Elastoplastic Compression Research Articles

Repeated Collision of a Planar Robotic Arm with a Surface Using Generalized Active Forces

The periodic impact of a planar two-arm robot is investigated in this study. Lagrange’s equations of motion are developed, and the symbolic expression of the generalized active forces are used for the control torques. The actuator torques derived with generalized active forces are compared with PD and PID controllers. The robot collides with a rebound on a rough surface. Different nonlinear functions describe the three stages of the impact: elastic compression, elasto-plastic compression, and elastic restitution. A Coulomb model describes the friction force and the sliding velocity at the impact point. At the end of the impact period, the kinetic energy of the non-impacting link is increasing, and the total kinetic energy of the robot decreases. The motion of the robot with generalized active forces controllers is periodic. The important implication of this study is the generalized forces controller and the impact with friction for the periodic robot.

ЧИСЛЕННО-ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ НЕЛИНЕЙНОГО СЖАТИЯ ПАКЕТОВ МЕТАЛЛИЧЕСКИХ ПЛЕТЕНЫХ СЕТОК

The results of numerical simulation of elastoplastic compression of symmetrical fragments of a package of woven steel meshes are presented. The thickness of the symmetrical fragment is one and two layers. The study was carried out under dynamic loading conditions in the ANSYS LS-DYNA computer system. The mesh package is formed by superimposing layers on top of each other while maintaining the direction of the wires. The packet has a quasi-periodic structure; therefore, symmetrical fragments can be distinguished. For two mesh layers, a fragment is accepted, taking into account the shift of the layer in the lateral directions by half the size of the cell. The compression was carried out by a pair of absolutely rigid plates moving symmetrically towards each other at a constant speed for a given time interval. A multilinear plasticity model with isotropic hardening was used to describe the behavior of the material. If the maximum specified deformation is exceeded in the calculation, the diagram automatically continues with a small linear hardening modulus. A comparative analysis of numerical solutions for the compression of symmetrical fragments from one and two layers of a woven mesh is carried out. When the fragments are compressed, a strongly uneven stress-strain state arises in the wires, especially large irreversible deformations occur in the knots of weaving. The deformation curves of the fragments have characteristic inflections associated with the fact that the deformation process includes not only knots of weaving, but also deformations of wire compression along its entire length. The numerical results are compared with the experimental dynamic compression curve of a multilayer mesh package. The compression curves are different for one and two layers. For two layers of grids, the deformation curve at low pressure is more consistent with the experimental data. Two stages of behavior of the deformation diagram are observed at low and high degrees of compression, the characteristic inflection is formed somewhat earlier than in the numerical solution for one layer. Numerical dependences of the relative area of the normal and lateral passage sections of a symmetrical fragment of a mesh package on the compression strain are obtained. These data can be used to simulate the propagation of shock waves through multilayer woven mesh packages.

Impact of a Multiple Pendulum with a Non-Linear Contact Force

This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.

Creep consolidation in land subsidence modelling; integrating geotechnical and hydrological approaches in a new MODFLOW package (SUB-CR)

Abstract. Creep and secondary consolidation are important phenomena in settlement caused by surface loads, but not commonly considered in land subsidence driven by groundwater extraction. To explore the role of creep in such settings, a new MODFLOW-2005 land subsidence package was developed that incorporates a creep formulation gleaned from geotechnical software. This formulation, which is based on the isotache concept, is an extension of, and incorporates the classical elastoplastic compression model of Terzaghi as a limiting case. The package is introduced, and results are presented of an application to a site in northern Jakarta. It is shown that the isotache model requires considerably higher overconsolidation levels of clays than the Terzaghi model, and that creep contributes to subsidence long after drawdown in pumped aquifers has stabilized, a phenomenon that is traditionally attributed to “hydrodynamic lag”.

Numerical modeling of nonlinear dynamic and static compression of the metal mesh

Simulation of elastoplastic compression of a symmetric fragment of a bundle of woven steel grids was carried out. The simulation was carried out under static and dynamic loading modes in ANSYS and ANSYS LS-DYNA computing systems. A porous mesh package is formed by overlaying the layers on top of each other while maintaining the directions of wires. Such a packet has a quasiperiodic structure; therefore, a certain symmetric fragment can be distinguished. The compression was carried out by a pair of absolutely rigid plates moving symmetrically towards each other. In the calculations, a multilinear plasticity model with isotropic hardening was used. The diagram of static deformation of the material was used which was obtained experimentally. The calculations were carried out according to the algorithm of a perfect symmetric contact of bodies without friction and with friction. The dynamic loading of a fragment of the mesh packet was carried out at a constant speed. The characteristics of the pulse and the loading rate correspond to those observed in previous experimental studies. The dynamic strain diagram was assumed to be similar to a static one with an increased yield strength. Calculations showed that in all loading modes there is a high level of internal stresses, and complex inhomogeneous stress-strain state. We investigated two factors that could cause differences in the behavior of the curves of deformation of a porous medium - the finite length of the acting pulse and the differences in the dynamic and static compression diagrams of the initial mesh material. The main influence on the dynamic behavior of a fragment of a porous packet of a steel mesh is exerted by the dynamic properties of the wire material. The strain curves of the porous fragment qualitatively change in accordance with the behavior observed in static and dynamic experiments. The final duration of the loading pulse and the friction between the wires for this type of mesh do not have a significant effect. The numerical dependences of the relative area of the normal and lateral through sections of the symmetric fragment of the grid packet on the compression deformation are obtained.

