Hypervelocity Cavity Expansion in Porous Elastoplastic Solids

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Tal Cohen ◽  
David Durban
Keyword(s):  
Large Strain ◽  
Constitutive Relations ◽  
Critical Value ◽  
Cavity Expansion ◽  
Expansion Velocity ◽  
Jump Conditions ◽  
Gurson Model ◽  
Numerical Examples ◽  
The Mathematical Model ◽  
Material Porosity

Dynamic steady-state spherical cavitation fields are examined with emphasis on material porosity at large strain. Cavity expansion is driven by constant internal pressure in presence of remote tension or compression. The plastic branch of constitutive relations is described by the Gurson model, with arbitrary strain hardening. The mathematical model is reduced to a system of four ordinary nonlinear coupled differential equations. Numerical examples show that a plastic shock wave builds up as expansion velocity approaches a critical value and jump conditions across the shock are accounted for. At critical levels of remote tension, quasi-static cavitation of all internal voids is induced before dynamic cavity expansion occurs.

scholarly journals A Dynamic Cavity Expansion Model for Rigid Projectile Penetration into Concrete considering the Compressibility and Nonlinear Constitutive Relations

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Fei Gao ◽  
Zhen Wang ◽  
Zhu Wen ◽  
Yuguo Ji
Keyword(s):  
Yield Criterion ◽  
Constitutive Relations ◽  
Cavity Expansion ◽  
Depth Of Penetration ◽  
Proposed Model ◽  
Rigid Projectile ◽  
Calculation Results ◽  
Expansion Model ◽  
Constitutive Parameters ◽  
Nonlinear Constitutive Relations

The P-α equation of state (EOS) and a nonlinear yield criterion are utilized to characterize the dynamic constitutive behavior of concrete targets subjected to projectile normal penetration. A dynamic cavity expansion model considering the compressibility and nonlinear constitutive relations for concrete material is developed. Then, a theoretical model to calculate the depth of penetration (DOP) for rigid projectile is established. Furthermore, the proposed model is validated based on the available test data as well as the calculation results by the linear compressible EOS and linear yield criterion. This study shows that the proposed model derived using the P-α EOS and nonlinear yield criterion can effectively reflect the plastic mechanical properties of concrete and is also suitable for predicting the DOP of concrete targets. In addition, the influence law of concrete constitutive parameters such as the cohesion strength, shear strength, internal friction coefficient, and elastic limit pressure on the DOP is revealed.

Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

The Time Dependent Behavior of Linear Viscoelastic Polymers

2011 ◽  
Vol 675-677 ◽  
pp. 435-438
Author(s):  
Wei Xiang Zhang ◽  
Xing Shao ◽  
Zhao Ran Xiao
Keyword(s):  
Mechanical Behavior ◽  
Mechanical Characteristics ◽  
Mechanical Response ◽  
Constitutive Relations ◽  
Time Dependent ◽  
Numerical Examples ◽  
General Methodology ◽  
Inverse Transform ◽  
Dependent Behavior ◽  
Linear Viscoelastic

Polymers have been proved to have attractive mechanical characteristics, which made it desirable to choose these materials over traditional materials for numerous types of applications. As the uses of polymers increase, a thorough understanding of the mechanical behavior of these materials becomes vital in order to perform innovative and economical designs of various components. The main objective of this paper is to develop an effective method with the use of the Laplace inverse transform to describe the time dependent mechanical response of viscoelastic polymers. This general methodology is based on differential constitutive relations for viscoelastic polymers, avoiding the use of relaxation integral functions. As its application, the creep and relaxation properties of the materials are exhibited in the numerical examples.

An Improved Alternating Active-Phase Algorithm for Multi-Material Topology Optimization Problems

2014 ◽  
Vol 635-637 ◽  
pp. 105-111 ◽  
Author(s):  
Ming Tao Cui ◽  
Hong Fang Chen
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Active Phase ◽  
Optimality Criteria ◽  
Numerical Examples ◽  
Original Algorithm ◽  
Minimum Compliance ◽  
Object Based ◽  
The Mathematical Model ◽  
Improved Algorithm

For the multi-material topology optimization problems which take structural minimum compliance as the object, based on the weight function and optimality criteria, an improvement to the original alternating active-phase algorithm is achieved in establishing and calculating the mathematical model of multi-material topology optimization problems. Simulations of numerical examples are implemented respectively by the improved alternating active-phase algorithm and the original algorithm. It can be found that the minimum compliance obtained by the improved algorithm is generally lower than that obtained by the original algorithm in each numerical example, whereupon the feasibility and efficiency of the improved algorithm are manifested.

