arXiv subjects

Junzhi Cui

Publications and source records attributed to Junzhi Cui.

10 recordsLinked to original sources

arXiv2023

Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of random composite materials with temperature-dependent properties

Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order multi-scale (SHOMS) method for nonlinear thermo-mechanical simulation of random composite materials, which is designed to overcome limitations of prohibitive computation involving the macro-scale and micro-scale. By virtue of statistical multi-scale asymptotic analysis and Taylor series method, the SHOMS computational model is rigorously derived for accurately analyzing nonlinear thermo-mechanical responses of random composite materials both in the macro-scale and micro-scale. Moreover, the local error analysis of SHOMS solutions in the point-wise sense clearly illustrates the crucial indispensability of establishing the higher-order asymptotic corrected terms in SHOMS computational model for keeping the conservation of local energy and momentum. Then, the corresponding space-time multi-scale numerical algorithm with off-line and on-line stages is designed to efficiently simulate nonlinear thermo-mechanical behaviors of random composite materials. Finally, extensive numerical experiments are presented to gauge the efficiency and accuracy of the proposed SHOMS approach.

math.NA↗

arXiv2023

Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials

The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials with highly oscillatory and discontinuous coefficients. In this novel HOMS-DRM, higher-order multi-scale analysis and modeling are first employed to overcome limitations of prohibitive computation and Frequency Principle when direct deep learning simulation. Then, improved deep Ritz method are designed to high-accuracy and mesh-free simulation for macroscopic homogenized equation without multi-scale property and microscopic lower-order and higher-order cell problems with highly discontinuous coefficients. Moreover, the theoretical convergence of the proposed HOMS-DRM is rigorously demonstrated under appropriate assumptions. Finally, extensive numerical experiments are presented to show the computational accuracy of the proposed HOMS-DRM. This study offers a robust and high-accuracy multi-scale deep learning framework that enables the effective simulation and analysis of multi-scale problems of authentic composite materials.

math.NA↗

arXiv2023

Homogenization with quasistatic Tresca's friction law: qualitative and quantitative results

Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law, and studies the homogenization theories under the frameworks of H-convergence and small $ε$-periodicity. The qualitative result is based on H-convergence, which shows the original oscillating solutions will converge weakly to the homogenized solution, while our quantitative result provides an estimate of asymptotic errors in $H^1$-norm for the periodic homogenization. This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.

math.AP↗

arXiv2022

Quantification of the atomic surfaces and volumes of a metal cluster based on the molecular surface model

The atomic volume and surface are important geometric quantities for calculating various macroscopic physical quantities from atomic models. This paper proposes a new analytical method to calculate the atomic volumes and surfaces of a metal cluster. This method adopts metallic radii to describe atom sizes and constructs the overall volume/surface by the molecular surface (MS) model. It divides cluster atoms into two types: interior atoms and boundary atoms. For an interior atom, the method defines a variational Voronoi cell as its volume. For a boundary atom, the method defines the intersection of the overall cluster volume and its variational Voronoi cell as its volume. The atomic surfaces are calculated along with the volume calculations. This new method considers the effect of atom sizes and can calculate not only the overall volume of a cluster but also the individual volume for each atom. This method provides computational support for multiscale coupled calculations from the microscale to macroscale.

cond-mat.mtrl-sci↗

arXiv2020

Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems

In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called boundary correctors is a common technique in existing methods to prove the convergence rate of MsFEM, while we think not reflects the essence of those problems. Instead, we focus on the first-order expansion structure. Through recently developed estimations in homogenization theory, our convergence rate is provided with milder assumptions and in neat forms.

math.NA↗

arXiv2019

A First-order Two-scale Analysis for Contact Problems with Small Periodic Configurations

This paper is devoted to studying a type of contact problems modeled by hemivariational inequalities with small periodic coefficients appearing in PDEs, and the PDEs we considered are linear, second order and uniformly elliptic. Under the assumptions, it is proved that the original problem can be homogenized, and the solution weakly converges. We derive an $O(ε^{1/2})$ estimation which is pivotal in building the computational framework. We also show that Robin problems--- a special case of contact problems, it leads to an $O(ε)$ estimation in $L^2$ norm. Our computational framework is based on finite element methods, and the numerical analysis is given, together with experiments to convince the estimation.

