Phenomenological and numerical modelling of short fibre reinforced cementitious composites

An orthotropic material model for steel fibre reinforced concrete based on the orientation distribution of fibres

“…The values of the scalar order-parameter are assumed in the range S ∈ [− 1 2 , 1], where the following values correspond to special configurations: S = 1 corresponds to the transversely isotropic material symmetry with well aligned fibres, S = 0 to the isotropy and S = − 1 2 describes the plane transversely isotropic case. The detailed derivation of the parameter S, as well as the bases for its ranges are presented in [20].…”

“…Another approach is the orientation profile (OP) [25], which extends the concept of the orientation number counting the amount of fibres (out of the total number of fibres given) within different inclination intervals assuming a pre-defined statistical distribution. An alternative would be the use of full orientation information of fibres and tensor quantities, as it is done for other materials containing or consisting of orientable particles [1,2,12,14,20,45,46]. In spherical coordinates the position of a point is specified by three numbers: radial distance, inclination angle , azimuth (in-plane) angle.…”

Modeling of delamination in fiber-reinforced composite using high-dimensional model representation-based cohesive zone model

“…However, many tests using the DCB specimen are plagued by fiber bridging. Despite the fact that the fiber bridging is undesirable, the researchers try to characterize the behavior of the structure at the occurrence of fiber bridging during structural failure [1,2]. To understand the sensitivity of the fiber bridging on the interlaminar fracture, an experimental study is conducted on DCB specimen [3]; as a result, the energy plot showed a steadily raising pattern in ERR with the increase in crack length, and this increasing phenomenon is known as R-curve effect [4,5].…”

“…In CZM, crack and material separation are represented by a traction-separation law using the zerothickness fracture process zone (FPZ) [19]. The CZM was implemented to study the different types of material failures in concrete [20,21], fiber-reinforced concrete [1,22], functionally gradient materials [23,24]. A new cohesive zone law was utilized to understand the effects of fiber bridging in fiber-reinforced composites and study the effectiveness in predicting the delamination [25].…”

“…Similarly from i = 2 to 5 and j = 1−5 expression are given by Expansion of (x 2 )f (c 1 , x1 2 , c 3 , c 4 , c 5 )+ ϕ 2 (x 2 )f (c 1 , x 2 2 , c 3 , c 4 , c 5 ) + ϕ 3 (x 2 )f (c 1 , x 3 2 , c 3 , c 4 , c 5 ) + ϕ 4 (x 2 )f (c 1 , x 4 2 , c 3 , c 4 , c 5 ) + 5 (x 2 )f (c 1 , x 5 Expansion (x 3 )f (c 1 , c 2 , x 1 3 , c 4 , c 5 ) + ϕ 2 (x 3 )f (c 1 , c 2 , x 2 3 , c 4 , c 5 ) + ϕ 3 (x 3 )f (c 1 , c 2 , x 3 3 , c 4 , c 5 ) + ϕ 4 (x 3 )f (c 1 , c 2 , x 4 3 , c 4 , c 5 ) + ϕ 5 (x 3 )f (c 1 , c 2 , x 5 Expansion (x 4 )f (c 1 , c 2 , c 3 , x 1 4 , c 5 ) + ϕ 2 (x 4 )f (c 1 , c 2 , c 3 , x 2 4 , c 5 ) + ϕ 3 (x 4 )f (c 1 , c 2 , c 3 , x 3 4 , c 5 ) + ϕ 4 (x 4 )f (c 1 , c 2 , c 3 , x 4 4 , c 5 ) + ϕ 5 (x 4 )f (c 1 , c 2 , c 3 , x 5 Expansion (x 5 )f (c 1 , c 2 , c 3 , c 4 , x 1 5 ) + ϕ 2 (x 5 )f (c 1 , c 2 , c 3 , c 4 , x 2 5 ) + ϕ 3 (x 5 )f (c 1 , c 2 , c 3 , c 4 , x 3 5 ) + ϕ 4 (x 5 )f (c 1 , c 2 , .c 3 , c 4 , x 4 5 ) + ϕ 5 (x 5 )f (c 1 , c 2 , c 3 , c 4 , x 5 c 2 , c3 , c 4 , c 5 ) = f (100, 4, 0.455, 210, 8.5) = 127.26; 0.1522 f (x 2 1 , c 2 , c 3 , c 4 , c 5 ) = f (250, 4, 0.455, 210, 8.5) = 171.92; 0.1523 f (x 3 1 , c 2 , c 3 , c 4 , c 5 ) = f (400, 4, 0.455, 210, 8.5) = 208.67; 0.1489 f (x 4 1 , c 2 , c 3 , c 4 , c 5 ) = f (550, 4, 0.455, 210, 8.5) = 243.50; 0.1440 f (x 5 1 , c 2 , c 3 , c 4 , c 5 ) = f (700, 4, 0.455, 210, 8.5) = 275.26; 0.1417 Similarly, all the function evaluations are carried out up to i = 5 and j = 1−0.0403x 3 + 2.4750 × 10 4 x 4 4 − 2.0773 × 10 4 x 3 4 + 6.5261 × 10 3 x 2 4 − 909.2747x 4 − 2.63389 × 10 −5 x 4 1993 × 10 −4 x 3 5 − 0.0117x 2 5 + 0.0645x 5…”