Realizable effective fractional viscoelasticity in heterogeneous materials

被引:4
作者
Brenner, R. [1 ]
机构
[1] Sorbonne Univ, CNRS, Inst Jean Rond Alembert, F-75005 Paris, France
关键词
MODELS; RELAXATION; EQUATIONS; CALCULUS; BOUNDS; MEDIA; LAW;
D O I
10.1016/j.mechrescom.2019.02.006
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
This note addresses the overall viscoelastic behaviour of composite materials made of elastic and viscous phases. By considering different microstructures, it is shown that classical or fractional viscoelasticity can be achieved. Hierarchical checkerboard microstructures are proposed to build fractional viscoelastic materials. (C) 2019 Published by Elsevier Ltd.
引用
收藏
页码:22 / 25
页数:4
相关论文
共 16 条
[1]   A THEORETICAL BASIS FOR THE APPLICATION OF FRACTIONAL CALCULUS TO VISCOELASTICITY [J].
BAGLEY, RL ;
TORVIK, PJ .
JOURNAL OF RHEOLOGY, 1983, 27 (03) :201-210
[2]   VARIATIONAL-PRINCIPLES FOR COMPLEX CONDUCTIVITY, VISCOELASTICITY, AND SIMILAR PROBLEMS IN MEDIA WITH COMPLEX MODULI [J].
CHERKAEV, AV ;
GIBIANSKY, LV .
JOURNAL OF MATHEMATICAL PHYSICS, 1994, 35 (01) :127-145
[3]   Power-law hereditariness of hierarchical fractal bones [J].
Deseri, Luca ;
Di Paola, Mario ;
Zingales, Massimiliano ;
Pollaci, Pietro .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, 2013, 29 (12) :1338-1360
[4]   HOMOGENIZATION AND OPTIMAL BOUNDS IN LINEAR ELASTICITY [J].
FRANCFORT, GA ;
MURAT, F .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 94 (04) :307-334
[5]   A method of analyzing experimental results obtained from elasto-viscous bodies [J].
Gemant, Andrew .
PHYSICS-A JOURNAL OF GENERAL AND APPLIED PHYSICS, 1936, 7 (01) :311-317
[6]   On the effective viscoelastic moduli of two-phase media. III. Rigorous bounds on the complex shear modulus in two dimensions [J].
Gibiansky, LV ;
Milton, GW ;
Berryman, JG .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1986) :2117-2149
[7]   FRACTAL RHEOLOGICAL MODELS AND FRACTIONAL DIFFERENTIAL-EQUATIONS FOR VISCOELASTIC BEHAVIOR [J].
HEYMANS, N ;
BAUWENS, JC .
RHEOLOGICA ACTA, 1994, 33 (03) :210-219
[8]   APPLICATIONS OF FRACTIONAL CALCULUS TO THE THEORY OF VISCOELASTICITY [J].
KOELLER, RC .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1984, 51 (02) :299-307
[9]   Creep, relaxation and viscosity properties for basic fractional models in rheology [J].
Mainardi, F. ;
Spada, G. .
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2011, 193 (01) :133-160
[10]  
Mainardi F., 2000, Fractional Calculus and Waves in Linear Viscoelasticity: an Introduction to Mathematical Models, DOI DOI 10.1142/P926