math.NA↗

arXiv2019

Heat capacity and thermal expansion of metal crystalline materials based on dynamic thermal vibration

A novel approach based on dynamic thermal vibration is proposed to calculate the heat capacity and thermal expansion coefficient (TEC) for metal crystalline materials from 0K to the melting point. The motion of metal atomic clusters is decomposed into structural deformation and thermal vibration. Then thermal vibration equations are established by the fourth-order Taylor expansion of Hamiltonian at the transient structural deformation position $\bar{\mathbf{x}}$. As a result, the thermal vibration frequencies dynamically change with the structural deformation positions and temperatures. A parameter $\barδ(\bar{\mathbf{x}}, T)$ is newly introduced to illustrate how the thermal vibration frequencies vary with the temperature $T$. Besides, the modified temperature-dependent Grüneisen parameter $\bar γ(\bar{\mathbf{x}}, T)$ is given. Finally, the formulae of heat capacity and TEC for metal crystalline materials are derived from the dynamic thermal vibration frequencies and $\bar δ(\bar{\mathbf{x}}, T)$ as well as $\bar γ(\bar{\mathbf{x}}, T)$. The numerical results of heat capacity and TEC for metals Cu, Al, Au, Ag, Ni, Pd, Pt and Pb show a temperature dependence and agree well with the experimental data from 0K to the melting point. This work suggests an efficient approach to calculate thermodynamic properties of metal materials for a wide range of temperatures, up to the melting point.

cond-mat.stat-mech↗

arXiv2017

Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on asymptotic homogenization method. Then, the error analysis in the pointwise sense is given to illustrate the importance of developing SOTS solutions. Furthermore, the error estimates for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

math.NA↗

arXiv2016

Shock responses of nanoporous aluminum by molecular dynamics simulations

We present systematic investigations on the shock responses of nanoporous aluminum (np-Al) by nonequilibrium molecular dynamics simulations. The dislocation nucleation sites are found to concentrate in low latitude region near the equator of the spherical void surfaces. We propose a continuum wave reflection theory and a resolved shear stress model to explain the distribution of dislocation nucleation sites. The simulations reveals two mechanisms of void collapse: the plasticity mechanism and the internal jetting mechanism. The plasticity mechanism, which leads to transverse collapse of voids, prevails under relatively weaker shocks; while the internal jetting mechanism, which leads to longitudinal filling of the void vacuum, plays more significant role as the shock intensity increases. In addition, an abnormal thermodynamic phenomenon (i.e., arising of temperature with pressure dropping) in shocked np-Al is discovered. This phenomenon is incompatible with the conventional Rankine-Hugoniot theory, and is explained by the nonequilibrium processes involved in void collapse. The influences of void collapse on spall fracture of np-Al is studied. Under the same loading velocity, the spall strength of np-Al is found to be lower than that of single-crystal Al; but the spall resistance is higher in np-Al than in single-crystal Al. This is explained by the combined influences of thermal dissipation and stress attenuation during shock wave propagation in np-Al.

physics.comp-ph↗

arXiv2014

Quantum-Atomic-Continuum-Coupled Model for Mechanical Behaviors in Micro-nano Simulations

For the numerical simulations of physical and mechanical behaviors of materials at the micro-nano scale, a coupled model with the effect of local quantum is presented in this paper. Unlike traditional methods, the transition region is not needed since the non-local mechanical effects and the constitutive relations are naturally involved by first principle density functional calculations. In order to identify and calculate the mechanical quantities at different scales, some necessary assumptions are made when solving Kohn-Sham equations. Basic deformation elements are introduced and mechanical tensors are explicitly derived based on the complex Bravais lattice. The responses of 3-demensional copper nanowires which composed of 25313 atoms under different external loads are simulated. Strain and stress fields are calculated and dislocation distributions are predicted during the damage process. Numerical results confirm the validity and transferability of this model.

cond-mat.mtrl-sci↗