A Study of the Effects of Baffles on Rotating Compressible Flows

1989 ◽  
Vol 56 (3) ◽  
pp. 710-712
Author(s):  
Max D. Gunzburger ◽  
Houston G. Wood ◽  
Rosser L. Wayland
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Compressible Flows ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Gas Centrifuge ◽  
Mass Injection ◽  
Flow Domain ◽  
The Mathematical Model ◽  
Element Algorithm

Onsager’s pancake equation for the fluid dynamics of a gas centrifuge is modified for the case of centrifuges with baffles which render the flow domain doubly connected. A finite element algorithm is used for solving the mathematical model and to compute numerical examples for flow fields induced by thermal boundary conditions and by mass injection and extraction.

scholarly journals Building a mathematical model of technological processes in the acetic acid synthesis reactor

2021 ◽  
Vol 5 (2 (113)) ◽  
pp. 94-104
Author(s):  
Zhanna Samojlova
Keyword(s):  
Mathematical Model ◽  
Acetic Acid ◽  
Acid Synthesis ◽  
Critical Value ◽  
Reaction Mass ◽  
Stationary Mode ◽  
Fisher Criterion ◽  
Technological Processes ◽  
Level Of Significance ◽  
The Mathematical Model

The result of the study reported in this paper is the proposed mathematical model of technological processes occurring in the reactor for acetic acid synthesis. The initial parameters of the reactor considered were the value of the concentration of acetic acid at the reactor outlet, temperature, the level of reaction mass, and pressure in the reactor. The input parameters included the amount of methanol and carbon monoxide supplied. Material and thermal balances of reactor technological processes were used to construct the mathematical model of the reactor. Fisher criterion was applied to test the mathematical model for adequacy. At the specified 5 % level of significance, the value of Fisher criterion for the concentration of acetic acid, temperature, and the level of reaction mass in the reactor does not exceed its critical value for a stationary mode. The reproducibility of the modeling results was tested using the Cochran criterion. The value of the Cochrane criterion, at the predefined 5 % level of significance, for the concentration of acetic acid, temperature, and the level of reaction mass in the reactor does not exceed its critical value for different modes. The relative error for the modeled output parameters was calculated. The relative error of the initial parameters did not exceed the level of 10 %. The model built makes it possible to calculate with satisfactory accuracy the value of the concentration of acetic acid at the reactor output, the temperature and level of the reaction mass in the reactor under a stationary mode. The resulting model could be used to automate the control of technological processes in the acetic acid synthesis reactor under a stationary mode. The study results open additional opportunities to manage the stationary mode of the reactor

scholarly journals Multiscale analysis of instabilities in heterogeneous materials using ANM and multilevel FEM

2012 ◽  
Author(s):  
Saeid Nezamabadi ◽  
Hamid Zahrouni ◽  
Julien Yvonnet ◽  
Michel Potier-Ferry
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Multiscale Analysis ◽  
Numerical Technique ◽  
Constitutive Relations ◽  
Heterogeneous Materials ◽  
Perturbation Approach ◽  
Element Analysis ◽  
Numerical Examples ◽  
Asymptotic Numerical Method

In this study, we propose a numerical technique which combines a perturbation approach (asymptotic numerical method) and a multilevel finite element analysis. This procedure allows dealing with instability phenomena in the context of heterogeneous materials where buckling may occur at both macroscopic and/or microscopic scales. Different constitutive relations are applied and geometrical non-linearity is taken into account at both scales. Numerical examples involving instabilities at both micro and macro levels are presented.

scholarly journals Dynamic cylindrical cavity expansion in orthotropic porous ductile materials

2020 ◽  
Author(s):  
Jose Rodriguez-Martinez ◽  
Alvaro Vaz-Romero ◽  
Tiago dos Santos
Keyword(s):  
Theoretical Model ◽  
Shock Waves ◽  
Cylindrical Cavity ◽  
Plastic Anisotropy ◽  
Cavity Expansion ◽  
Expansion Velocity ◽  
Ballistic Performance ◽  
Plastic Properties ◽  
Cylindrical Cavity Expansion ◽  
Anisotropic Porous Medium

This paper investigates the steady-state elastoplastic fields induced by a pressurized cylindrical cavity expanding dynamically in an anisotropic porous medium. For that task, we have developed a theoretical model which: (i) incorporates into the formalism developed by Cohen and Durban (2013b) the effect of plastic anisotropy using the constitutive framework developed by Benzerga and Besson (2001) and (ii) uses the artifical viscosity approach developed by Lew et al. (2001) to capture the shock waves that emerge at high cavity expansion velocities. We have shown that while the development of the shock waves is hardly affected by the material anisotropy, the directionality of the plastic properties does have an effect on the elastoplastic fields that evolve near the cavity. The importance of this effect is strongly dependent on the cavity expansion velocity, the initial porosity and the strain hardening of the material. In addition, the theoretical model has been used in conjunction with the Recht and Ipson (1963) formulas to assess the ballistic performance of porous anisotropic targets against high velocity perforation.

A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue

2008 ◽  
Vol 601 ◽  
pp. 189-198 ◽  
Author(s):  
ASLAN R. KASIMOV
Keyword(s):  
Surface Tension ◽  
Hydraulic Jump ◽  
Stokes Equations ◽  
Critical Value ◽  
Water Model ◽  
Navier Stokes ◽  
Jump Conditions ◽  
Shallow Water Model ◽  
Finite Radius ◽  
Navier Stokes Equations

We propose a theory of a steady circular hydraulic jump based on the shallow-water model obtained from the depth-averaged Navier–Stokes equations. The flow structure both upstream and downstream of the jump is determined by considering the flow over a plate of finite radius. The radius of the jump is found using the far-field conditions together with the jump conditions that include the effects of surface tension. We show that a steady circular hydraulic jump does not exist if the surface tension is above a certain critical value. The solution of the problem provides a basis for the hydrodynamic stability analysis of the hydraulic jump. An analogy between the hydraulic jump and a detonation wave is pointed out.

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