Related papers: The variational modeling of hierarchical structure…
We consider ferroelastic first-order phase transitions with $N_{OP}$ order-parameter strains entering Landau free energies as invariant polynomials, that have $N_V$ structural-variant Landau minima. The total free energy includes (seemingly…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
A simultaneous variational principle is introduced that offers a novel avenue to the description of the equilibrium configurations, and at the same time of the elementary excitations, or undulations, of fluid lipid membranes, described by a…
We present a simple variational framework for planar elastica that enables distributed energies, such as gravitational loading or magnetic body torques, to be incorporated in a modular and unified manner. The formulation is based on…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
In this paper, a force-based beam finite element model based on a modified higher-order shear deformation theory is proposed for the accurate analysis of functionally graded beams. In the modified higher-order shear deformation theory, the…
One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization.…
Oscillatory sheared suspensions, when observed stroboscopically, exhibit a reversible-irreversible transition as a function of the strain amplitude, which is a kind of absorbing phase transition. So far studies of this transition focused on…
Plastic deformation in amorphous solids is carried by localized shear transformations that self-organize into avalanches. In amorphous carbon modeled with a machine-learned interatomic potential, we find that the energetics and organization…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…
We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen…
Extreme deformation can drastically morph a structure from one structural form into another. Programming such deformation properties into the structure is often challenging and in many cases an impossible task. The morphed forms do not hold…
The rising demand for high-performing batteries requires new technological concepts. To facilitate fast charge and discharge, hierarchically structured electrodes offer short diffusion paths in the active material. However, there are still…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called…
In this chapter, we discuss avalanches in glasses and disordered systems, and the macroscopic dynamical behavior that they mediate. We briefly review three classes of systems where avalanches are observed: depinning transition of disordered…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…