Contact Law and Coefficient of Restitution in Elastoplastic Spheres

2015 ◽  
Vol 82 (12) ◽  
Author(s):  
Daolin Ma ◽  
Caishan Liu
Keyword(s):  
Analytical Approximation ◽  
Coefficient Of Restitution ◽  
Elastic Plastic ◽  
Plastic Regime ◽  
Material Hardness ◽  
Spherical Expansion ◽  
Transition Points ◽  
Complete Contact ◽  
C1 Continuity ◽  
Expansion Model

A complete contact cycle of an elastoplastic sphere consists of loading and unloading phases. The loading phase may fall into three sequential regimes: elastic, mixed elastic–plastic, and fully plastic. In this paper, we distinguish the transition points among the three regimes via the material hardness and a dimensionless geometric parameter corresponding to the onset of the fully plastic regime. Based on Johnson’s simplified spherical expansion model, together with the well-supported force–indentation relationships in the elastic and fully plastic regimes, we build an analytical approximation for the mixed elastic–plastic regime by enforcing the C1 continuity of a loading force–indentation curve. Unloading responses of the elastoplastic sphere are characterized by an elastic force–indentation relation, which has a Hertzian-type form but takes into account the effects of the strain hardening that occurs in the mixed elastic–plastic regime. We validate the model by comparing with existing quasi-static and impact experiments and show that the model can precisely capture the force–indentation responses. Further validation is performed by employing the proposed compliance model to investigate the coefficient of restitution (COR). We achieve agreement between our numerical results and the experimental data reported in other studies. Particularly, we find that the COR is inversely proportional to the impacting velocity with an exponent equal to 1/6, instead of 1/4 reported by many other models.

High Velocity Oblique Impact and Coefficient of Restitution for Head Disk Interface Operational Shock

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Raja R. Katta ◽  
Andreas A. Polycarpou ◽  
Jorge V. Hanchi ◽  
Robert M. Crone
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Impact Damage ◽  
Element Model ◽  
Oblique Impact ◽  
Coefficient Of Restitution ◽  
Energy Losses ◽  
Elastic Plastic ◽  
Impact Angles ◽  
Operational Shock

With the increased use of hard disk drives (HDDs) in mobile and consumer applications combined with the requirement of higher areal density, there is enhanced focus on reducing head disk spacing, and consequently there is higher susceptibility of slider/disk impact damage during HDD operation. To investigate this impact process, a dynamic elastic-plastic finite element model of a sphere (representing a slider corner) obliquely impacting a thin-film disk was created to study the effect of the slider corner radius and the impact velocity on critical contact parameters. To characterize the energy losses due to the operational shock impact damage, the coefficient of restitution for oblique elastic-plastic impact was studied using the finite element model. A modification to an existing physics-based elastic-plastic oblique impact coefficient of restitution model was proposed to accurately predict the energy losses for a rigid sphere impacting a half-space. The analytical model results compared favorably to the finite element results for the range from low impact angles (primarily normal impacts) to high impact angles (primarily tangential impacts).

scholarly journals The Effect of the Contact Model on the Design of Mechanical Systems

2012 ◽  
Author(s):  
M. R. Brake ◽  
D. S. Aragon ◽  
D. J. VanGoethem ◽  
H. Sumali
Keyword(s):  
Constant Coefficient ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Constitutive Models ◽  
Coefficient Of Restitution ◽  
Rigid Body Dynamics ◽  
Contact Model ◽  
Elastic Plastic ◽  
Contact Models ◽  
The Impact

Impact is a wide-spread phenomenon in mechanical systems that can have a significant effect on the system’s dynamics, stability, wear, and damage. The simulation of impact in complex, mechanical systems, however, is often too computationally intensive for high fidelity finite element analyses to be useful as design tools. As a result, rigid body dynamics and reduced order model simulations are often used, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or a penalty stiffness. The consequences of the choice of contact model are studied in this paper for a representative multiple-degrees of freedom mechanical system. Four contact models are considered in the analysis: a constant coefficient of restitution model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. The predictions of wear, mechanical failure, and stability are assessed for each of the contact models, and the subsequent effect on the system design is investigated. These results emphasize the importance of choosing a realistic contact model when simulations are being used to drive the design of a system.

scholarly journals The combined effect of size, inertia and porosity on the indentation response of ductile materials

