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298 Random Composites functions adequate to composite materials are summarised below.The most simplified and natural formulation of the limit function is a difference between allowable and computed values of the structural state function or functions. All limit state functions proposed and used for composites can be divided basically into three different groups.The most generalised functions,independent from the composite components type,and even from homogeneity or heterogeneity of a medium and fracture character as well as physical mechanisms of the whole process,can be classified into the first group.The functions included in the second one obey a precise definition of material fracture mechanism in terms of elastoplastic behaviour,crack formation and its propagation into the composite during the whole process.The last group is characterised by the presence of the failure function in the limit function and is therefore usually oriented to the specific groups and types of composite materials. The most general relations are maximum stress and strain laws formulated in terms of longitudinal and transverse stresses and strain for both compression and tension as follows: maximum stress law: 8x(K)= o-oxox≥0) OLe+Gx(Gx <0) (6.9) 8,(K)= 0-0,6,20) OLe +o,(,<0) 8,(X)=O-s maximum strain law: 8x(X)= 「e-exex≥0) ELe+Ex(Ex<0) (6.10) 8,(X)= e-e,e,≥0 ELe+E,(E,<0) 8,(X)=EL-Esl As can be seen,the limit functions are independent from of composite material type (fibre-reinforced or laminated)as well as from the character of its components (polymer-based,metal matrix,etc.).They originate from the mechanics of homogeneous media.However,brittle or ductile character of material damage is not taken into account in the analysis as well as the possibility of crack formation during the fatigue process.That is why more sophisticated criteria are proposed as,for instance,the one formulated as298 Random Composites functions adequate to composite materials are summarised below. The most simplified and natural formulation of the limit function is a difference between allowable and computed values of the structural state function or functions. All limit state functions proposed and used for composites can be divided basically into three different groups. The most generalised functions, independent from the composite components type, and even from homogeneity or heterogeneity of a medium and fracture character as well as physical mechanisms of the whole process, can be classified into the first group. The functions included in the second one obey a precise definition of material fracture mechanism in terms of elastoplastic behaviour, crack formation and its propagation into the composite during the whole process. The last group is characterised by the presence of the failure function in the limit function and is therefore usually oriented to the specific groups and types of composite materials. The most general relations are maximum stress and strain laws formulated in terms of longitudinal and transverse stresses and strain for both compression and tension as follows: - maximum stress law: ( ) ( ) ⎩ ⎨ ⎧ + < − ≥ = 0 0 ( ) , , L c X X L t X X g X X σ σ σ σ σ σ ( ) ( ) ⎩ ⎨ ⎧ + < − ≥ = 0 0 ( ) , , L c y y L t y y g y X σ σ σ σ σ σ g y X =σ LT − σ S ( ) (6.9) - maximum strain law: ( ) ( ) ⎩ ⎨ ⎧ + < − ≥ = 0 0 ( ) , , L c X X L t X X g X X ε ε ε ε ε ε ( ) ( ) ⎩ ⎨ ⎧ + < − ≥ = 0 0 ( ) , , L c y y L t y y g y X ε ε ε ε ε ε g y X LT S ( ) = ε − ε (6.10) As can be seen, the limit functions are independent from of composite material type (fibre-reinforced or laminated) as well as from the character of its components (polymer-based, metal matrix, etc.). They originate from the mechanics of homogeneous media. However, brittle or ductile character of material damage is not taken into account in the analysis as well as the possibility of crack formation during the fatigue process. That is why more sophisticated criteria are proposed as, for instance, the one formulated as
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