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This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like…

Computational Engineering, Finance, and Science · Computer Science 2023-04-17 Fengwen Wang , Ole Sigmund

Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bends{\o}e and Kikuchi from 1988, which…

Computational Engineering, Finance, and Science · Computer Science 2023-05-01 Christoffer Fyllgraf Christensen , Fengwen Wang , Ole Sigmund

Buckling strength estimation of architected materials has mainly been restricted to load cases oriented along symmetry axes. However, realistic load scenarios normally exhibit more general stress distributions. In this paper we propose a…

Applied Physics · Physics 2021-05-14 Morten N. Andersen , Yiqiang Wang , Fengwen Wang , Ole Sigmund

Efficient optimization of topology and raster angle has shown unprecedented enhancements in the mechanical properties of 3D printed materials. Topology optimization helps reduce the waste of raw material in the fabrication of 3D printed…

Graphics · Computer Science 2022-06-08 Ahmed Moter , Mohamed Abdelhamid , Aleksander Czekanski

Triply periodic minimal surface (TPMS) shell lattices are attracting increasingly attention due to their unique combination of geometric and mechanical properties, and their open-cell topology. However, uniform thickness TPMS shell lattices…

Numerical Analysis · Mathematics 2021-09-24 Qingping Ma , Lei Zhang , Junhao Ding , Shuo Qu , Jin Fu , Mingdong Zhou , Ming Wang Fu , Xu Song , Michael Yu Wang

The focus of this paper is on topology optimization of continuum structures subject to thermally induced buckling. Popular strategies for solving such problems include Solid Isotropic Material with Penalization (SIMP) and Rational…

Computational Engineering, Finance, and Science · Computer Science 2022-03-31 Shiguang Deng , Suresh Krishnan

This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process. Building upon established multiscale methodologies, we develop a new…

Computational Engineering, Finance, and Science · Computer Science 2025-05-08 Christoffer Fyllgraf Christensen , Fengwen Wang , Ole Sigmund

While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…

Soft Condensed Matter · Physics 2021-05-25 H. G. Wood , J. A. Hanna

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

Computational Engineering, Finance, and Science · Computer Science 2020-05-20 Reza Behrou , Maroun Abi Ghanem , Brianna C. Macnider , Vimarsh Verma , Ryan Alvey , Jinho Hong , Ashley F. Emery , Hyunsun Alicia Kim , Nicholas Boechler

We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements…

Numerical Analysis · Mathematics 2018-09-25 Federico Ferrari , Ole Sigmund

The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The…

Materials Science · Physics 2007-12-20 V. J. Challis , A. P. Roberts , A. H. Wilkins

Entangled matter displays unusual and attractive properties and mechanisms: tensile strength, capabilities for assembly and disassembly, damage tolerance. While some of the attributes and mechanisms share some traits with traditional…

Soft Condensed Matter · Physics 2025-04-09 Saeed Pezeshki , Youhan Sohn , Vivien Fouquet , Francois Barthelat

Variable stiffness is a key capability in biological and robotic systems, enabling adaptive interaction across tasks and environments. Mechanical metamaterials offer an alternative to conventional mechatronic solutions by encoding stiffness…

Soft Condensed Matter · Physics 2026-05-06 Hugo de Souza Oliveira , Michele Curatolo , Renate Sachse , Edoardo Milana

For their excellent stiffness-to-weight characteristics, triply periodic minimal surfaces (TPMS) are widely adopted in architected materials. However, their geometric regularity often leads to elastic anisotropy, limiting their…

Computational Physics · Physics 2025-05-21 Minwoo Park , Junheui Jo , Seunghwa Ryu

A tunable stiffness bone rod was designed, optimized, and 3D printed to address the common shortcomings of existing bone rods in the healing of long fractured bones. The common deficiencies of existing bone fixations are high stiffness,…

Applied Physics · Physics 2025-07-25 Mohammad Saber Hashemi , Karl H. Kraus , Azadeh Sheidae

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz.,…

Numerical Analysis · Mathematics 2013-11-14 S Natarajan , S Chakraborty , M Ganapathi , M Subramaniam

Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…

Computational Engineering, Finance, and Science · Computer Science 2025-02-05 Yingqi Jia , Xiaojia Shelly Zhang

Advances in manufacturing techniques may now realize virtually any imaginable microstructures, paving the way for architected materials with properties beyond those found in nature. This has lead to a quest for closing gaps in…

Materials Science · Physics 2020-11-10 Morten N. Andersen , Fengwen Wang , Ole Sigmund

This paper is devoted to the mechanical buckling analysis of thin composite plates under straight single-walled carbon nanotubes reinforcement with uniform distribution and random orientations. In order to develop the fundamental equations,…

Computational Engineering, Finance, and Science · Computer Science 2018-03-02 Hamid Foroughi , Hamidreza Askarieh Yazdi , Mojtaba Azhari

A buckled sheet offers a reservoir of material that can be unfurled at a later time. For sufficiently thin yet stiff materials, this geometric process has a striking mechanical feature: when the slack runs out, the material locks to further…

Soft Condensed Matter · Physics 2025-11-18 Pan Dong , Mengfei He , Nathan C. Keim , Joseph D. Paulsen
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