Elastic-plastic Stress Waves Research Articles

Influence of the Elastic-Plastic Dynamic Artificial Boundary on the Progressive Collapse Performance of Truss Structures

The traditional fixed boundary could not transmit the elastic-plastic stress waves in the progressive collapse analysis of the truss structures, leading to discrepancies in understanding the true response of structures. To solve the critical problem, a new dynamic artificial boundary is proposed and integrated into the truss structure to transmit elastic-plastic stress waves. The new dynamic artificial boundary is established through the integration of the elastic-plastic constitutive model into the governing equation of the stress wave. This boundary is subsequently implemented within the ABAQUS finite element software for the purpose of conducting progressive collapse analysis of the truss structures. The progressive collapse simulation of the truss structures involves a comparative analysis between the new dynamic artificial boundary and the traditional fixed boundary. Numerical analysis demonstrates that the dynamic artificial boundary led to varied initial failure and collapse compared to the fixed boundary. The failure typically occurs at the mid-span under the dynamic boundary. In contrast, additional failures occur near the support columns under the fixed boundary due to stress wave reflections. The dynamic artificial boundary more closely reflects the physical reality and provides a new method for the progressive collapse analysis of the truss structures in practical applications.

Ultrasonic vibration-induced severe plastic deformation of Cu foils: effects of elastic-plastic stress wave bounce, acoustic softening, and size effect

Ultrasonic vibration-induced severe plastic deformation of Cu foils: effects of elastic-plastic stress wave bounce, acoustic softening, and size effect

Shock-induced plasticity in semi-coherent {111} Cu-Ni multilayers

Using atomistic simulations, dislocation dynamics modeling, and continuum elastic-plastic stress wave theory, we present a systematic investigation on shock-induced plasticity in semi-coherent Cu-Ni multilayers. The features of stress wave evolutions in the multilayers, including wave-front stress attenuation and strong interfacial discontinuities, are revealed by atomistic simulations. Continuum models are proposed to explain the shock wave propagation features. The simulations provide insight into microplasticity behaviors including interactions between lattice and misfit dislocations. The formation of hybrid Lomer-Cottrell locks through the attraction and combination of lattice and misfit dislocations is found to be a major mechanism for trapping gliding lattice dislocations at interfaces. The relationship between dislocation activity and dynamic stress wave evolution history is explored. The hybrid Lomer-Cottrell locks can dissociate under shock compression or reverse yielding. This dissociation facilitates slip transmission. The influence of coherent stress causes direction dependency in the slip transmission: a lattice dislocation can transmit more smoothly across an interface from Ni to Cu than from Cu to Ni. The interaction forces between lattice and misfit dislocations are calculated using dislocation dynamics code. Lattice dislocation nucleation from semi-coherent interfaces under shock compression is also reported.

Dynamic buckling of elastic-plastic column impacted by rigid body

The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation.

The bifurcation problem of columns caused by elastic-plastic stress wave propagation

In this paper, the dynamic buckling of an elastic-plastic column is studied. Let its dynamic buckling under step load be reduced to a bifurcation problem caused by the propagation of axial elastic-plastic stress wave. The critical buckling condition is given and the reflection of the elastic-plastic stress wave is taken into consideration. In the end, numerical computation and conclusions are presented and obtained.

One-Dimensional Theory of Stress Waves of Solids in Uniaxial Stress State.

Using an elastic-plastic-viscoplastic constitutive equation, an equation relating stress wave speed, particle velocity and strain is derived. The derived equation is of the same form as that of the theory of the elastic-plastic stress wave (Karman's theory). However, contents of both equations are different because the former takes into account the viscoplastic strain and the latter does not. It is shown from numerical values for the derived equations that the stress wave speed decreases with increasing particle velocity and the stress wave speed corresponding to particle velocity increases with increasing strain rate. Also, it is shown that the propagation speed corresponding to particle velocity agrees qualitatively with the experimental results. Moreover, every equation of existing theories of the elastic-plastic, elastic-viscoplastic and longitudinal elastic stress waves is derived in consistent mathematical form from the theory of elastic-plastic-viscoplastic stress waves.