Influence of High-Temperature Annealing on the Resistance to High Strain Rate and Fracture of Tantalum at Temperatures of 20 and 500°C

Two series of shock-wave experiments have been conducted in order to measure the Hugoniot elastic limit and determine the strain rate dependence of critical fracture stress for tantalum experiencing spall fracture. Tantalum specimens have been preannealed in vacuum at 1000°C. The evolution of elastoplastic compression shock waves at room and elevated up to 500°C temperatures has been presented from complete wave profiles recorded by a VISAR laser Doppler velocimeter. The spall strength dependence on the strain rate during the expansion of the material in a rarefaction wave has been determined.

Влияние высокотемпературного отжига на сопротивление высокоскоростному деформированию и разрушению тантала при температуре 20 и 500-=SUP=-o-=/SUP=-C

AbstractTwo series of shock-wave experiments have been conducted in order to measure the Hugoniot elastic limit and determine the strain rate dependence of critical fracture stress for tantalum experiencing spall fracture. Tantalum specimens have been preannealed in vacuum at 1000°C. The evolution of elastoplastic compression shock waves at room and elevated up to 500°C temperatures has been presented from complete wave profiles recorded by a VISAR laser Doppler velocimeter. The spall strength dependence on the strain rate during the expansion of the material in a rarefaction wave has been determined.

Unusual plasticity and strength of metals at ultra-short load durations

This paper briefly reviews recent experimental results on the temperature-rate dependences of flow and fracture stresses in metals under high strain rate conditions for pulsed shock-wave loads with durations from tens of picoseconds up to microseconds. In the experiments, ultimate (‘ideal’) values of the shear and tensile strengths have been approached and anomalous growth of the yield stress with temperature at high strain rates has been confirmed for some metals. New evidence is obtained for the intense dislocation multiplication immediately originating in the elastic precursor of a compression shock wave. It is found that under these conditions inclusions and other strengthening factors may have a softening effect. Novel and unexpected features are observed in the evolution of elastoplastic compression shock waves.

Erratum to: An Investigation of the Mechanical Properties of Some Martian Regolith Simulants with Respect to the Surface Properties at the InSight Mission Landing Site

In support of the InSight mission in which two instruments (the SEIS seismometer and the $\mbox{HP}^{3}$ heat flow probe) will interact directly with the regolith on the surface of Mars, a series of mechanical tests were conducted on three different regolith simulants to better understand the observations of the physical and mechanical parameters that will be derived from InSight. The mechanical data obtained were also compared to data on terrestrial sands. The density of the regolith strongly influences its mechanical properties, as determined from the data on terrestrial sands. The elastoplastic compression volume changes were investigated through oedometer tests that also provided estimates of possible changes in density with depth. The results of direct shear tests provided values of friction angles that were compared with that of a terrestrial sand, and an extrapolation to lower density provided a friction angle compatible with that estimated from previous observations on the surface of Mars. The importance of the contracting/dilating shear volume changes of sands on the dynamic penetration of the mole was determined, with penetration facilitated by the $\sim1.3~\mbox{Mg/m}^{3}$ density estimated at the landing site. Seismic velocities, measured by means of piezoelectric bender elements in triaxial specimens submitted to various isotropic confining stresses, show the importance of the confining stress, with lesser influence of density changes under compression. A power law relation of velocity as a function of confining stress with an exponent of 0.3 was identified from the tests, allowing an estimate of the surface seismic velocity of 150 m/s. The effect on the seismic velocity of a 10% proportion of rock in the regolith was also studied. These data will be compared with in situ data measured by InSight after landing.

Influence of strain rate, temperature and fatigue on the radial compression behaviour of Norway spruce

Abstract A dynamic elastoplastic compression model of Norway spruce for virtual computer optimization of mechanical pulping processes was developed. The empirical wood behaviour was fitted to a Voigt-Kelvin material model, which is based on quasi static compression and high strain rate compression tests (QSCT and HSRT, respectively) of wood at room temperature and at high temperature (80–100°C). The effect of wood fatigue was also included in the model. Wood compression stress-strain curves have an initial linear elastic region, a plateau region and a densification region. The latter was not reached in the HSRT. Earlywood (EW) and latewood (LW) contributions were considered separately. In the radial direction, the wood structure is layered and can well be modelled by serially loaded layers. The EW model was a two part linear model and the LW was modelled by a linear model, both with a strain rate dependent term. The model corresponds well to the measured values and this is the first compression model for EW and LW that is based on experiments under conditions close to those used in mechanical pulping.

