A New Simple Non Linear Modelling of the Quasi Statics of Granular Media: predictions, comparisons with experiments

2000 ◽  
Vol 627 ◽  
Author(s):  
Pierre Evesque
Keyword(s):  
Granular Material ◽  
Granular Media ◽  
Stress Ratio ◽  
Rheological Behaviour ◽  
Stress Strain ◽  
Linear Modelling ◽  
Non Linear ◽  
Strain Paths ◽  
Contact Distribution

ABSTRACTFirst, a non linear incremental modelling is proposed to describe rheological behaviour of granular material under different simple (i.e. triaxial-, oedometric-, undrained-) stress-strain paths. Validity of isotropic-response assumption is demonstrated whatever the stress ratio as far as deformation range remains small (ε1<5%). This contradicts some recent hypothesis made on the evolution of contact distribution during anisotropic loading.

scholarly journals An Incremental Formulation of Constitutive Equations for Deposited Snow

1980 ◽  
Vol 25 (92) ◽  
pp. 289-307 ◽  
Author(s):  
J. Desrues ◽  
F. Darve ◽  
E. Flavigny ◽  
J.P. Navarre ◽  
A. Taillefer
Keyword(s):  
Experimental Data ◽  
Axial Strain ◽  
Triaxial Tests ◽  
Stress Strain ◽  
Theoretical Formulation ◽  
Non Linear ◽  
Incremental Formulation ◽  
Strain Relationship ◽  
Strain Paths ◽  
Incremental Form

Abstract The behaviour of a snow mass under natural loadings (gravity forces, boundary conditions) can be computed by the finite-element method, in so far as a convenient formulation of the stress–strain relationship for snow is available. This paper deals with such a formulation given in incremental form. Experiments have been performed, which show that deposited snow can be considered as a non-linear visco-elastic material with memory effect. The proposed theoretical formulation takes into account these properties. The elastic part of the deformation is assumed to be isotropic and non-linear; the viscous part is expressed in terms of a creep-rate, which results from a superposition of elementary creep-rates according to Boltzmann’s principle. The values of parameters can be obtained from isotropic creep experiments. The experimental data and the resulting parameters are reported. Since the parameters were determined, the formulation of the rheological law was then tested by integration on “stress–strain paths" corresponding to other experiments of a different type, performed on the same snow. The experiments are triaxial tests at constant axial strain-rate, with a preliminary stage of isotropic compression. Experimental data are compared to theoretical curves obtained by integration of the rheological law. The calculated behaviour is consistent with the experimental results.

An Incremental Formulation of Constitutive Equations for Deposited Snow

1980 ◽  
Vol 25 (92) ◽  
pp. 289-307 ◽  
Author(s):  
J. Desrues ◽  
F. Darve ◽  
E. Flavigny ◽  
J.P. Navarre ◽  
A. Taillefer
Keyword(s):  
Experimental Data ◽  
Axial Strain ◽  
Triaxial Tests ◽  
Stress Strain ◽  
Theoretical Formulation ◽  
Non Linear ◽  
Incremental Formulation ◽  
Strain Relationship ◽  
Strain Paths ◽  
Incremental Form

AbstractThe behaviour of a snow mass under natural loadings (gravity forces, boundary conditions) can be computed by the finite-element method, in so far as a convenient formulation of the stress–strain relationship for snow is available. This paper deals with such a formulation given in incremental form.Experiments have been performed, which show that deposited snow can be considered as a non-linear visco-elastic material with memory effect. The proposed theoretical formulation takes into account these properties. The elastic part of the deformation is assumed to be isotropic and non-linear; the viscous part is expressed in terms of a creep-rate, which results from a superposition of elementary creep-rates according to Boltzmann’s principle.The values of parameters can be obtained from isotropic creep experiments. The experimental data and the resulting parameters are reported.Since the parameters were determined, the formulation of the rheological law was then tested by integration on “stress–strain paths" corresponding to other experiments of a different type, performed on the same snow. The experiments are triaxial tests at constant axial strain-rate, with a preliminary stage of isotropic compression. Experimental data are compared to theoretical curves obtained by integration of the rheological law. The calculated behaviour is consistent with the experimental results.

