Elastoplastic Flows Research Articles

Qualitative study of a geodynamical rate-and-state model for elastoplastic shear flows in crustal faults

The Dieterich–Ruina rate-and-state friction model is transferred to a bulk variant and the state variable (aging) influencing the dissipation mechanism is here combined also with a damage influencing standardly the elastic response. As the aging has a separate dynamics, the overall model does not have a standard variational structure. A one-dimensional model is investigated as far as the steady-state existence, localization of the cataclastic core, and its time response, too. Computational experiments with a damage-free variant show stick-slip behavior (i.e. seismic cycles of tectonic faults) as well as stable slip under very large velocities.

HLLEPJ and HLLCEPJ Riemann solvers for the Wilkins model of elastoplasticity

This paper presents three Riemann solvers for the Wilkins model of hypoelasticity with the Jaumann derivative correction. The solvers are developed as extensions of the HLL and HLLC Riemann solvers for the Euler hydrodynamic model and differ in the number of waves considered (two-wave HLLEPJ Riemann solver, three-wave HLLCEPJ Riemann solver and five-wave HLLCEPJ Riemann solver). The discontinuous solution of the Wilkins system of equations is obtained using generalized Rankine-Hugoniot relations developed on the basis of the path-conservative DLM approach. A special choice of the path in the phase space allows to avoid any iterative processes in the solver construction. The proposed Riemann solvers are implicated in the first order Finite Volume numerical scheme for testing on the set of 1D, 2D and 3D problems of elastoplastic flows.

Lagrangian multiscale simulation of complex flows

A general multiscale and multiphysics simulation framework for inhomogeneous viscoelastic and elastoplastic complex flows, such as nanobubble flows, blood vessel flows, or polymer composite flows, is presented for use on massive parallel computers. Our simulation methodology is based on a particle simulation of macroscopic flows where a microscopic simulator is embedded in each of the hydrodynamic particles of macroscopic flow simulations to evaluate the local stress as a function of its flow history from the microscopic point of view. We developed a platform named MSSP (MultiScale Simulation Platform for complex flows) by combining the smoothed particle hydrodynamics (SPH) method and the microscopic molecular simulators. In such a technique, the main difficulty is the large amount of computation cost due to a large number of microscopic particles (typically of the order of 109−1010), and the inhomogeneity of the flow. To solve this problem, we propose a dynamical switching of the microscopic models between realistic particle simulations and linearized constitutive relations. An appropriate boundary condition for moving boundaries is also introduced in the SPH simulations that enables us to simulate complex flows with deformable objects such as phase-separated domains or biomembranes. A benchmark test of MSSP has been done by simulating nonlinear and non-Markovian fluids passing by an obstacle, giving good quantitative agreement with experiments in the same situation.

A nonlinear viscoelastic plate equation with [formula omitted]-Laplace operator: Blow up of solutions with negative initial energy

In this paper we consider a nonlinear class viscoelastic plate equation with a lower order by perturbation of p⃗(x,t)-Laplace operator of the form utt+Δ2u−Δp⃗(x,t)u+∫0tg(t−s)Δu(s)ds−ϵΔut+f(u)=0,(x,t)∈QT=Ω×(0,T), associated with initial and Dirichlet–Neumann boundary conditions.Under suitable conditions on g,f and the variable exponent of the p⃗(x,t)-Laplace operator, we prove a blow up in finite time with negative initial energy in the presence of a strong damping ϵΔut(ϵ>0) acting in the domain. This equation corresponds to a viscoelastic version arising in dynamics of elastoplastic flows and plate vibrations.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ТРЕХМЕРНЫХ ПРОЦЕССОВ РАЗГОНА УПРУГОПЛАСТИЧЕСКИХ ТЕЛ ВЗРЫВОМ

