PSI - Issue 37

Alexandru Vasile et al. / Procedia Structural Integrity 37 (2022) 857–864 Vasile et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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stages such as sizing optimization and shape optimization, developments are spectacular. In this paper we mainly focused on the material optimization process, (Kato, 2010). The scope of our work is to design a tridimensional heterogeneous structure that is based on an epoxy-polyamine resin, created using a base material and a hardener. Thus, we intend to obtain a configuration composed from hard and soft microscale subdomains, which will be designed by modelling such as to enhance the overall material toughness, without compromising its strength and modulus. 2. Problem formulation To support the modelling effort and develop the concept and tools required for microstructural design of parts that will then be used for inkjet reactive printing, we started with a fairly simple problem. We considered a bidimensional domain, as shown in Fig. 1a, since the layer height of the epoxy is in the order of micrometers, made up of two different materials for which we know, or can determine, the Young ’s modulus. It is assumed that the Young’s modulus of the soft material is E soft = 1000 MPa and for the hard material is 10 times greater, E hard =10000 MPa. In order to not differentiate between plane stress and plane strain we considered that the Poisson ratio of each material is 0.0. The goal is to find material distributions in this domain that ensure the best possible mechanical properties. To this purpose we identify a representative cell of the domain (Fig. 1b), and to further simplify the results, we analyzed only a quarter of the cell due to symmetry conditions (Fig. 1c). We can have a fixed percentage of material 1 and 2, 50% each being the case in this study, or consider different ratios. Fig, 1d shows the boundary conditions that were applied to our cell with 16 equal quadratic quadrilateral finite element. We constrained the X = 0 and Y = 0 lines of the model and used coupled sets of nodes (sets that have the same displacement) on the other lines so that we could introduce the force or displacements. For a linear elastic analysis, the stress distribution for each finite element is variable (Fig. 1e) if we do not consider a reduced integration element or stress mediation on the whole element but, for simplification, we considered that the stress is constant on each element (Fig. 1f).

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Fig. 1. Problem description a) 2D periodic microstructure b) Symmetric cell from the domain c) A quarter of the cell for analysis d) Boundary conditions e) Von Mises distribution for tensioning on the OX axis f) Stress distribution considered constant on each finite element. Finite element analyses were performed by using the PyAnsys software. This allowed us to define our input parameters and create an algorithm in a way as to ensure that it is as easy to reconfigure as possible, in order to