Mechanical Properties and Energy Absorption Characteristics of Additively Manufactured Lightweight Novel Re-Entrant Plate-Based Lattice Structures

In this work, three novel re-entrant plate lattice structures (LSs) have been designed by transforming conventional truss-based lattices into hybrid-plate based lattices, namely, flat-plate modified auxetic (FPMA), vintile (FPV), and tesseract (FPT). Additive manufacturing based on stereolithography (SLA) technology was utilized to fabricate the tensile, compressive, and LS specimens with different relative densities (ρ). The base material’s mechanical properties obtained through mechanical testing were used in a finite element-based numerical homogenization analysis to study the elastic anisotropy of the LSs. Both the FPV and FPMA showed anisotropic behavior; however, the FPT showed cubic symmetry. The universal anisotropic index was found highest for FPV and lowest for FPMA, and it followed the power-law dependence of ρ. The quasi-static compressive response of the LSs was investigated. The Gibson–Ashby power law (≈ρn) analysis revealed that the FPMA’s Young’s modulus was the highest with a mixed bending–stretching behavior (≈ρ1.30), the FPV showed a bending-dominated behavior (≈ρ3.59), and the FPT showed a stretching-dominated behavior (≈ρ1.15). Excellent mechanical properties along with superior energy absorption capabilities were observed, with the FPT showing a specific energy absorption of 4.5 J/g, surpassing most reported lattices while having a far lower density.

Solid Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs

The need for quick and easy deflection calculations of various prefabricated slabs causes simplified procedures and numerical tools to be used more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Based on the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on the RVE boundary and generalized strains.

Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. That is why numerical analyzes are becoming a common standard in this branch of manufacturing. Such trend causes either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and / or perforation of corrugated board, i.e. processes that undoubtedly weaken the stiffness and strength of the corrugated board locally. However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing, as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

Randomly Dispersed Coated Composites Study by Statistical Approach and Numerical Homogenization Method

The aim of this work is the computation of effective elastic properties of 3D 3-phase random heterogeneous coated materials. For that, a new expression of the integral range for 3-phase random coated heterogeneous materials is used. The computation is achieved using a representative microstructure with non-overlapping inclusions. Numerical simulations is used under periodic boundary conditions (PBC) and kinematic uniform boundary conditions (KUBC) prescribed over Representative Volume Element (RVE). The obtained effective elastic properties are compared with different analytical models as Hashin and Shtrikman bounds and the n+1 phase model. Using the statistical methods, a new extension of the integral range for 3-phase coated materials is proposed.

Solid-Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs

The need for quick and easy deflection calculations of various prefabricated slabs causes that simplified procedures and numerical tools are used more and more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Using the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on RVE boundary and generalized strains.