Response Of Elastoplastic Structures Research Articles

A unified multi-phase and multi-material formulation for combustion modeling

The motivation of this work is to produce an integrated formulation for material response (e.g., elastoplastic, viscous, viscoplastic) due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we want to capture miscible and immiscible behavior within condensed-phase explosives arising from the co-existence of a reactive carrier mixture of miscible materials and several material interfaces due to the presence of immiscible impurities such as particles or cavities. The dynamic and thermodynamic evolution of the explosive is communicated to one or more inert confiners through their shared interfaces, which may undergo severe topological change. We also wish to consider elastic and plastic structural response of the confiners rather than make a hydrodynamic assumption for their behavior. The previous work by these authors has met these requirements by means of the simultaneous solution of appropriate systems of equations for the behavior of the condensed-phase explosive and the elastoplastic behavior of the confiners. To that end, both systems were written in the same mathematical form as a system of inhomogeneous hyperbolic partial differential equations (PDEs), which were solved on the same discrete space using the same algorithms, as opposed to coupling fluid and solid algorithms (co-simulation). In the present work, we employ a single system of PDEs proposed by Peshkov and Romenski [Peshkov and Romenski, “A hyperbolic model for viscous Newtonian flows,” Continuum Mech. Thermodyn. 28, 85 (2016)], which is able to account for different states of matter by means of generalizing the concept of distortion tensors beyond solids. We amalgamate that formulation with a single system of PDEs, which meets the requirement of co-existing miscible and immiscible explosive mixtures. We present the mathematical derivation and construct appropriate algorithms for its solution. The resulting model is validated against exact solutions for several one-dimensional use-cases, including mechanically and thermally induced, inviscid, and viscous detonations. Results indicate that the model can accurately simulate a very broad range of problems involving the nonlinear interaction between reactive and inert materials within a single framework.

A multi-physics methodology for the simulation of reactive flow and elastoplastic structural response

We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic equations. These systems of equations are usually solved by coupling finite element and CFD models. Here we solve them simultaneously, by recasting all the equations in the same, hyperbolic form and solving them on the same grid with the same finite-volume numerical schemes. The proposed compressible, multiphase, hydrodynamic formulation can employ a hierarchy of five reactive and non-reactive flow models, which allows simple to more involved applications to be directly described by the appropriate selection. The communication between the hydrodynamic and elastoplastic systems is facilitated by means of mixed-material Riemann solvers at the boundaries of the systems, which represent physical material boundaries. To this end we derive approximate mixed Riemann solvers for each pair of the above models based on characteristic equations. The components for reactive flow and elastoplastic solid modelling are validated separately before presenting validation for the full, coupled systems. Multi-dimensional use cases demonstrate the suitability of the reactive flow-solid interaction methodology in the context of impact-driven initiation of reactive flow and structural response due to violent reaction in automotive (e.g. car crash) or defence (e.g. explosive reactive armour) applications. Several types of explosives (C4, Detasheet, nitromethane, gaseous fuel) in gaseous, liquid and solid state are considered.

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

AbstractThe seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.

Sensitivity analysis of yield level for seismic response of elastoplastic structure.

From the past research, it is known that the maximum rms relative displacement of an elastoplastic structure subjected to a nonstationary input has a minimum value at an appropriate yielding level owing to the energy absorption. In order to obtain the optimal yielding level, this paper presents a sensitivity analysis of the yielding level for the seismic response of elasto plastic structures. Herein the sensitivity analysis is to find the sensitivity coefficient of the yielding level to the maximum rms relative displacement. By using these sensitivity coefficients, the probability distribution of the rms relative displacement can be evaluated from that of the yielding level of the structure. The seismic response of the structure was studied assuming that the restoring force characteristics of structure are represented by a simplified Clough model with the stiffness degradation, and the covariance of responses were computed by using an equivalent linearization technique on the assumption of narrow band response. The theoretical results were compared with those of digital computer simulation.

Probabilistic Analysis of Elastoplastic Structures

An efficient method for performing first passage analyses and inelastic response analyses is presented. The first passage problem is solved by discretizing the equation of motion for the structure in space and in time to obtain the transition probabilities for the displacement of the structure. The response of elastoplastic structures to stationary excitation is characterized by the probability distributions of cumulative plastic deformation and permanent set. The response process of the structure is discretized in time and in space, and an equivalent vibration process is obtained. The half-cycle information is used to predict response information over a given length of time. Results of numerical examples indicate that the accumulation of plastic displacements differs only slightly between the zero-start case and the stationary-start case for elastoplastic structures.