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Effective properties of general closed-cell lattice metamaterials in 3D undergoing finite deformations
Effective properties of general closed-cell lattice metamaterials in 3D undergoing finite deformations
Keywords: closed cell lattices, metamaterials, truss network, homogenization, FE calculation
All materials have in common that an underlying microstructure -- e.g. the grain structure in metals or the fiber orientation in wood -- is governing the macroscopic response as we perceive it. Modern manufacturing techniques allow us to design the underlying structure on the micro- and nanoscale towards our needs. Hence, we may change the paradigm of engineering from material selection to material design. Closed-cell lattices are one promising class of microstructures, as it has been shown that they perform very close to theoretical limits (see Figure). The modeling of complex microstructures, containing millions of individual elements, becomes computationally prohibitively expensive, demanding for efficient continuum descriptions to approximate their mechanical behaviour. This project involves the development of a homogenization approach for plate-based lattices undergoing finite deformations to advance the understanding and structural integration of closed-cell lattice materials.
All materials have in common that an underlying microstructure -- e.g. the grain structure in metals or the fiber orientation in wood -- is governing the macroscopic response as we perceive it. Modern manufacturing techniques allow us to design the underlying structure on the micro- and nanoscale towards our needs. Hence, we may change the paradigm of engineering from material selection to material design. Closed-cell lattices are one promising class of microstructures, as it has been shown that they perform very close to theoretical limits (see Figure). The modeling of complex microstructures, containing millions of individual elements, becomes computationally prohibitively expensive, demanding for efficient continuum descriptions to approximate their mechanical behaviour. This project involves the development of a homogenization approach for plate-based lattices undergoing finite deformations to advance the understanding and structural integration of closed-cell lattice materials.
To this extend, we will (i) adapt an existing homogenization approach for (open-cell) periodic truss-based lattices under finite deformations to plates and (ii) use it to characterize and explore the design space of effective properties.
The project requires the construction of a discrete shell formulation that can be subsequentially inserted into an homogenization framework. The resulting two-scale model will be capable of efficiently predicting the nonlinear mechanical response of shell-networks, making the discrete FE calculation obsolete.
To this extend, we will (i) adapt an existing homogenization approach for (open-cell) periodic truss-based lattices under finite deformations to plates and (ii) use it to characterize and explore the design space of effective properties. The project requires the construction of a discrete shell formulation that can be subsequentially inserted into an homogenization framework. The resulting two-scale model will be capable of efficiently predicting the nonlinear mechanical response of shell-networks, making the discrete FE calculation obsolete.