Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures

被引:97
作者
Giorgio, Ivan [1 ,2 ]
机构
[1] Univ Roma La Sapienza, Dept Struct & Geotech Engn, Rome, Italy
[2] Univ Aquila, Int Res Ctr Math & Mech Complex Syst MeMoCS, Cisterna Latina, Italy
来源
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2016年 / 67卷 / 04期
关键词
Nonlinear elasticity; Second gradient models; Elastic surface theory; Numerical parameter identification; MIXED FINITE-ELEMENT; POSTBUCKLING BEHAVIOR; REINFORCED COMPOSITE; ELASTICITY; BEAM; CONTINUUM; HOMOGENIZATION; STABILITY; DYNAMICS; SYSTEMS;
D O I
10.1007/s00033-016-0692-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In order to design the microstructure of metamaterials showing high toughness in extension (property to be shared with muscles), it has been recently proposed (Dell'Isola et al. in Z Angew Math Phys 66(6):3473-3498, 2015) to consider pantographic structures. It is possible to model such structures at a suitably small length scale (resolving in detail the interconnecting pivots/cylinders) using a standard Cauchy first gradient theory. However, the computational costs for such modelling choice are not allowing for the study of more complex mechanical systems including for instance many pantographic substructures. The microscopic model considered here is a quadratic isotropic Saint-Venant first gradient continuum including geometric nonlinearities and characterized by two Lame parameters. The introduced macroscopic two-dimensional model for pantographic sheets is characterized by a deformation energy quadratic both in the first and second gradient of placement. However, as underlined in Dell'Isola et al. (Proc R Soc Lond A 472(2185):20150790, 2016), it is needed that the second gradient stiffness depends on the first gradient of placement if large deformations and large displacements configurations must be described. The numerical identification procedure presented in this paper consists in fitting the macro-constitutive parameters using several numerical simulations performed with the micro-model. The parameters obtained by the best fit identification in few deformation problems fit very well also in many others, showing that the reduced proposed model is suitable to get an effective model at relevantly lower computational effort. The presented numerical evidences suggest that a rigorous mathematical homogenization result most likely holds.
引用
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页数:17
相关论文
共 104 条
[1]   Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof [J].
Alibert, Jean-Jacques ;
Della Corte, Alessandro .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (05) :2855-2870
[2]   Truss modular beams with deformation energy depending on higher displacement gradients [J].
Alibert, JJ ;
Seppecher, P ;
Dell'Isola, F .
MATHEMATICS AND MECHANICS OF SOLIDS, 2003, 8 (01) :51-73
[3]   On the linear theory of micropolar plates [J].
Altenbach, Holm ;
Eremeyev, Victor A. .
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2009, 89 (04) :242-256
[4]   A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis [J].
AminPour, H. ;
Rizzi, N. .
MATHEMATICS AND MECHANICS OF SOLIDS, 2016, 21 (02) :168-181
[5]  
AminPour H., 2014, CIV COMP P
[6]   On the Modelling of Carbon Nano Tubes as Generalized Continua [J].
Aminpour, Hossein ;
Rizzi, Nicola .
GENERALIZED CONTINUA AS MODELS FOR CLASSICAL AND ADVANCED MATERIALS, 2016, 42 :15-35
[7]   Experimental and numerical investigations of the responses of a cantilever beam possibly contacting a deformable and dissipative obstacle under harmonic excitation [J].
Andreaus, Ugo ;
Baragatti, Paolo ;
Placidi, Luca .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2016, 80 :96-106
[8]   Soft-impact dynamics of deformable bodies [J].
Andreaus, Ugo ;
Chiaia, Bernardino ;
Placidi, Luca .
CONTINUUM MECHANICS AND THERMODYNAMICS, 2013, 25 (2-4) :375-398
[9]  
[Anonymous], 2011, PAMM
[10]  
[Anonymous], 13 INT C CIV STRUCT