2020 ◽  
Author(s):  
Jose Rodriguez-Martinez ◽  
Tiago dos Santos ◽  
Ankit Srivastava
Keyword(s):  
Plastic Strain ◽  
Size Effect ◽  
Porous Materials ◽  
Strain Gradient ◽  
Cavity Expansion ◽  
Material Hardness ◽  
Parametric Analyses ◽  
Expansion Model ◽  
Indentation Response ◽  
Plastic Strain Gradient

Herein, we present a self-similar cavity expansion model that follows from the work of Cohen and Durban (2013b) to analyze the dynamic indentation response of elasto-plastic porous materials while accounting for the plastic strain gradient induced size effect. The incorporation of the plastic strain gradient induced size effect in the dynamic cavity expansion model for elasto-plastic porous materials is the key novelty of our model. The predictions of the cavity expansion model for the material hardness, for different indentation depths and speeds, are compared against the available experimental results for OFHC copper, for strain rates varying from 10−4 s−1 to 108 s−1. We note that despite several simplifying assumptions, the predictions of our cavity expansion model show a reasonable agreement with the experimentally measured material hardness over a wide range of indentation depths and speeds. In addition, we have also carried out parametric analyses to elucidate the specific roles of indentation speed, size effect and initial porosity, on the material hardness and cavitation fields that develop during the indentation process. In particular, our parametric analyses show that there exists a critical value of the indentation speed beyond which the contribution of inertial effect becomes extremely important and the material hardness increases rapidly. While the influence of the initial porosity on the material hardness is found to increase with increasing indentation speed and decrease with increasing size effect.

An Analytical Elastic-Plastic Contact Model

2011 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Yield Criterion ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Elastic Regime ◽  
Plastic Regime ◽  
Elastic Process ◽  
New Formulation ◽  
Von Mises ◽  
The Impact ◽  
Force Displacement

This paper presents a new formulation for elastic-plastic contact in the normal direction between two round surfaces that is solely based on material properties and contact geometries. The problem is formulated as three separate domains: the elastic regime, mixed elastic-plastic behavior, and unconstrained (fully plastic) flow. Solutions for the force-displacement relationship in the elastic regime follow from Hertz’s classical solution. In the fully plastic regime, two assumptions are made: that there is a uniform pressure distribution and that there is conservation of volume. The force-displacement relationship in the intermediate, mixed elastic-plastic regime is approximated by enforcing continuity between the elastic and fully plastic regimes. Transitions between the three regimes are determined based on empirical quantities: the von Mises yield criterion is used to determine the initiation of mixed elastic-plastic deformation, and Brinell’s hardness for the onset of unconstrained flow. Unloading from each of these three regimes is modeled as an elastic process with different radii of curvature based on the regime in which the maximum force occurred. Simulation results explore the relationship between the impact velocity and coefficient of restitution. Further comparisons are made between the model, experimental results found in the literature, and other existing elastic-plastic models.

The Role of Epistemic Uncertainty of Contact Models in the Design of Mechanical Systems

2013 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Constant Coefficient ◽  
Epistemic Uncertainty ◽  
Piecewise Linear ◽  
Mechanical Systems ◽  
Coefficient Of Restitution ◽  
Rigid Body Dynamics ◽  
Contact Model ◽  
Elastic Plastic ◽  
Contact Models ◽  
The Impact

Impact is a wide-spread phenomenon in mechanical systems that can have a significant effect on the systems dynamics, stability, wear, and damage. The simulation of impact in complex, mechanical systems, however, is often too computationally intensive for high fidelity finite element analyses to be useful as design tools. As a result, rigid body dynamics and reduced order model simulations are often used, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The effect of epistemic uncertainty in the choice of contact model is investigated in this paper for a representative multiple-degree of freedom mechanical system. Five contact models are considered in the analysis: a constant coefficient of restitution model, a piecewise-linear stiffness and damping (i.e. Kelvin-Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. The predictions of wear and mechanical failure are assessed for each of the contact models. The ramifications of the choice of the contact model for an optimization study of the system’s geometric design are also presented. These results emphasize the importance of choosing an accurate contact model when simulations are being used to drive the design of a system.