Stress fields in granular material and implications for performance of robot locomotion over granular media

2015 ◽  
Vol 8 (1) ◽  
pp. 2005-2009
Author(s):  
Diandong Ren ◽  
Lance M. Leslie ◽  
Congbin Fu
Keyword(s):  
Mechanical Properties ◽  
Granular Material ◽  
Granular Media ◽  
Rotation Frequency ◽  
Legged Locomotion ◽  
Working Environment ◽  
Navier Stokes ◽  
Maximum Speed ◽  
Sigmoid Curve ◽  
Multi Body

 Legged locomotion of robots has advantages in reducing payload in contexts such as travel over deserts or in planet surfaces. A recent study (Li et al. 2013) partially addresses this issue by examining legged locomotion over granular media (GM). However, they miss one extremely significant fact. When the robot’s wheels (legs) run over GM, the granules are set into motion. Hence, unlike the study of Li et al. (2013), the viscosity of the GM must be included to simulate the kinematic energy loss in striking and passing through the GM. Here the locomotion in their experiments is re-examined using an advanced Navier-Stokes framework with a parameterized granular viscosity. It is found that the performance efficiency of a robot, measured by the maximum speed attainable, follows a six-parameter sigmoid curve when plotted against rotating frequency. A correct scaling for the turning point of the sigmoid curve involves the footprint size, rotation frequency and weight of the robot. Our proposed granular response to a load, or the ‘influencing domain’ concept points out that there is no hydrostatic balance within granular material. The balance is a synergic action of multi-body solids. A solid (of whatever density) may stay in equilibrium at an arbitrary depth inside the GM. It is shown that there exists only a minimum set-in depth and there is no maximum or optimal depth. The set-in depth of a moving robot is a combination of its weight, footprint, thrusting/stroking frequency, surface property of the legs against GM with which it has direct contact, and internal mechanical properties of the GM. If the vehicle’s working environment is known, the wheel-granular interaction and the granular mechanical properties can be grouped together. The unitless combination of the other three can form invariants to scale the performance of various designs of wheels/legs. Wider wheel/leg widths increase the maximum achievable speed if all other parameters are unchanged.

scholarly journals An Improved Lagrangian-Inverse Method for Evaluating the Dynamic Constitutive Parameters of Concrete

Materials ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1871
Author(s):  
Xinlu Yu ◽  
Yingqian Fu ◽  
Xinlong Dong ◽  
Fenghua Zhou ◽  
Jianguo Ning
Keyword(s):  
High Speed ◽  
Inverse Method ◽  
Image Correlation ◽  
Analysis Method ◽  
Stress Strain ◽  
Optical Techniques ◽  
Element Simulation ◽  
Non Linear ◽  
Constitutive Parameters ◽  
Inverse Analysis Method

The dynamic constitutive behaviors of concrete-like materials are of vital importance for structure designing under impact loading conditions. This study proposes a new method to evaluate the constitutive behaviors of ordinary concrete at high strain rates. The proposed method combines the Lagrangian-inverse analysis method with optical techniques (ultra-high-speed camera and digital image correlation techniques). The proposed method is validated against finite-element simulation. Spalling tests were conducted on concretes where optical techniques were employed to obtain the high-frequency spatial and temporal displacement data. We then obtained stress–strain curves of concrete by applying the proposed method on the results of spalling tests. The results show non-linear constitutive behaviors in these stress–strain curves. These non-linear constitutive behaviors can be possibly explained by local heterogeneity of concrete. The proposed method provides an alternative mean to access the dynamic constitutive behaviors which can help future structure designing of concrete-like materials.

Non-linear modelling and optimal control of a hydraulically actuated seismic isolator test rig

2013 ◽  
Vol 35 (1-2) ◽  
pp. 255-278 ◽  
Author(s):  
Stefano Pagano ◽  
Riccardo Russo ◽  
Salvatore Strano ◽  
Mario Terzo
Keyword(s):  
Optimal Control ◽  
Test Rig ◽  
Seismic Isolator ◽  
Linear Modelling ◽  
Non Linear ◽  
Hydraulically Actuated
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