Optimization of a Unit Periodic Cell in Lattice Block Materials Aimed at Thermo-Mechanical Applications

Muñoz-Rojas, Pablo A.; Carniel, Thiago André; Silva, Emilío Carlos Nelli; Öchsner, Andreas

doi:10.1007/8611_2010_32

Cited by 6 publications

(10 citation statements)

References 49 publications

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“…A brief review of the particular formulation for trusslike cells used in this article can be found in Yan et al (2006) and Muñoz-Rojas et al (2010).…”

Section: Homogenization Of Thermal and Mechanical Constitutive Tensorsmentioning

confidence: 99%

Optimization of three-dimensional truss-like periodic materials considering isotropy constraints

Guth

Luersen

Muñoz-Rojas

2015

Struct Multidisc Optim

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In recent years, much attention has been directed to the study of ultralight periodic cellular materials, such as the so called Periodic Truss Materials (PTMs), which are made up of truss-like unit cells. Application of these materials has its best potential in structures subjected to multifunctional, and sometimes conflicting, engineering requirements. Hence, optimization techniques can be employed to help finding the shape of the optimal unit cell for a given multifunctional application. Although the result can be geometrically complex, this difficulty can be minored in view of modern additive manufacturing technologies. This work presents a parameter/ topology optimization procedure to design the particular unit cell geometry (that is, finding the cross sections of the bars) that results in a macroscopic material with optimum homogenized elastic or/and thermal constitutive properties. Emphasis is devoted to analyze the effect of enforcing independently elastic or thermal isotropy in the macroscopic material behavior. Although isotropic behavior can be imposed through adequate cell symmetries, an equivalent effect can be achieved by satisfying equality constraints relating constitutive coefficients. A sequential quadratic programming algorithm (SQP) is adopted, thus enforcing equality constraints gradually and within a tolerance range. This results in an enlarged search space at intermediate stages, rendering an effective strategy to solve the optimization problem. Different 3D cases with engineering appeal are solved and the results discussed.

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“…A brief review of the particular formulation for trusslike cells used in this article can be found in Yan et al (2006) and Muñoz-Rojas et al (2010).…”

Section: Homogenization Of Thermal and Mechanical Constitutive Tensorsmentioning

confidence: 99%

Optimization of three-dimensional truss-like periodic materials considering isotropy constraints

Guth

Luersen

Muñoz-Rojas

2015

Struct Multidisc Optim

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“…In this Section, the main homogenization equations for elastic and thermal behavior of periodic structures are briefly sketched. For details the reader is refered to [7].…”

Section: Homogenization Of Thermal and Mechanical Constitutive Tensorsmentioning

confidence: 99%

“…(10) and (13) may be solved numerically using the Finite Element Method, as first proposed by Guedes and Kikuchi [8]. The detailed formulation for truss-like unit cells has been presented in [7] and will not be repeated here owing to text conciseness.…”

Section: Numerical Determination Of V and Rmentioning

confidence: 99%

Optimization of periodic truss materials including constitutive symmetry constraints

Guth

Luersen

Muñoz-Rojas³

2012

Materialwissenschaft Werkst

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Periodic truss materials (PTM) -or Lattice Block Materials (LBM) -belong to the family of the so called ultralight cellular materials, which have attractive engineering properties such as high stiffness/weight ratio and high energy absorption capability. These materials are obtained by the periodic repetition of a unit cell given by a truss structure, so that the orientation of the bars and the cross sectional areas define the material9s macroscopic behavior. In recent years, the development of new process technologies for manufacturing PTMs have brought increased interest in modeling their structural and thermal behavior. In addition to usual analytical and numerical approaches for analyzing the effect of different unit cell configurations on macroscopic properties, optimization techniques have been applied in order to tailor unit cells for achieving desired macroscopic constitutive properties. The present contribution uses mathematical programming for tailoring PTMs through a number of optimization problems in which selected homogenized elastic or thermal constitutive properties are maximized, at the same time that isotropy tries to be enforced by the inclusion of adequate material symmetry constraints. Cross sectional areas and nodal coordinates of the bars are adopted as design variables. 2D examples are presented showing qualitative agreement with results available for 2D elasticity.

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“…Figures 1 (a) and (b) display, respectively, an example of a 3D unit PTM cell and the corresponding porous material obtained by its periodic repetition. (Muñoz-Rojas et al, 2010); (b) Corresponding material (Guth et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Yan et al (2006) optimized truss-made unit cells adopting joint positions as design variables. Muñoz-Rojas et al (2010) proposed the layout optimization (simultaneous cross sectional areas and coordinates as design variables) of truss-made unit cells for achieving optimum thermo-mechanical periodic truss metamaterials. Guth et al (2012Guth et al ( , 2015 optimized the layout of PTMMs including mechanical and thermal isotropic behavior as constraints in the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

An Extended Multiscale Finite Element Method (EMsFEM) Analysis of Periodic Truss Metamaterials (PTMM) Designed by Asymptotic Homogenization

Jagiello

Muñoz-Rojas

2021

Lat. Am. j. solids struct.

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Asymptotic Homogenization (AH) and the Extended Multiscale Finite Element Method (EMsFEM) are both procedures that allow working on a structural macroscale that incorporates the effect of averaged microscopic heterogeneities, thus resulting in computationally efficient strategies. EMsFEM works directly on coupled finite micro and macroscales using numerically built discrete interpolation functions. Periodic Truss Metamaterials (PTMMs) are cellular materials formed by the periodic repetition of a truss-like unit cell and engineeringly tailored to show a given macroscopic response. In this work we analyze the numerical behavior of selected PTMMs that were designed for extreme Poisson ratios using AH theory. As a first issue, we study macroscopic structures made of finite unit cells and verify how close their average behavior coincides with the material properties predicted by AH. For comparison, we solve the macroscopic plane stress associate problems that employ the elastic constitutive tensor obtained by AH. The second issue is concerned with the ability of EMsFEM to reproduce the structural behavior of the full macro-micro model. We employ two versions of the EMsFEM, adopting linear (LBC) and periodic (PBC) boundary conditions to build the numerical interpolation functions. The third and most important aspect discussed in this research concerns evaluation of the EMsFEM downscaled displacement fields. We observe that according to the layout of the AH designed unit cell, to the use of LBC or PBC and, depending on the boundary conditions present in the macroscopic problem, spurious downscaled displacements might occur. Such spurious displacements are due to excessive compliance of the corresponding unit cell and can be detected when building the numerical interpolation functions. We conclude that the layout optimization of PTMM using AH must be carefully interpreted and that EMsFEM is a good tool to detect a macroscopic excessively compliant response at an early design stage.

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Optimization of a Unit Periodic Cell in Lattice Block Materials Aimed at Thermo-Mechanical Applications

Cited by 6 publications

References 49 publications

Optimization of three-dimensional truss-like periodic materials considering isotropy constraints

Optimization of three-dimensional truss-like periodic materials considering isotropy constraints

Optimization of periodic truss materials including constitutive symmetry constraints

An Extended Multiscale Finite Element Method (EMsFEM) Analysis of Periodic Truss Metamaterials (PTMM) Designed by Asymptotic Homogenization

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