Role of cell regularity and relative density on elasto-plastic compression response of random honeycombs generated using Voronoi diagrams

The Voronoi tessellation technique and solid modeling methods are used in this work to create virtual random structures and link cell morphology with the mechanical behavior. Their compression responses are analyzed using the finite element method. First, the effect of loading direction is analyzed for structures with different levels of randomness characterized by a regularity parameter to assess the degree of scatter in the results. Subsequently, morphological characteristics such as arrangement of cells and randomness are analyzed separately. The effect of relative density on structures with different levels of randomness is also studied. Simulations suggest that at low relative densities the arrangement of cells has a negligible effect on the compression response of random honeycombs. On the contrary, the cellular randomness has significant influence on the elastic and plastic characteristics especially when fully random structures are compared with the regular counterparts.

Role of cell regularity and relative density on elastoplastic compression response of 3-D open-cell foam core sandwich structure generated using Voronoi diagrams

The Voronoi tessellation technique in a 3-D space is used for modeling the structural foam core used in sandwich configurations. The procedure involves stochastic generation of nuclei in a control volume. The level of randomness of the microstructure is controlled with a simple sequential inhibition (SSI) process and quantified using a regularity parameter. The influence of the cell regularity on the compression response of open-cell microstructures is studied in the elastic and plastic deformation regimes. Additionally, the effect of relative density is analyzed for different regularities and results are compared with available analytical and semi-empirical models. The low probability of generating highly regular structures using the SSI process has led to the development of a perturbation approach to complement the SSI methodology. Models for estimating elastoplastic properties based on the density of the foam and the regularity parameter are presented. Simulations suggest a monotonic and direct relationship between mechanical properties and the regularity parameter for the entire range of strains considered.

An asymptotic model for elastoplasticity

This paper describes the asymptotic analysis of a model for one-dimensional elastoplastic compression at high stress. We identify a new wave phenomenon that can occur when a singular asymptotic limit reduces the order of a nonlinear hyperbolic system.

Elastoplastic compression of a rectangular body: An alternative approach

The elastoplastic compression of a body of rectangular cross section in a state of plane deformation is considered. In the proposed method, a system of nonlinear equations is solved by software minimizing the discrepancy of functions.

Performance study of a bridge involving sliding decks and pounded abutment during a violent earthquake

This paper presents a case study on the sliding of bridge decks and pounding at abutment-backfill. It involves a multi-span concrete bridge supported on simple rubber bearings, subjected to longitudinal as well as vertical ground motions from the 1999 Chi-Chi earthquake. To account for soil–structure interaction, the stiffness and strength constants of backfill soils are determined by relating the tilting movement of the abutment to the bearing pressure of backfill soils. In order to evaluate the performance of the bridge, incremental time history analyses are conducted on a number of discrete mass-spring models to simulate various nonlinear behaviors of the bridge including frictional sliding at bearings, pounding among decks/abutments and elasto-plastic compression of backfill soils. Major parameters in the models are varied in ranges, which include gaps at expansion joints, friction coefficients at bearings, and strength limits in soils. Simulation results demonstrate that frictional sliding on bearing pads together with plastic deformation in backfill soils are essential to preventing deck fall-off disaster during large earthquakes. In the case the friction coefficient at bearings rises from 0.1 to 0.2, the maximum abutment tilting by pounding is reduced by ten times. Even if the soil strength were down by half, the maximum deck movement would be less than doubled. In any case, deck fall-off is very unlikely.

Characteristic-value analysis for plastic dynamic buckling of columns under elastoplastic compression waves

The characteristic-value analysis of plastic dynamic buckling is presented for columns under the action of elastoplastic compression wave caused by an axial-step load. Two critical conditions constituting a dynamic instability criterion are derived on the basis of transformation and conservation of energy. The governing equations, the boundary conditions and the continuity conditions derived by the use of the first critical condition are the same as those given by the adjacent-equilibrium criterion and are insufficient for determining two characteristic parameters involved in the governing equations. A supplementary restraint equation for buckling deformations at the plastic-wave front and the elastic-wave front is derived by the use of the second critical condition. Then, a couple of characteristic equations for two characteristic parameters are derived on the condition that the governing equations have non-trivial solutions satisfying the boundary conditions, the continuity conditions and the supplementary restraint equation. The critical-load parameters, dynamic characteristic parameter (exponent parameter of inertia term) and dynamic buckling modes are calculated from the solutions of the characteristic equations.

Enhanced finite element formulation for geometrically linear fluid-saturated porous media

This contribution is concerned with a new mixed finite element formulation for geometrically linear Terzaghi–Biot type fluid-saturated porous media. To this end, an extended Hu–Washizu type mixed variational principle is presented for fluid-saturated porous continua. Then, a suitable discretization and its implementation are discussed, resulting in an improved element behaviour especially in numerical localization analyses. The intriguing element performance is firstly demonstrated for the case of localization within an elastoplastic compression problem. Finally, an elastoplastic slope stability problem is examined, whereby the new element formulation proves to render more pronounced failure modes as compared with a standard element expansion. © 1997 John Wiley & Sons, Ltd.