Metal Foams: A Design Guide

Table 6.1 Constitutive equations for mechanical response
Isotropic solids: elastic deformation
Uniaxial ε1 D 1
E
General ε1 D 1
E E ⊲ 2 C 3⊳
Isotropic solids: plastic deformation
Uniaxial 1 � y
Design formulae for simple structures 63
General 1 3 D y ⊲ 1 > 2 > 3 ) (Tresca)
e � y (Von Mises) with
2 1
e D 2 [⊲ 1 2⊳2 C ⊲ 2 3⊳2 C ⊲ 3 1⊳2 ]
Metal foams: elastic deformation
Uniaxial As isotropic solids – though some foams are
General anisotripic
Metal foams: plastic deformation
Uniaxial 1 � y
General O � y
with O 2 D 1
⊲1 C ⊲˛/3⊳ 2 ⊳ [ 2 e C ˛2 2 m ]
and m D 1
3⊲ 1 C 2 C 3⊳
Material properties
E D Young’s modulus y D Yield strength
D Poisson’s ratio ˛ D Yield constant
volume when deformed plastically (unlike fully dense metals), a hydrostatic
pressure influences yielding. A constitutive equation which describes their
plastic response is listed in Table 6.1. It differs fundamentally from those for
fully dense solids. Details are given in Chapter 7.