Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDeriving peridynamic influence functions for one-dimensional elastic materials with periodic microstructure
122
0
0.0
(
0
)
Added by
Xiao Xu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The influence function in peridynamic material models has a large effect on the dynamic behavior of elastic waves and in turn can greatly effect dynamic simulations of fracture propagation and material failure. Typically, the influence functions that are used in peridynamic models are selected for their numerical properties without regard to physical considerations. In this work, we present a method of deriving the peridynamic influence function for a one-dimensional initial/boundary value problem in a material with periodic microstructure. Starting with the linear local elastodynamic equation of motion in the microscale, we first use polynomial anzatzes to approximate microstructural displacements and then derive the homogenized nonlocal dynamic equation of motion for the macroscopic displacements; which, is easily reformulated as linear peridyamic equation with a discrete influence function. The shape and localization of the discrete influence function is completely determined by microstructural mechanical properties and length scales. By comparison with a highly resolved microstructural finite element model and the standard linear peridynamic model with a linearly decaying influence function, we demonstrate that the influence function derived from microstructural considerations is more accurate in predicting time dependent displacements and wave dynamics.
rate research
Read More
Determining a process-structure-property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials design are often considered in the context of process-property linkage by bypassing the materials structure, or in the context of structure-property linkage as in microstructure-sensitive design problems. However, there is a lack of research effort in studying materials design problems in the context of process-structure linkage, which has a great implication in reverse engineering. In this work, given a target microstructure, we propose an active learning high-throughput microstructure calibration framework to derive a set of processing parameters, which can produce an optimal microstructure that is statistically equivalent to the target microstructure. The proposed framework is formulated as a noisy multi-objective optimization problem, where each objective function measures a deterministic or statistical difference of the same microstructure descriptor between a candidate microstructure and a target microstructure. Furthermore, to significantly reduce the physical waiting wall-time, we enable the high-throughput feature of the microstructure calibration framework by adopting an asynchronously parallel Bayesian optimization by exploiting high-performance computing resources. Case studies in additive manufacturing and grain growth are used to demonstrate the applicability of the proposed framework, where kinetic Monte Carlo (kMC) simulation is used as a forward predictive model, such that for a given target microstructure, the target processing parameters that produced this microstructure are successfully recovered.
We study the momentum distribution of the electrons in an extended periodic Anderson model, where the interaction, $U_{cf}$, between itinerant and localized electrons is taken into account. In the symmetric half-filled model, due to the increase of the interorbital interaction, the $f$ electrons become more and more delocalized, while the itinerancy of conduction electrons decreases. Above a certain value of $U_{cf}$ the $f$ electrons become again localized together with the conduction electrons. In the less than half-filled case, we observe that $U_{cf}$ causes strong correlations between the $f$ electrons in the mixed valence regime.
Uncertainty involved in computational materials modeling needs to be quantified to enhance the credibility of predictions. Tracking the propagation of model-form and parameter uncertainty for each simulation step, however, is computationally expensive. In this paper, a multiscale stochastic reduced-order model (ROM) is proposed to propagate the uncertainty as a stochastic process with Gaussian noise. The quantity of interest (QoI) is modeled by a non-linear Langevin equation, where its associated probability density function is propagated using Fokker-Planck equation. The drift and diffusion coefficients of the Fokker-Planck equation are trained and tested from the time-series dataset obtained from direct numerical simulations. Considering microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations. It is demonstrated that once calibrated correctly using the available time-series datasets from these ICME models, the proposed ROM is capable of propagating the microstructure descriptors dynamically, and the results agree well with the ICME models.
A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $hbar$-expansions and suitable quantization conditions, the recursion formulae obtained have the same simple form both for ground and excited states and can be easily applied to any renormalization scheme. As an example, the renormalized expansions for the sextic anharmonic oscillator are considered.
We study the one-dimensional Schrodinger operators $$ S(q)u:=-u+q(x)u,quad uin mathrm{Dom}left(S(q)right), $$ with $1$-periodic real-valued singular potentials $q(x)in H_{operatorname{per}}^{-1}(mathbb{R},mathbb{R})$ on the Hilbert space $L_{2}left(mathbb{R}right)$. We show equivalence of five basic definitions of the operators $S(q)$ and prove that they are self-adjoint. A new proof of continuity of the spectrum of the operators $S(q)$ is found. Endpoints of spectrum gaps are precisely described.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
