ABSTRACT
Hypothesis:”e two materials are in principle bonded together. More precisely, we make the following assumptions:
◾ Both matrix m and ber f have the same longitudinal strain value noted εℓ. ◾ ”ere is afreedom along zon the interface between the two materials, allowing distinct
values of normal strain in each of the two materials:
ε εz m
≠
”e state of stress resulting from an applied force F can therefore be written as
∑→
∑ →
σ σ 0 0 0 0 0
0 0 0
0 0
0 0 0
0 0 0
and the corresponding state of strain as
∑ ∑ m
→
→
ε ε
ε
ε ε
ε
0 0
0 0
0 0
0 0
0 0
0 0
Eachmaterialbeingassumedlinearlyelasticandisotropic,itsbehaviorlaw(so-calledHooke’s law), is written in the form
∑ = + ∑− ∑( ) ( )1 v
E v E
trace I (10.1)
inwhichΣrepresentsthestraintensor,Σthestresstensor,andI theunitarytensor.E andvare the elastic constants of the considered material.
