Molecular dynamics for the finite deformation of random elastic grids

Structural foams are widely used as energy absorbing materials for impact protection. The microstructure of these materials is often modeled as a periodic lattice of elastic beams. In previous studies [High strain compression of random open cell foams, MMC2001, San Diego, 2001; Int. J. Solids Struct...

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Published in:	Mechanics of materials Vol. 36; no. 12; pp. 1231 - 1245
Main Authors:	Alaoui-Soulimani, A., Sab, K., Pradel, F.
Format:	Journal Article Conference Proceeding
Language:	English
Published:	Lausanne Elsevier Ltd 01.12.2004 Amsterdam Elsevier Science New York, NY
Subjects:	Buckling Elasticity Exact sciences and technology Finite strains Fundamental areas of phenomenology (including applications) Homogenization Physics Random Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Theory and numerical methods Homogenization Elasticity Finite strains Random Buckling High strain Open cell porosity Scale effect Molecular dynamics method Molecular dynamics Periodic solution Porous material Modeling Periodic structure Micromechanics Finite element method Uniaxial compression Size effect Mechanical protection Surface instability Cell structure Probabilistic approach Strain energy Yield criterion Cable structure Beam(mechanics) Heterogeneous material Strain wave Lattice model Microstructure Energy absorption
ISSN:	0167-6636, 1872-7743
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Abstract	Structural foams are widely used as energy absorbing materials for impact protection. The microstructure of these materials is often modeled as a periodic lattice of elastic beams. In previous studies [High strain compression of random open cell foams, MMC2001, San Diego, 2001; Int. J. Solids Struct. 39 (2001) 3599; Détermination de la charge de flambement dans un matériau cellulaire périodique, XVme Congrès Français de Mécanique, Nancy, 2001; Scale effects in high strain compression of periodic open cell foams, ICTAM, 2000], a tetrakaidecahedral foam unit cell geometry was considered. The corresponding macroscopic buckling yield surface, defined as the first instability of the periodic solution, for proportional loading paths was numerically computed using finite element. In addition, for uniaxial compression, the post-buckling response has been computed and exhibits the well-known plateau regime of foam materials. In reality however, imperfections always arise during the foaming process. This leads to a random distribution of the constitutive material at cell edges, which modifies the material response and especially the plateau stress. If the microstructure were modeled as a random network of elastic beams [Eur. J. Mech. A/Solids 11 (1992) 585], the concept of buckling yield surface would not apply, and the stress level of the plateau could not be determined in this way. Some authors have carried out time consuming incremental finite element simulations on these random networks, in order to get the plateau region behavior. In our study, we have applied the molecular dynamics method to this problem. In order to illustrate our approach, we have considered a square network of elastic beams defined by a cross pattern, in which the material description has been randomly defined. The boundary conditions applied on the cell are strain-controlled. The elastic energy of each beam can be expressed in terms of the displacements of its ends. Therefore, total energy can be expressed in terms of the displacements of the lattice nodes U . The problem then is to identify the minimum of the total potential energy of the network under prescribed boundary conditions. The idea herein is to compute the solution as follows: each node is ascribed a virtual mass. Starting from arbitrary nodal displacements, with zero velocity, molecular dynamics are applied to compute system oscillations during a prescribed period of time T. We then determined the moment when the potential is minimized and we iterated the algorithm with nodal displacements corresponding to this minimum at zero velocity. We will begin by showing that this method is able to capture both the first instability of the perfectly periodic lattice (obtained analytically) and the post-buckling response. We will then study the random case, in order to demonstrate the capabilities of this methodology.