A methodology for numerically modeling 3D processes of acceleration of deformable bodies by detonation products of solid explosives in the air is described. Simultaneous motion of the explosion products, the air and the elastoplastic medium is numerically analyzed in Euler variables, using a modified Godunov scheme, which is applicable for both fluid dynamics and elastoplastic flows, and an exact solution of Riemann problem of discontinuity breakage in the media and along the gas-elastic body interface. The methodology uses three types of spatial grids. The grids of the first type are sets of triangles (STL files) defining the surfaces of the objects and updating those surfaces in the process of motion. The grids of the second type are base fixed Cartesian grids nested into each medium. The grids of the third type are local orthogonal movable grids coupled with each of the triangles of the grids of the first type. The integration of dynamic equations of continua and mutual interpolation of parameters among the different kinds of grids is done on base and local grids. To simulate the detonation propagation process in a solid explosive, an algorithm based on Huygens principle and the account of energy release upon the arrival of the detonation wave into the integrated cell are used. Examples of numerically modeling propagation of elastic and elastoplastic disc-shaped, tetrahedral and cubic bodies of various materials adjacent to the charge are given. The results of the analyses testify to the applicability of the above methodology for modeling coupled processes of acceleration of deform-able bodies by detonation products up to deceleration in the ambient medium. Certain laws of the acceleration process have been found for the case where detonation is initiated in the center of a spherical charge. In particular, the duration of the acceleration of a body is comparable with the time of the arrival of the detonation wave at the surface of the contact; the major residual strains altering the geometry of the bodies occur at the initial stage of the acceleration and affect both the interaction with the detonation products and the parameters of the motion of the bodies; the final acceleration velocity is observed to depend considerably on the initial geometry of the accelerated body, its orientation relative to the detonation front and the deformation properties for the same mass.Keywords: modeling, detonation, 3D processes, multi-grid approach, interpolation, Godunov scheme, nonlinear coupled problems, aeroelastoplasticity, acceleration of bodies.

Cell-centered Lagrangian Lax–Wendroff HLL hybrid method for elasto-plastic flows

The Wilkins hypoelastic model of the solid dynamics is numerically treated by the cell-centered Lagrangian Lax–Wendroff HLL hybrid scheme proposed recently for the Lagrangian hydrodynamics. The scheme is applied to the mass, momentum and energy conservation laws, while the elastic part of the incremental constitutive law is treated by the numerical method introduced by Maire et. al. [P.H. Maire et. al., J, Comput. Phys. 235:626,(2013)] and the plastic part by the Wilkins radial return. The performance of the numerical scheme is demonstrated on several test cases.

On the general decay of a nonlinear viscoelastic plate equation with a strong damping and [formula omitted]-Laplacian

In this paper we consider a nonlinear viscoelastic plate equation with a lower order perturbation of a p⃗(x,t)-Laplacian operator of the formutt+Δ2u−Δp⃗(x,t)u+∫0tg(t−s)Δu(s)ds−ϵΔut+f(u)=0,(x,t)∈QT=Ω×(0,T), associated with initial and Dirichlet–Neumann boundary conditions.Under suitable conditions on g,f and the variable exponent of the p⃗(x,t)-Laplacian operator, we prove a general decay result in the presence of a strong damping ϵΔut(ϵ>0) acting in the domain. This equation corresponds to a viscoelastic version arising in dynamics of elastoplastic flows and plate vibrations.

Numerical modeling of elastoplastic flows by the Godunov method on moving Eulerian grids

The paper proposes a numerical method for calculating elastoplastic flows on adaptive Eulerian computational grids. Elastoplastic processes are described using the Prandtl-Reuss model. The spatial discretization of the Euler equations is carried out by the Godunov method on a moving grid. In order to improve the accuracy of the scheme, piecewise linear reconstruction of the grid functions is employed using a MUSCL-type interpolation scheme generalized to unstructured grids. The basic idea of the method is to split the system of governing equations into a hydrodynamic and an elastoplastic component. The hydrodynamic equations are solved by an absolutely stable explicit-implicit scheme, and the constitutive equations (elastoplastic component) are solved by a two-stage Runge-Kutta scheme. Theoretical analysis is performed and analytical solutions are obtained for a one-dimensional model describing the structures of a shock wave and a rarefaction wave in an elastoplastic material in the approximation of uniaxial strains. The proposed method is verified by the obtained analytical solutions and the solutions calculated using alternative approaches.

