Qinglin Duan

Interfacial effect on physical properties of composite media: Interfacial volume fraction with non-spherical hard-core-soft-shell-structured particles

Interfaces are known to be crucial in a variety of fields and the interfacial volume fraction dramatically affects physical properties of composite media. However, it is an open problem with great significance how to determine the interfacial property in composite media with inclusions of complex geometry. By the stereological theory and the nearest-surface distribution functions, we first propose a theoretical framework to symmetrically present the interfacial volume fraction. In order to verify the interesting generalization, we simulate three-phase composite media by employing hard-core-soft-shell structures composed of hard mono-/polydisperse non-spherical particles, soft interfaces, and matrix. We numerically derive the interfacial volume fraction by a Monte Carlo integration scheme. With the theoretical and numerical results, we find that the interfacial volume fraction is strongly dependent on the so-called geometric size factor and sphericity characterizing the geometric shape in spite of anisotropic particle types. As a significant interfacial property, the present theoretical contribution can be further drawn into predicting the effective transport properties of composite materials.

Mixed FEM–Crushable DEM Nested Scheme in Second-Order Computational Homogenization for Granular Materials

AbstractA mixed FEM–crushable discrete-element method (DEM) nested scheme in the frame of second-order computational homogenization for granular materials was proposed. The particle breakage followed by the discontinuity and dissipative relative movements between each of two immediate neighboring particles were modeled at the mesoscale to perform both the downscaling and upscaling between the mixed FEM at the macroscopic continuum scale and the crushable DEM at the mesoscopic discrete particle assembly scale. To develop the crushable DEM for modeling the mesostructural evolution within representative volume elements (RVEs) assigned to integrating points of the macroscopic Cosserat continuum in the homogenization, two grain breakage models consisting of crushing criteria and the fracture mode for an individual crushable particle were developed. Not only the contact forces, but also contact moments exerted on each individual grain via the contacting points on the grain surface, were taken into account to se...

Thermodynamic framework for damage-healing-plasticity of granular materials and net damage variable

Based on the meso-structured Voronoi cell model for discrete particle assembly and the derived meso-mechanically informed constitutive relations of anisotropic Cosserat continuum, thermodynamic framework of isothermal meso-mechanically informed damage-healing and plastic process for granular materials is presented. The accumulated net (effective) damage factor tensor combining both material damage and healing effects is defined in terms of the initial (undamaged) and current (damaged) elastic moduli tensors of the meso-structured Voronoi cell attributed to the material point. According to the non-negativity of thermodynamic energy dissipations, the net damage variable is separated into the two component internal state variables; i.e. the damage and healing variables, which are accumulated in terms of incremental damage and healing variables, respectively. The meso-mechanically informed macroscopic damage-healing and plastic characterization are achieved without the need to specify macroscopic phenomenological damage, healing and plastic criteria, and their evolution laws. The merit of the proposed tensorial net damage and healing variables in modeling healing effects on initial weakened elastic stiffness (i.e. initial material defects) is demonstrated in terms of their isotropic scalar forms and integrated into the continuum damage-healing mechanics. The numerical results conceptually illustrate the performance of the proposed definitions of meso-mechanically informed net damage, damage, and healing variables. The coupled damage-healing and plastic process in anisotropic Cosserat continuum for granular materials is characterized in terms of densities of thermodynamic dissipations that make effects of the damage-healing and the plastic component processes on the material failure quantitatively comparable.

On the Stabilization of Stress-Point Integration in the Element Free Galerkin Method

Stabilized stress-point integration schemes based on Least-Squares Stabilization (LSS), Taylor series Expansion Based Stabilization (TEBS) and Finite Increment Gradient (FIG) are compared for linear elastostaticity problems and some relations between them are described. Particular emphasis is placed on stress-point integration procedures with stabilization. The convergence and stability properties of stabilized methods in the framework of the element free Galerkin (EFG) method with stress-point integration are studied by numerical examples. It is shown that stabilized stress-point integration consumes much less computational time than full integration and exhibits higher accuracy and much better convergence and stability than unstabilized stress-point integration and stabilized nodal integration.

Modelling of Non-Isothermal Non-Newtonian Viscoelastic Flows

An adaptive coupled finite element (FE) and meshfree (MF) method in ALE description for numerical simulation of injection molding processes is proposed. In combination with the proposed method, an iterative stabilized fractional step algorithm using Characteristic Based Split procedure for numerical simulation of incompressible non-isothermal non-Newtonian fluid flows is developed. The pressure stabilization is further enhanced with introduction of the modified version of finite increment calculus (FIC) process into the proposed algorithm. A mixed finite element formulation for viscoelastic flows is derived, in which the FIC pressure stabilization process and the DEVSS method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU method is particularly chosen to deal with the convective terms in the constitutive equation of viscoelastic flows. With the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables are successfully used with numerical stability and high convergence rate even for viscoelastic flows with high Weissenberg numbers. Numerical experiments demonstrate the significance and performance of the proposed method.