Long-yuan Li

Rebound behaviour of spheres for plastic impacts

Abstract This paper presents a study on the rebound behaviour of spheres impacted normally against a target wall using finite element methods. The emphasis is on the prediction of the coefficient of restitution and the effects of material properties and impact velocities on the rebound behaviour of the sphere. Finite deformation during plastic impact is addressed. The finite element results show that, for impacts of small plastic deformation, the coefficient of restitution is mainly dependent on the ratio of the impact velocity Vi to the yield velocity Vy which is consistent with those predicted by the theory of impact mechanics; while for impacts of finite-plastic-deformation it is also dependent on the ratio of the representative Youngs Modulus E* to the yield stress Y. The FEA results suggest that for impacts of finite-plastic-deformation the coefficient of restitution can be approximated to be proportional to [(Vi/Vy)/(E*/Y)]−1/2.

A theoretical model for the contact of elastoplastic bodies

Abstract The paper presents a theoretical model for the normal contact of a rigid sphere with an elastic-perfectly plastic half-space or an elastic-perfectly plastic sphere with a rigid wall. Formulae describing the force-displacement relationship for static contact problems and the coefficient of restitution for dynamic impact problems are derived. The present model can be considered as a modification of Johnsons model by using a more detailed pressure distribution function which is based on finite element analysis (PEA) results and considering the variation in the curvature of the contact surface during the contact interaction. In order to verify the theoretical model, finite element analyses are also conducted, and results are compared with those predicted by the model for both contact force-displacement relations and restitution coefficients. Good agreements between the model predictions and the FEA results are found.

A semi-analytical model for oblique impacts of elastoplastic spheres

Results of finite-element analysis (FEA) of oblique impacts of elastic and elastic, perfectly plastic spheres with an elastic flat substrate are presented. The FEA results are in excellent agreement with published data available in the literature. A simple model is proposed to predict rebound kinematics of the spheres during oblique impacts. In this model, the oblique impacts are classified into two regimes: (i) persistent sliding impact, in which sliding occurs throughout the impact, the effect of tangential (elastic or plastic) deformation is insignificant and the model reproduces the well-established theoretical solutions based on rigid body dynamics for predicting the rebound kinematics and (ii) non-persistent sliding impact, in which sliding does not occur throughout the impact duration and the rebound kinematics depends upon both Poissons ratio and the normal coefficient of restitution (i.e. the yield stress of the materials). For non-persistent sliding impacts, the variation of impulse ratio with impact angle is approximated using an empirical equation with four parameters. These parameters are sensitive to the values of Poissons ratio and the normal coefficient of restitution, but can be obtained by fitting numerical data. Consequently, a complete set of solutions is obtained for the rebound kinematics, including the tangential coefficient of restitution, the rebound velocity at the contact patch and the rebound rotational speed of the sphere during oblique impacts. The accuracy and robustness of this model is demonstrated by comparisons with FEA results and data published in the literature. The model is capable of predicting complete rebound behaviour of spheres for both elastic and elastoplastic oblique impacts.

Modelling of electrochemical chloride extraction from concrete: Influence of ionic activity coefficients

This paper presents a mathematical model for simulating electrochemical chloride extraction from concrete. The model considers the effects of ionic concentrations on diffusion and migration of charged ions. The transport equations of charged ions under the influence of an externally applied electrical field in concentrated solutions are derived. Numerical results are shown and they are compared with experiments.

Coefficients of restitution for elastoplastic oblique impacts

The paper presents results of a finite element analysis of both elastic and elastoplastic oblique impacts of a sphere with a target wall using the DYNA3D code. For elastic oblique impacts, the results are in complete agreement with previous publications. For elastoplastic oblique impacts, the rebound kinematics depend on the normal coefficient of restitution, which is conventionally assumed to be a function of the normal impact velocity irrespective of the impact angle. The results of the finite element simulations of elastoplastic impacts demonstrate that this is not the case.

A two-dimensional model of electrochemical chloride removal from concrete

Abstract This paper presents a two-dimensional computer model of electrochemical chloride removal (ECR) from concrete. The model involves consideration of not only the effects of electrostatic coupling of charged ions in a multi-component mixture but also the influence of a number of other factors, viz, adsorption of ions at interfaces between the electrolyte liquid and cement solid phases due to ionic binding, effects of porosity and tortuosity of pore structure. The model yields a system of non-linear convection–diffusion equations with variable coefficients which is solved using Galerkin finite element methods. Numerical results associated with electrochemical chloride removal are presented and some important features are highlighted.

Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

Abstract This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.

Nonlinear bending response and buckling of ring-stiffened cylindrical shells under pure bending

Abstract In this paper, the nonlinear bending response of finite length cylindrical shells with stiffening rings is investigated by using a modified Brazier approach. The basic assumptions for the present study are that the deformation of a shell subjected to pure bending can be simplified into a two-stage process. One is that the shell ovalizes but its axis remains straight; the other is that the bending of the shell is regarded as a beam with nonuniform ovalization. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding critical moment, associated with local buckling, is determined by employing the Seide–Weingarten approximation. Numerical results are shown and compared with those obtained from other methods, which demonstrates that the assumptions used in the present study are reasonable.

Contact Mechanics and Coefficients of Restitution

We assume that the energy dissipated during collisions between solid bodies is due to plastic deformation at the contact. The normal and tangential interactions between elastic and elastic-perfectly plastic spheres are discussed. For elastic-perfectly plastic spheres an analytical solution for the normal coefficient of resitution is presented which is velocity dependent. The predicted rebound kinematics for oblique impacts of elastic spheres are shown to be in excellent agreement with experimentaldata. Comparisons between predictions and experimentaldata for oblique impacts of elastoplastic spheres are only in agreement if sliding occurs throughout the impact duration.

Numerical simulation of corneal transport processes

This paper presents a numerical study on the transport of ions and ionic solution in human corneas and the corresponding influences on corneal hydration. The transport equations for each ionic species and ionic solution within the corneal stroma are derived based on the transport processes developed for electrolytic solutions, whereas the transport across epithelial and endothelial membranes is modelled by using phenomenological equations derived from the thermodynamics of irreversible processes. Numerical examples are provided for both human and rabbit corneas, from which some important features are highlighted.