PSI - Issue 37

Iulian Constantin Coropețchi et al. / Procedia Structural Integrity 37 (2022) 755 – 762 Coropetchi et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Natural materials exhibit high defect tolerance and insensitivity to flaws in their microstructure (Radi, 2020). These materials display the ability to combine complementary properties such as brittle and ductile or soft and stiff. For example, Nacre, made up 95% of calcite minerals and with only 5% of a compliant biopolymer protein, has a toughness that is 3000 times larger than the brittle minerals alone (Gao et al., 2003). Given the fact that natural composite materials have better properties than their components and that the current technology allows us to build similar composites, in this paper we discuss a way to replicate natural composite microstructure using numerical modelling. We used a brute force approach to evaluate all the possible solutions in our vector space and a modified Greedy algorithm that takes a random initial distribution of materials and evolves that distribution into an optimal solution. The objective of the optimization is to maximize the effective stiffness on both in-plane directions on a representative volume element (mentioned as RVE in the paper) made up of 50% soft material and 50% hard (stiff) material. 2. Problem description We considered a 2D periodic domain (Fig. 1a) made of 2 different materials for which we know the Young modulus E 1 = 1000 MPa (soft material - blue), E 2 = 10 E 1 (hard material - purple). The two materials are present in equal proportions: 50% material 1 and 50% material 2. The objective is to find material distributions that ensure extreme effective properties (homogenized). For this purpose, we identify a cell from our periodic domain (Fig. 1b) that can be analyzed, and due to symmetry conditions only by a quarter of the cell (Fig. 2a).

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Fig. 1. (a) 2D periodic microstructure; (b) Symmetric cell from the domain.

The quarter of the cell, which is a RVE, of general dimensions a and b (in our case a = b = 1 mm) can be analyzed by using proper boundary conditions (DOF constraints and forces/displacements) as in Fig. 2d with 16 equal Q8 finite elements. We constrained the X = 0 and Y = 0 lines of the model as shown in this figure and used coupled sets of nodes (sets that have the same displacement) on the X = a and Y = b lines so that we could introduce the imposed displacements.

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Fig. 2. (a) A quarter of the cell for analysis; (b) Boundary conditions.