One-Dimensional Theory of Elastic-Plastic-Viscoplastic Stress Wave Propagation.

In the present paper, a one-dimensional theory of elastic-plastic-viscoplastic stress wave propagation is evolved. The concepts of understress and overstress are introduced to the constitutive equation used. The strain dependence and the strain-rate dependence of the wave propagation speed of the stress wave are given. A few forms of the wave propagation speed of the elastic-plastic-viscoplastic stress wave are newly derived. It is also shown that the theory of elastic-plastic-viscoplastic stress wave propagation given here contains a theory of elastic-plastic stress wave propagation and a theory of elastic-viscoplastic stress wave propagation. Moreover, a precursor and an unloading wave are also mentioned.

Arrest characteristics of an impacted crack dissipating plastic energy

When a structural member is accidentally struck, an initial defect may grow and then arrest. An estimate of its size increase is made by considering the geometry of a centrally cracked panel subjected to a step function load in time. Two load amplitudes differing by a factor of five are considered. Under impact, the crack accelerates and then decelerates prior to arrest. The dynamic characteristics depend on the interaction of the elastic-plastic stress waves intervening with the physical boundaries. This effect is assessed quantitatively by computing for the energy stored in a unit volume of material and by incorporating sliding nodes in the finite element method. The energy dissipated by plastic deformation must be accounted for as it is no longer available for creating new macrocrack surface. Obtained are the near tip normal stresses that are found to change from compression to tension. Their magnitude is considerably larger than the corresponding static values. Increase in crack length changes from 0.87% to 20.6% when the magnitude of the impact load is raised five times. The rate of change of the strain energy density factor ΔS with crack growth Δa is found to be governed by the condition ΔS/Δa = const. during loading while dynamic relaxation corresponded to a nonlinear behavior. The physical implication of this remains to be clarified in view of the fact that plasticity theory may not adequately explain the near tip crack behavior.

Impact Strength of Materials

This book presents a compilation of information and analytical methods on the subject of the impact strength of materials. It contains ten chapters dealing with: 1, elementary one-dimensional elastic stress waves in long uniform bars due to impact; 2, applications of elementary one-dimensional stress wave theory; 3, elastic stress waves: more general considerations; 4, plasticity theory and some quasi-static analyses; 5, one dimensional elastic-plastic stress waves in bars; 6, impulsive loading of beams; 7, dynamic loading of rings and frames; 8, dynamic plastic deformation of plates; 9, plastic deformation in a semi-infinite medium due to impact; and 10, plastic deformation in plates due to impact. Two appendices contain: 1, useful conversion factors; and 2, text tables in SI units. (TRRL)

A Note on the Unloading Boundary in Elastic-Plastic Stress Wave Propagation

A Note on the Unloading Boundary in Elastic-Plastic Stress Wave Propagation

Determination of the Unloading Boundary in Longitudinal Elastic-Plastic Stress Wave Propagation

For several types of excitation of one-dimensional elastic-plastic stress waves in a rod, unloading waves propagate which interact with the loading waves. The moving boundary at which this interaction occurs is the unloading boundary. A knowledge of the location of this boundary and the behavior exhibited on it is necessary for the solution of wave-propagation problems of this kind. A technique is presented to obtain an arbitrary number of terms in series expressions describing the response in semi-infinite rods. Several examples, including finite mass impact of the rod, are given to illustrate the use of the technique. The technique will determine the initial portion of the boundary in a finite length rod.

The influence of dynamical thermal expansion on the propagation of plane elastic-plastic stress waves

In this paper the implications of the classical heat conduction equation for the problem of the propagation of plane waves caused by mechanical impulse and sudden heating at the boundary of an elastic-plastic half-space are presented. It is shown that the effect of dynamical thermal expansion is to reduce the jump in the stress at waves of strong discontinuity. The stress and temperature fields dealt with here are assumed to be thermodynamically uncoupled.