Computational modelling of single crystals

The physical basis of computationally tractable models of crystalline plasticity is reviewed. A statistical mechanical model of dislocation motion through forest dislocations is formulated. Following Franciosi and co-workers (1980-88) the strength of the short-range obstacles introduced by the forest dislocations is allowed to depend on the mode of interaction. The kinetic equations governing dislocation motion are solved in closed form for monotonic loading, with transients in the density of forest dislocations accounted for. This solution, coupled with suitable equations of evolution for the dislocation densities, provides a complete description of the hardening of crystals under monotonic loading. Detailed comparisons with experiment demonstrate the predictive capabilities of the theory. An adaptive finite element formulation for the analysis of ductile single crystals is also developed. Calculations of the near-tip fields in Cu single crystals illustrate the versatility of the method

Constitutive model for plasticity in an amorphous polycarbonate

A constitutive model for describing the mechanical response of an amorphous glassy polycarbonate is proposed. The model is based on an isotropic elastic phase surrounded by an SO(3) continuum of plastic phases onto which the elastic phase can collapse under strain. An approximate relaxed energy is developed for this model on the basis of physical considerations and extensive numerical testing, and it is shown that it corresponds to an ideal elastic-plastic behavior. Kinetic effects are introduced as rate-independent viscoplasticity, and a comparison with experimental data is presented, showing that the proposed model is able to capture the main features of the plastic behavior of amophous glassy polycarbonate

Unsupervised Emergence of Egocentric Spatial Structure from Sensorimotor Prediction

Despite its omnipresence in robotics application, the nature of spatial knowledgeand the mechanisms that underlie its emergence in autonomous agents are stillpoorly understood. Recent theoretical works suggest that the Euclidean structure ofspace induces invariants in an agent’s raw sensorimotor experience. We hypothesizethat capturing these invariants is beneficial for sensorimotor prediction and that,under certain exploratory conditions, a motor representation capturing the structureof the external space should emerge as a byproduct of learning to predict futuresensory experiences. We propose a simple sensorimotor predictive scheme, applyit to different agents and types of exploration, and evaluate the pertinence of thesehypotheses. We show that a naive agent can capture the topology and metricregularity of its sensor’s position in an egocentric spatial frame without any a prioriknowledge, nor extraneous supervision

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement

A bilayer Double Semion Model with Symmetry-Enriched Topological Order

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topo- logical orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bi- layer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braid- ing self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry.Comment: revtex4 file, color figure

Asynchronous Variational Integrators

We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton’s variational principle. As a consequence of this variational structure, the algorithms conserve local momenta and a local discrete multisymplectic structure exactly. To guide the development of the discretizations, a spacetime multisymplectic formulation of elastodynamics is presented. The variational principle used incorporates both configuration and spacetime reference variations. This allows a unified treatment of all the conservation properties of the system.A discrete version of reference configuration is also considered, providing a natural definition of a discrete energy. The possibilities for discrete energy conservation are evaluated. Numerical tests reveal that, even when local energy balance is not enforced exactly, the global and local energy behavior of the AVIs is quite remarkable, a property which can probably be traced to the symplectic nature of the algorith

Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals

A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g. grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self-hardening of a crystal slip. Latent hardening occurs as the formation of new dislocation walls limits motion of new mobile dislocations, thus hardening future slip systems. Self-hardening is accomplished by an evolution of the subgrain structure length scale. The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms are also directly minimized within the subgrain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path is taken into account, giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements while modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependence due to the formation of the subgrain structures. Validation is accomplished by comparison with single crystal tension test results

Effect of atomic scale plasticity on hydrogen diffusion in iron: Quantum mechanically informed and on-the-fly kinetic Monte Carlo simulations

We present an off-lattice, on-the-fly kinetic Monte Carlo (KMC) model for simulating stress-assisted diffusion and trapping of hydrogen by crystalline defects in iron. Given an embedded atom (EAM) potential as input, energy barriers for diffusion are ascertained on the fly from the local environments of H atoms. To reduce computational cost, on-the-fly calculations are supplemented with precomputed strain-dependent energy barriers in defect-free parts of the crystal. These precomputed barriers, obtained with high-accuracy density functional theory calculations, are used to ascertain the veracity of the EAM barriers and correct them when necessary. Examples of bulk diffusion in crystals containing a screw dipole and vacancies are presented. Effective diffusivities obtained from KMC simulations are found to be in good agreement with theory. Our model provides an avenue for simulating the interaction of hydrogen with cracks, dislocations, grain boundaries, and other lattice defects, over extended time scales, albeit at atomistic length scales