Home-Imperial College London researchers develop topology optimization framework for nonlinear mechanical metamaterials
Researchers atImperial College Londonhave developed a computational framework for the inverse design of nonlinear mechanical metamaterials, using topology optimization to generate microscale unit cells from prescribed homogenized stress–strain targets.
Published inAdvanced Engineering Materials, the study was authored by Charlie Aveline, Matthew Santer, and Robert Hewson from Imperial College London’s Department of Aeronautics. The framework incorporates internal contact, snap-through buckling, and bistability in a single workflow, allowing designers to synthesize unit cells with complex mechanical responses without starting from predefined unit cell geometries or machine learning datasets.
The authors state that the approach could support the development of mechanical metamaterials for morphing structures, soft robotics, and energy absorbing materials. Mechanical metamaterials derive their unusual properties from the geometry of their internal unit cells. Additive manufacturing has expanded the range of physically realizable metamaterial geometries, but the paper notes that their unintuitive and multiscale behavior still requires robust design tools.
Designing unit cells from target stress–strain behavior
This framework uses density-based topology optimization to tune microscale unit cells. Each element in the design domain is assigned a density value between 0 and 1, representing void and solid material. The optimizer iteratively updates these densities until the simulated homogenized stress–strain response matches the user-defined goal points.
The workflow uses open-source Python libraries including Firedrake, pyadjoint, and cyipopt. For each design iteration, macroscale strain is applied across the unit cell, the microscale equilibrium is solved using finite element analysis, and the resulting homogenized stresses are compared with target values. Sensitivities are then calculated and used to update the unit cell geometry.
A key element of the framework is its use of the third medium contact method. This allows void-like regions between solid members to stiffen when highly compressed, enabling the model to transmit contact forces without explicitly defining contact interfaces. This differentiable contact formulation makes it suitable for gradient-based topology optimization.
The authors also added constraints to improve the physical realism of the generated designs. These include a volume constraint, a penalty against intermediate “gray” densities, and a tensile stiffness constraint to avoid disconnected structures or unit cells that only become stiff once contact occurs.
Pseudo-ductile, monostable, and bistable responses
Source: 3D Printing Industry
