Related papers: A Framework for FFT-based Homogenization on Anisot…
With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
Homogenization in linear elliptic problems usually assumes coercivity of the accompanying Dirichlet form. In linear elasticity, coercivity is not ensured through mere (strong) ellipticity so that the usual estimates that render…
This paper proposes an original adaptive refinement framework using Radial Basis Functions-generated Finite Differences method. Node distributions are generated with a Poisson Disk Sampling-based algorithm from a given continuous density…
We present a novel de-homogenization approach for efficient design of high-resolution load-bearing structures. The proposed approach builds upon a streamline-based parametrization of the design domain, using a set of space-filling and…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
We analyze fermionic response of strongly correlated holographic matter in presence of inhomogeneous periodically modulated potential mimicking the crystal lattice. The modulation is sourced by a scalar operator that explicitly breaks the…
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-mechanical setting, by promoting the design of unit cells characterized both by an…
We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary…
We show how the newly developed method of Periodic Unfolding on Riemannian manifolds can be applied to PDE problems: We consider the homogenization of an elliptic model problem. In the limit, we obtain a generalization of the well-known…
The homogenization of one-dimensional acoustic or elastic structures of finite extent is considered. A new homogenization method based on transfer matrices is derived. The new homogenization method may account for variable cross sectional…
Designing anisotropic structured materials by reducing symmetry results in unique behaviors, such as shearing under uniaxial compression or tension. This direction-dependent coupled mechanical phenomenon is crucial for applications such as…
We develop a general continuum mechanics framework for active anisotropic plates within the F\"oppl-von K\'arm\'an limit, incorporating a preferential direction and inelastic active contractions in geometrically nonlinear plate theory.…
Recent advances in scanning transmission electron and scanning tunneling microscopies allow researchers to measure materials structural and electronic properties, such as atomic displacements and charge density modulations, at an Angstrom…
This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present a general majorization framework for…
We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of…
Ultracold atoms in optical lattices are pristine model systems with a tunability and flexibility that goes beyond solid-state analogies, e.g., dynamical lattice-geometry changes allow tuning a graphene lattice into a boron-nitride lattice.…
Complete polarimeters deliver the full polarization transfer matrix of a medium that relates input polarization states to output polarization states. In order to interpret the Mueller matrix of a luminescent medium at the emission…