PSI - Issue 79

Lorenzo Leonetti et al. / Procedia Structural Integrity 79 (2026) 485–492

487

Fig. 1. 2D modelling of a bioinspired staggered composite: (a) microstructure of natural nacre; (b) idealized periodic microstructure; (c) simplified micro-model.

2.2. Macro-modeling At the macroscale, a staggered composite is modelled as a homogeneous medium equipped with a nonlinear anisotropic constitutive behaviour. The related damage-dependent overall elastic properties are found via nonlinear homogenization. After assuming the existence of a macroscopic strain energy  also in the damaged configuration, the macroscopic constitutive law reads as: ( ) ( ) ( ) ( ) ( ) , , :  = =        u C u C C u , (3) where C is the homogenized damaged elastic moduli tensor, here playing the role of tensorial damage variable. By referring to standard thermodynamic consistency arguments, the related damage evolution law must satisfy the following damage dissipation inequality involving the damaged moduli rate tensor:

1 2

: :    C



.

(4)

0

D =−



2.3. Nonlinear homogenization for micro-to-macro transition The micro-to-macro relations for periodic composites with embedded cohesive interfaces can be expressed as:

1



d



=







\  

RVE coh

RVE

,

(5)

)

(

1





d  +    u n d



=



s

s



\  



RVE coh

coh

RVE

where the last term in the expression of  represents the strain contribution of embedded cohesive interfaces. Such relations satisfy the following extended Hill-Mandel principle: