When mechanical and structural engineers design machines, bridges, and buildings, they calculate loads, stresses, and deformation of metal, steel, concrete, glass, wood, and plastic to find the optimal geometry that bears loads with the minimum cost of material.
Designing for relatively hard materials that do not deform too much is commonly handled by software that calculates and optimizes structures using mathematical models that are well understood and easily applied.
But there is an expanding class of design challenges for things that incorporate soft materials—biological materials, engineered tissues, membranes, and even shape-shifting fluids that respond to electromagnetic fields. Predicting how these soft and fluidic materials respond to forces is more challenging than predicting the behavior of hard materials. Real world applications can include design of artificial hearts and heart valves or robot materials that mimic flesh and soft tissue.
To meet this challenge, a team of Tufts researchers led by Tim Atherton, professor of physics, created Morpho, an open-source programmable environment that enables researchers and engineers to solve shape optimization problems for soft materials. The software recently described in Nature Computational Science is meant to be easy to use, free to use , and applicable to a broad range of scenarios. Among the team developing the software were James Adler, professor of mathematics, and Chaitanya Joshi, postdoctoral scholar in physics.
"Many things that are interesting in science and engineering are shape optimization problems," said Atherton. That might mean coming up with the best possible contours for a city to accommodate traffic and pedestrians, or the shape of a riverbed with water flowing over it. The question then is, how to make flexible materials that respond in different ways to forces, light, temperature.
"Traditional modeling packages are used for geometric optimization of rigid structures, and are not usually designed to solve shape optimization problems for soft materials," he said. "Engineers typically have to come up with their own mathematical formulations for soft materials, which can be challenging. Morpho provides a set of tools to help anyone conveniently solve these problems."
Soft materials have an inherent complexity in their response to their environment. Membranes, for example, can be susceptible to compression, liquid flows, pressure, and vibrations. Particulate material can experience random turbulence when in motion. Their final shape can be very different than their starting point, and less predictable relative to rigid structures.
The Morpho program models the soft materials with a process known as finite elements, mathematically dividing them into small, simple shapes (2D or 3D shapes like triangles or tetrahedrons), while equations modeling material properties, forces, and boundary constraints are generated for each node around the shapes. Then the whole system of equations is solved to predict the optimal shape of the system.
In addition to soft materials, the program can model packing problems as well, whether it's the flow of granular particles in pharmaceutical manufacturing, coffee, or wine (yes, their properties are due mostly to the particles in these fluids) or how companies can optimally pack and ship products to minimize use of space and packing materials.
Morpho can also model heterogeneous systems, which include both hard and soft components. For example, a cardiovascular stent is a metal mesh surrounded by the soft tissue of the heart and arteries. Researchers can get a better idea of a stent's expected performance using the Morpho modeling software.
"You don't really need a lot of training on the program to tackle complex problems," said Atherton. "I've seen undergrads within a couple of weeks of learning Morpho use the package to solve research grade problems, which is amazing."
