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Recent advances in nanoscale fabrication enable atomic-scale manipulation of two-dimensional (2D) materials by introducing engineered pores and perforations. This provides new opportunities to tailor functional properties of 2D materials…
The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
Development of lightweight materials with enhanced mechanical properties has been a long-standing challenge in science and engineering. Lightweight auxetic metastructures (AMSs) provide attractive solutions to this problem. AMSs' negative…
Pentamode metamaterials are a class of acoustic metafluids that are characterized by a divergence free modified stress tensor. Such materials have an unconventional anisotropic stiffness and isotropic mass density, which allow themselves to…
Metal rolling is a widespread and well-studied process, and many finite-element (FE) rolling simulations can be found in the scientific literature. However, these FE simulations are typically limited in their resolution of through-thickness…
We develop a model for ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies. This model applies to (i) magnetic materials with both uniaxial and cubic anisotropies, and (ii) magnetic nanoparticles with effective…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
The increasing number of protein-based metamaterials demands reliable and efficient theoretical and computational methods to study the physicochemical properties they may display. In this regard, we develop a simulation strategy based on…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…
Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…
Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, {\it e.g.} "rheochaos" in solutions of wormlike micelles and "elastic turbulence" in polymer solutions. Since both phenomena involve…
Process-structure-property relationships are fundamental in materials science and engineering and are key to the development of new and improved materials. Symbolic regression serves as a powerful tool for uncovering mathematical models…
The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The…
The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…
We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We…
A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric…
Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues.…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…