Ultralight Metallic/Composite Materials
with Architected Cellular Structures
Maryam Tabatabaei 1(B) and Satya N. Atluri 2
1 Department of Materials Science and Engineering, Pennsylvania State University, University
Park, Pennsylvania, PA 16802, USA
smt366@psu.edu
2 Texas Tech University, Lubbock, TX, USA
Abstract. Due to the emergence of technologies enabling the fabrication of complex cellular materials, new materials with higher mechanical efficiency than
the constituent material have been introduced. Combination of optimized cellular architectures with high-performance metals and composites can result in
lightweight materials with mechanical properties previously unattainable at low
densities. Consequently, new materials can be designed to maximally fit the target
application. There is a wide range of important applications including energy
absorption, metamaterial, thermal management, and bioscaffold for ultralight
architected cellular metals as well as airframes and shape morphing for ultralight architected cellular composites. Therefore, it is of importance to propose a
nearly exact and highly efficient methodology to study low-mass metal and composite systems with architected cellular structures. We present the simplest initial
computational framework for the analysis, design, and topology optimization of
such cellular materials. In the present methodology, the repetitive Representative
Volume Element (RVE) approach is employed to model the actual cellular metallic/composite micro-lattices. Each member of the cellular material is modeled
using only one finite beam element with 12 degrees of freedom (DOF), and the
nonlinear coupling of axial, bidirectional-bending, and torsional deformations is
studied for each spatial three-dimensional (3D) beam element. The large deformation analysis of the cellular strut members is performed utilizing mixed variational
principle in the updated Lagrangian co-rotational reference frame. The explicit
form of the stiffness matrix is calculated under the effect of plasticity for the case
of the cellular metals and under the effect of nonlinear flexible connections for the
case of the cellular composites. Then, we use newly proposed homotopy methods
to solve the algebraic equations.
Keywords: Architected cellular metals/composites · Plastic hinge mechanism ·
Nonlinear flexible connections · Homotopy methods
1 Introduction
Nature benefits from high stiffness and strength low-weight materials by evolving architected cellular structures. For example, trabecular bone, beaks and bones of birds, plant
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. N. Atluri and I. Vušanovi´ c (Eds.): ICCES 2020, MMS 97, pp. 20–28, 2021.
https://doi.org/10.1007/978-3-030-64690-5_3
with Architected Cellular Structures
Maryam Tabatabaei 1(B) and Satya N. Atluri 2
1 Department of Materials Science and Engineering, Pennsylvania State University, University
Park, Pennsylvania, PA 16802, USA
smt366@psu.edu
2 Texas Tech University, Lubbock, TX, USA
Abstract. Due to the emergence of technologies enabling the fabrication of complex cellular materials, new materials with higher mechanical efficiency than
the constituent material have been introduced. Combination of optimized cellular architectures with high-performance metals and composites can result in
lightweight materials with mechanical properties previously unattainable at low
densities. Consequently, new materials can be designed to maximally fit the target
application. There is a wide range of important applications including energy
absorption, metamaterial, thermal management, and bioscaffold for ultralight
architected cellular metals as well as airframes and shape morphing for ultralight architected cellular composites. Therefore, it is of importance to propose a
nearly exact and highly efficient methodology to study low-mass metal and composite systems with architected cellular structures. We present the simplest initial
computational framework for the analysis, design, and topology optimization of
such cellular materials. In the present methodology, the repetitive Representative
Volume Element (RVE) approach is employed to model the actual cellular metallic/composite micro-lattices. Each member of the cellular material is modeled
using only one finite beam element with 12 degrees of freedom (DOF), and the
nonlinear coupling of axial, bidirectional-bending, and torsional deformations is
studied for each spatial three-dimensional (3D) beam element. The large deformation analysis of the cellular strut members is performed utilizing mixed variational
principle in the updated Lagrangian co-rotational reference frame. The explicit
form of the stiffness matrix is calculated under the effect of plasticity for the case
of the cellular metals and under the effect of nonlinear flexible connections for the
case of the cellular composites. Then, we use newly proposed homotopy methods
to solve the algebraic equations.
Keywords: Architected cellular metals/composites · Plastic hinge mechanism ·
Nonlinear flexible connections · Homotopy methods
1 Introduction
Nature benefits from high stiffness and strength low-weight materials by evolving architected cellular structures. For example, trabecular bone, beaks and bones of birds, plant
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. N. Atluri and I. Vušanovi´ c (Eds.): ICCES 2020, MMS 97, pp. 20–28, 2021.
https://doi.org/10.1007/978-3-030-64690-5_3