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We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…
Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other…
Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
Permitting multiple materials within a topology optimization setting increases the search space of the technique, which facilitates obtaining high-performing and efficient optimized designs. Structures with multiple materials involving…
At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of…
This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…
Hierarchically structured natural materials possess functionalities unattainable to the same components organized or mixed in simpler ways. For instance, the bones and teeth of mammals are far stronger and more durable than the mineral…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
Architected materials can achieve enhanced properties compared to their plain counterparts. Specific architecting serves as a powerful design lever to achieve targeted behavior without changing the base material. Thus, the connection…
Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. Hierarchical metamaterials utilize structure at multiple size scales to realize new and…
Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d'\^etre has been lacking. Here, we present a general theory in which hierarchies are obtained as the optimal design that…
Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This…
Hierarchical microstructures are often invoked to explain the high resilience and fracture toughness of biological materials such as bone and nacre. Biomimetic material models inspired by those structural arrangements face the obvious…
Soft robotic manipulators are attractive for a range of applications such as medical interventions or industrial inspections in confined environments. A myriad of soft robotic manipulators have been proposed in the literature, but their…
A topology optimization problem in a phase field setting is considered to obtain rigid structures, which are resilient to external forces and constructable with additive manufacturing. Hence, large deformations of overhangs due to gravity…
We present a theory for the toughness, damage tolerance, and tensile strength of a class of hierarchical, fractal, metamaterials. We show that the even though the absolute toughness and damage tolerance decrease with increasing number of…
Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…