Elements of homogenization for inelastic solid mechanics.

*(English)*Zbl 0645.73012
Homogenization techniques for composite media, Proc. Lect. CISM, Udine/Italy 1985, Lect. Notes Phys. 272, 193-278 (1987).

[For the entire collection see Zbl 0619.00027.]

This paper presents recent developments in the field of the behavior of composites with some emphasis on the nonlinear and inelastic range. It begins with general considerations on representative volume elements (r.v.e.) and averaging. It defines notions of homogenization and localization. The three possible boundary conditions on the r.v.e. are given and the convenient spaces are introduced for use of variational methods. Chapter 3 applies these considerations to linear problems in elasticity and viscoelasticity. Chapter 4 is devoted to the failure of ductile heterogeneous materials and the determination of the domain of admissible stresses for elastic plastic composites. In these two chapters comparisons experiments/computations are performed. The last chapter studies the difficult problem of describing the overall behaviour of a material made of the assembly of elastic perfectly plastic constituents. Three approximate models are given in order to obtain more quantitative results.

This paper presents recent developments in the field of the behavior of composites with some emphasis on the nonlinear and inelastic range. It begins with general considerations on representative volume elements (r.v.e.) and averaging. It defines notions of homogenization and localization. The three possible boundary conditions on the r.v.e. are given and the convenient spaces are introduced for use of variational methods. Chapter 3 applies these considerations to linear problems in elasticity and viscoelasticity. Chapter 4 is devoted to the failure of ductile heterogeneous materials and the determination of the domain of admissible stresses for elastic plastic composites. In these two chapters comparisons experiments/computations are performed. The last chapter studies the difficult problem of describing the overall behaviour of a material made of the assembly of elastic perfectly plastic constituents. Three approximate models are given in order to obtain more quantitative results.

Reviewer: Th.Lévy

##### MSC:

74E05 | Inhomogeneity in solid mechanics |

74E30 | Composite and mixture properties |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |

46S30 | Constructive functional analysis |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74B20 | Nonlinear elasticity |