Related Experiment Video
Updated: Jan 6, 2026
08:32
Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
Published on: May 14, 2016
12.9K
Stiff isotropic lattices beyond the Maxwell criterion.
Wen Chen1,2, Seth Watts1, Julie A Jackson1
1Engineering Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA.
Science Advances
|October 11, 2019
Summary
Topology optimization enables the design of stiff, isotropic architected materials. Experiments validate these novel lattice structures, showing performance comparable to rule-based designs.
Area of Science:
- Materials Science
- Mechanical Engineering
- Computational Materials Design
Background:
- Stochastic microstructures (e.g., foams) have low stiffness.
- Lattice materials with designed microarchitectures offer improved stiffness.
- Rule-based designs using the Maxwell criterion often result in anisotropic properties.
Purpose of the Study:
- To design stiff, isotropic lattice materials using topology optimization.
- To experimentally validate the performance of these novel lattice structures.
- To compare the efficiency of topology-optimized lattices with rule-based designs.
Main Methods:
- Topology optimization based on continuum finite element analysis.
- Additive manufacturing for lattice fabrication.
- Experimental validation of mechanical performance.
Main Results:
- Successfully designed stiff isotropic lattices de novo.
- Experimental results validate predicted performance.
- Topology-optimized lattices demonstrate comparable efficiency to rule-based designs, even when seemingly violating the Maxwell criterion.
Conclusions:
- Topology optimization is a powerful tool for designing advanced architected materials.
- Novel isotropic lattice structures exhibit high stiffness and efficiency.
- This approach opens new possibilities for materials with unprecedented properties.
Related Concept Videos
01:28Symmetry in Maxwell's Equations
4.1K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
4.1K
02:54Trends in Lattice Energy: Ion Size and Charge
26.4K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
26.4K
01:17Gauss's Law in Dielectrics
5.0K
Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
5.0K
01:27Gauss's Law: Planar Symmetry
9.3K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
9.3K
01:17Differential Form of Maxwell's Equations
1.1K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.1K
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
516
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
516