Viscoplastic Effects Occurring in Impacts of Aluminum and Steel Bodies and Their Influence on the Coefficient of Restitution

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
Robert Seifried ◽  
Hirofumi Minamoto ◽  
Peter Eberhard
Keyword(s):  
Kinetic Energy ◽  
Strain Rate ◽  
Yield Stress ◽  
Split Hopkinson Pressure Bar ◽  
Material Model ◽  
Coefficient Of Restitution ◽  
Material Behavior ◽  
Steel Sphere ◽  
Elastic Plastic ◽  
The Impact

Generally speaking, impacts are events of very short duration and a common problem in machine dynamics. During impact, kinetic energy is lost due to plastic deformation near the contact area and excitation of waves. Macromechanically, these kinetic energy losses are often summarized and expressed by a coefficient of restitution, which is then used for impact treatment in the analysis of the overall motion of machines. Traditionally, the coefficient of restitution has to be roughly estimated or measured by experiments. However, more recently finite element (FE) simulations have been used for its evaluation. Thereby, the micromechanical plastic effects and wave propagation effects must be understood in detail and included in the simulations. The plastic flow, and thus the yield stress of a material, might be independent or dependent of the strain-rate. The first material type is called elastic-plastic and the second type is called elastic-viscoplastic. In this paper, the influence of viscoplasticity of aluminum and steel on the impact process and the consequences for the coefficient of restitution is analyzed. Therefore, longitudinal impacts of an elastic, hardened steel sphere on aluminum AL6060 rods and steel S235 rods are investigated numerically and experimentally. The dynamic material behavior of the specimens is evaluated by split Hopkinson pressure bar tests and a Perzyna-like material model is identified. Then, FE impact simulations and impact experiments with laser-doppler-vibrometers are performed. From these investigations it is shown that strain-rate effects of the yield stress are extremely small for impacts on aluminum but are significant in impacts on steel. In addition, it is demonstrated that it is possible to evaluate for both impact systems the coefficient of restitution numerically, whereas for the aluminum body a simple elastic-plastic material model is sufficient. However, for the steel body an elastic-viscoplastic material model must be included.

Elastic–Plastic Response of Clamped Square Plates Subjected to Repeated Quasi-Static Uniform Pressure

2018 ◽  
Vol 10 (06) ◽  
pp. 1850067 ◽  
Author(s):  
Shiyun Shi ◽  
Ling Zhu ◽  
Tongxi Yu
Keyword(s):  
Elastic Strain ◽  
Plastic Material ◽  
Elastic Strain Energy ◽  
Uniform Pressure ◽  
Elastic Plastic ◽  
Whole Process ◽  
Perfectly Plastic ◽  
Plastic Regime ◽  
Loading And Unloading ◽  
Elastic Perfectly Plastic

In this paper, an elastic–plastic analytical method is proposed to predict the cyclic deformation of the fully clamped square plates made of elastic–perfectly plastic material under repeated quasi-static uniform pressure. The whole process can be divided into the loading and unloading phases. The loading phase is formulated as three separate regimes: the elastic regime, the mixed elastic–plastic regime and the fully plastic regime. Unloading from a status in each phase is modeled as an elastic process. The total and elastic strain energies are characterized by the loading and unloading paths together with the displacement profiles, respectively. It is theoretically revealed that the elastic strain energy and the structural stiffness of the plate increase with the increasing transverse deflection. In addition, the effect of material elasticity is highlighted in the scenario of repeated loadings. The theoretical results are validated against the numerical simulations conducted by the commercial software ABAQUS. It is shown that the proposed elastic–plastic theoretical model has reasonable accuracy and can be employed to predict pressure–deflection relationship for this class of problems.

A Continuous Force Model for Elastic-Plastic Impact of Solids

1993 ◽  
Author(s):  
Mohamed B. Trabia
Keyword(s):  
Relative Velocity ◽  
Impact Analysis ◽  
Permanent Deformation ◽  
Coefficient Of Restitution ◽  
Force Model ◽  
Hertz Contact ◽  
Elastic Plastic ◽  
Impact Forces ◽  
Contact Force Model ◽  
Deformation Coefficient

Abstract A model for elastic-plastic impact analysis of solids is presented. This model is valid for the cases when plasticity accounts for the absorption of energy during impact. It is assumed that impact forces follow continuous Hertz contact force model. The model depends on a new mechanism for energy absorption in the impacted solids. The method yields the relative velocity of impact needed to initiate permanent deformation, coefficient of restitution, and impact time. As an example, impact between spheres is considered. Comparison between analytical and experimental results is included.

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