Finite Element Modeling and Analysis of Natural Fiber-Reinforced Composite

Insight into numerical characteristics of embedded finite elements for pile‐type structures employing an enhanced formulation

“…x𝑏 (𝜉, 𝑅, 𝜑) = 𝐫 𝑏 (𝜉) + 𝑅 ⋅ cos (𝜑) ⋅ 𝐞 𝑙 1 (𝜉) + 𝑅 ⋅ sin (𝜑) ⋅ 𝐞 𝑙 2 (𝜉) ⏟⎴⎴⎴⎴⎴⎴⎴⎴⎴⎴⎴⎴⏟⎴⎴⎴⎴⎴⎴⎴⎴⎴⎴⎴⎴⏟ 𝐫 𝑐𝑠 (𝜉,𝑅,𝜑) (9) where x𝑏 , x𝑠 ∈ ℝ 3 denote the current positions of coupled solid and beam material points initially sharing the same location at Γ 𝑐 in the reference configuration (Figure 5B), 𝐫 𝑏 (𝜉) ∈ ℝ 3 defines the beam centerline curve connection cross-section centroids (Figure 6A), and 𝐫 𝑐𝑠 (𝜉, 𝑅, 𝜑) ∈ ℝ 3 represents cross-section position vectors that point from the cross-section centroid to Γ 𝑐 , defined by means of the polar coordinates 𝑅 ∈ ℝ + and 𝜑 ∈ [0, 2𝜋); compare Figure 4. The rate form of Equation ( 8) in the reference configuration is defined by the material time derivative:…”

“…In the literature, a variety of cross-disciplinary applications exists, for instance in the form of steel reinforcements within concrete structures in structural engineering [2][3][4][5] or fibre-reinforced composites in material science. [6][7][8][9][10] Likewise, this concept can be found in other fields than solid mechanics 11,12 ; for example, countless biological systems comprise biopolymer networks of highly slender filaments, whereas the latter govern crucial processes, including cell migration and cell division. 13 In a very recent publication, 14 focus is placed on the electro-chemical analysis of fibrous electrodes where discrete fibres are embedded in an electrolyte matrix, a multi-functional material that can be used for energy storage and harvesting.…”

“…In the context of computational modelling, as considered in the following, the former will be referred to as sub‐scale elements (SSE), the matrix material as macro‐scale element (MSE) and the composite material as embedded reinforcement model (ERM). In the literature, a variety of cross‐disciplinary applications exists, for instance in the form of steel reinforcements within concrete structures in structural engineering 2–5 or fibre‐reinforced composites in material science 6–10 . Likewise, this concept can be found in other fields than solid mechanics 11,12 ; for example, countless biological systems comprise biopolymer networks of highly slender filaments, whereas the latter govern crucial processes, including cell migration and cell division 13 .…”