal for Numerical Methods in Engineering, vol.20, issue.2, pp.359-373, 1987. ,
DOI : 10.1002/nme.1620240207
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab, Structural and Multidisciplinary Optimization, vol.74, issue.250, pp.309-328, 2012. ,
DOI : 10.1007/s00158-011-0706-z
PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes, Structural and Multidisciplinary Optimization, vol.89, issue.1???3, pp.329-357, 2012. ,
DOI : 10.1007/s00158-011-0696-x
Topological shape optimization of microstructural metamaterials using a level set method, Computational Materials Science, vol.87, pp.178-186, 2014. ,
DOI : 10.1016/j.commatsci.2014.02.006
Concurrent topology optimization design of material and structure within <mml:math altimg="si25.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>FE</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> nonlinear multiscale analysis framework, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.524-542, 2014. ,
DOI : 10.1016/j.cma.2014.05.022
A reduced multiscale model for nonlinear structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.280, pp.117-134, 2014. ,
DOI : 10.1016/j.cma.2014.07.024
Multiscale structural topology optimization with an approximate constitutive model for local material microstructure, Computer Methods in Applied Mechanics and Engineering, vol.286, pp.147-167, 2015. ,
DOI : 10.1016/j.cma.2014.12.018
A unified periodical boundary conditions for representative volume elements of composites and applications, International Journal of Solids and Structures, vol.40, issue.8, pp.1907-1921, 2003. ,
DOI : 10.1016/S0020-7683(03)00024-6
On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites, International Journal of Solids and Structures, vol.43, issue.2, pp.266-278, 2006. ,
DOI : 10.1016/j.ijsolstr.2005.03.055
A superelement formulation for the efficient layout design of complex multi-component system, Structural and Multidisciplinary Optimization, vol.78, issue.5, pp.643-655, 2012. ,
DOI : 10.1007/s00158-011-0720-1
An implicit model for the integrated optimization of component layout and structure topology, Computer Methods in Applied Mechanics and Engineering, vol.257, pp.87-102, 2013. ,
DOI : 10.1016/j.cma.2013.01.008
Optimality criteria method for topology optimization under multiple constraints, Computers & Structures, vol.79, issue.20-21, pp.20-211839, 2001. ,
DOI : 10.1016/S0045-7949(01)00126-2
Scale-related topology optimization of cellular materials and structures, International Journal for Numerical Methods in Engineering, vol.8, issue.9, pp.993-1011, 2006. ,
DOI : 10.1002/nme.1743
Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures, Acta Mechanica Sinica, vol.81, issue.22/23, pp.77-89, 2007. ,
DOI : 10.1007/s10409-006-0045-2
URL : https://hal.archives-ouvertes.fr/hal-00263914