Long-time dynamics for a class of Kirchhoff models with memory

This paper is concerned with a class of Kirchhoff models with memory effects \documentclass[12pt]{minimal}\begin{document}$u_{tt}\break + \alpha \Delta ^2 u - \mbox{div}(\vert \nabla u \vert ^{p-2}\nabla u) - \int _{0}^{\infty } \mu (s) \Delta ^{2}u(t-s)ds - \Delta u_t + f(u) = h,$\end{document}utt+αΔ2u−div(|∇u|p−2∇u)−∫0∞μ(s)Δ2u(t−s)ds−Δut+f(u)=h, defined in a bounded domain of \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^N$\end{document}RN. This non-autonomous equation corresponds to a viscoelastic version of Kirchhoff models arising in dynamics of elastoplastic flows and plate vibrations. Under assumptions that the exponent p and the growth of f(u) are up to the critical range, it turns out that the model corresponds to an autonomous dynamical system in a larger phase space, by adding a component which describes the relative displacement history. Then the existence of a global attractor is granted. Furthermore, in the subcritical case, this global attractor has finite Hausdorff and fractal dimensions.

Pseudoelastic hysteresis out of recoverable finite elastoplastic flows

The main objective of this study is to demonstrate that recoverable finite elastoplastic flows are derivable from classical elastoplasticity models and to further establish combined hardening finite J2-flow models of this property. With such models, it is shown that every axial strain of a uniaxially loaded bar well beyond the initial yielding is recoverable upon removal of applied load, thus producing a hysteresis loop above the strain axis. It is found that such hysteresis loops of any given shape may be generated by specifying suitable hardening functions. In particular, hardening functions are found to generate flag-like loops associated just with pseudoelastic hysteresis effects of shape memory alloys. This suggests that these effects may be characterized by classical elastoplasticity models from a direct phenomenological standpoint. Explicit, direct results are derived for a general case of multiaxial deformations in a sense of thermodynamic consistency.

Exponential stability for a plate equation with p‐Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p‐Laplacian type, urn:x-wiley:01704214:media:mma1552:mma1552-math-0001 with simply supported boundary condition, where Ω is a bounded domain of , g > 0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows. Copyright © 2012 John Wiley & Sons, Ltd.

Impulsive collapse of liquid-filled cylindrical steel shells

The paper reports the results of an experimental investigation of impulsive collapse of steel pipelines (filled with water or air) by an impact from two opposite sides by two massive plates accelerated simultaneously towards each other by an explosive charge. The experimental results confirmed that the proposed method of closing the walls of various standard-size pipelines filled with a liquid or gas is promising. The numerical results of a three-dimensional modeling of the dynamic collapse of tubes impacted by accelerated plates are presented. Some features of the Euler calculation technique for elastoplastic flows as applied to the description of processes occurring in devices for emergency shut-down of liquid-filled steel pipelines are considered.

A Conservative Eulerian Numerical Scheme for Elastoplasticity and Application to Plate Impact Problems

We present a numerical method for computing elastoplastic flows in metals. The method uses a conservative Eulerian formulation of elastoplasticity together with a higher order Godunov finite difference method combined with tracking of material boundaries. The Eulerian approach avoids the problem of mesh distortion caused by a Lagrangian remap, and can be easily extended to the computation of flows in multiple space dimensions using operator splitting. The method is validated by a comparison of computations with experiments on one-dimensional high-velocity plate impact. We obtain excellent agreement between our computations and experiment.

Instability of elastoplastic plane flows

Instability of elastoplastic plane flows

Analysis of elastoplastic flows on irregular triangular grids with restructuring

Analysis of elastoplastic flows on irregular triangular grids with restructuring

Nonisothermal instability of high-velocity elastoplastic flows

An important feature of the high-velocity deformation of solids is the localization of deformation, one of the causes of which may be the nonisothermal instability of plastic flow [1–6]. In connection with the intensive development of high-velocity technology in the treatment of materials, the investigation of the criteria for nonisothermal stability of processes of plastic deformation is of fundamental interest, since in certain cases they determine the optimum technological regimes [5]. The critical values of deformation velocities, above which the effects of thermal instability becomes decisive in the process of deformation of solids, are estimated by semiempirical methods in [1]. The non-boundary-value problem of the criteria for nonisothermal instability is analyzed in [2] for the point of view of flow stability in the so-called coupled formulation. The latter means that the heat-conduction equation is added to the basic equations determining the dynamics of an elastoplastic medium. The problem is solved in [6] in an analogous formulation, but for flow averaged over the spatial coordinate. The solution of the boundary-value problem for one-dimensional flow in this formulation is given in the present paper.

Stability of elastoplastic flows

Stability of elastoplastic flows