Related papers: Closing the gap between atomic-scale lattice defor…
Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling…
In many processes for crystalline materials such as precipitation, heteroepitaxy, alloying, and phase transformation, lattice expansion or compression of embedded domains occurs. This can significantly alter the mechanical response of the…
The phase-field crystal (PFC) model describes crystal structures at diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…
We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…
We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…
The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
The concept of a local linear elastic strain field is commonly used in the metallurgical research community to approximate the collective effect of atomic displacements around crystalline defects. Here we show that the elastic strain field…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic…
The modeling of the elastic properties of granular or nanoscale systems requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which a…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
The phase field crystal (PFC) approach extends the notion of phase field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance…
Atomistic simulations of the molecular dynamics/statics kind are regularly used to study small scale plasticity. Contemporary simulations are performed with tens to hundreds of millions of atoms, with snapshots of these configurations…
Phase field crystal (PFC) models constitute a field theoretical approach to solidification, melting and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain…
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.…