AbstractList	Structural foams are widely used as energy absorbing materials for impact protection. The microstructure of these materials is often modeled as a periodic lattice of elastic beams. In previous studies a tetrakaidecahedral foam unit cell geometry was considered. In reality however, imperfections always arise during the foaming process. This leads to a random distribution of the constitutive material at cell edges, which modifies the material response and especially the plateau stress. In our study, we have applied the molecular dynamics method to this problem. In order to illustrate our approach, we have considered a square network of elastic beams defined by a cross pattern, in which the material description has been randomly defined. The boundary conditions applied on the cell are strain-controlled. The elastic energy of each beam can be expressed in terms of the displacements of its ends. Therefore, total energy can be expressed in terms of the displacements of the lattice nodes U. The problem then is to identify the minimum of the total potential energy of the network under prescribed boundary conditions. The idea herein is to compute the solution as follows: each node is ascribed a virtual mass. Starting from arbitrary nodal displacements, with zero velocity, molecular dynamics are applied to compute system oscillations during a prescribed period of time T. We then determined the moment when the potential is minimized and we iterated the algorithm with nodal displacements corresponding to this minimum at zero velocity. We will begin by showing that this method is able to capture both the first instability of the perfectly periodic lattice (obtained analytically) and the post-buckling response. We will then study the random case, in order to demonstrate the capabilities of this methodology. Structural foams are widely used as energy absorbing materials for impact protection. The microstructure of these materials is often modeled as a periodic lattice of elastic beams. In previous studies [High strain compression of random open cell foams, MMC2001, San Diego, 2001; Int. J. Solids Struct. 39 (2001) 3599; Détermination de la charge de flambement dans un matériau cellulaire périodique, XVme Congrès Français de Mécanique, Nancy, 2001; Scale effects in high strain compression of periodic open cell foams, ICTAM, 2000], a tetrakaidecahedral foam unit cell geometry was considered. The corresponding macroscopic buckling yield surface, defined as the first instability of the periodic solution, for proportional loading paths was numerically computed using finite element. In addition, for uniaxial compression, the post-buckling response has been computed and exhibits the well-known plateau regime of foam materials. In reality however, imperfections always arise during the foaming process. This leads to a random distribution of the constitutive material at cell edges, which modifies the material response and especially the plateau stress. If the microstructure were modeled as a random network of elastic beams [Eur. J. Mech. A/Solids 11 (1992) 585], the concept of buckling yield surface would not apply, and the stress level of the plateau could not be determined in this way. Some authors have carried out time consuming incremental finite element simulations on these random networks, in order to get the plateau region behavior. In our study, we have applied the molecular dynamics method to this problem. In order to illustrate our approach, we have considered a square network of elastic beams defined by a cross pattern, in which the material description has been randomly defined. The boundary conditions applied on the cell are strain-controlled. The elastic energy of each beam can be expressed in terms of the displacements of its ends. Therefore, total energy can be expressed in terms of the displacements of the lattice nodes U . The problem then is to identify the minimum of the total potential energy of the network under prescribed boundary conditions. The idea herein is to compute the solution as follows: each node is ascribed a virtual mass. Starting from arbitrary nodal displacements, with zero velocity, molecular dynamics are applied to compute system oscillations during a prescribed period of time T. We then determined the moment when the potential is minimized and we iterated the algorithm with nodal displacements corresponding to this minimum at zero velocity. We will begin by showing that this method is able to capture both the first instability of the perfectly periodic lattice (obtained analytically) and the post-buckling response. We will then study the random case, in order to demonstrate the capabilities of this methodology.
Author	Alaoui-Soulimani, A. Pradel, F. Sab, K.
Author_xml	– sequence: 1 givenname: A. surname: Alaoui-Soulimani fullname: Alaoui-Soulimani, A. email: alaoui@lami.enpc.fr organization: Laboratoire Analyse des Matériaux et Identification (ENPC/LCPC), ENPC, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France – sequence: 2 givenname: K. surname: Sab fullname: Sab, K. email: sab@lami.enpc.fr organization: Laboratoire Analyse des Matériaux et Identification (ENPC/LCPC), ENPC, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France – sequence: 3 givenname: F. surname: Pradel fullname: Pradel, F. email: francis.pradel@ifp.fr organization: Institut Français du Pétrole, 1 et 4 avenue de Bois Preau, 92852 Rueil-Malmaison, France
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Cites_doi	10.5254/1.3539591 10.1016/S1359-6454(97)00453-9 10.1016/0167-6636(87)90020-2 10.1007/BF02417888 10.1016/0020-7403(66)90019-1 10.1016/S0020-7683(02)00172-5 10.1016/0001-6160(84)90177-9 10.1016/S0022-5096(97)00060-4 10.1016/S1251-8069(98)80002-X 10.1016/0022-5096(96)00047-6 10.1007/BF00380256 10.1016/S0022-5096(96)00090-7 10.1016/0022-5096(94)90085-X 10.3233/ASY-1997-15203 10.1098/rspa.1982.0087 10.1016/0022-5096(90)90041-2 10.1016/S0022-5096(97)00027-6 10.1098/rspa.1982.0088 10.1115/1.3173680 10.1115/1.2788979
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Keywords	Homogenization Elasticity Finite strains Random Buckling High strain Open cell porosity Scale effect Molecular dynamics method Molecular dynamics Periodic solution Porous material Modeling Periodic structure Micromechanics Finite element method Uniaxial compression Size effect Mechanical protection Surface instability Cell structure Probabilistic approach Strain energy Yield criterion Cable structure Beam(mechanics) Heterogeneous material Strain wave Lattice model Microstructure Energy absorption
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Snippet	Structural foams are widely used as energy absorbing materials for impact protection. The microstructure of these materials is often modeled as a periodic...
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SubjectTerms	Buckling Elasticity Exact sciences and technology Finite strains Fundamental areas of phenomenology (including applications) Homogenization Physics Random Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Theory and numerical methods
Title	Molecular dynamics for the finite deformation of random elastic grids
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