Elastoplastic Systems Research Articles

Parameter Calibration and Verification of Elastoplastic Wet Sand Based on Attention-Retention Fusion Deep Learning Mechanism

The discrete element method (DEM) is a vital numerical approach for analyzing the mechanical behavior of elastoplastic wet sand. However, parameter uncertainty persists within the mapping between constitutive relationships and inherent model parameters. We propose a Parameter calibration neural network based on Attention, Retention, and improved Transformer for Sequential data (PartsNet), which effectively captures the nonlinear mechanical behavior of wet sand and obtains the optimal parameter combination for the Edinburgh elasto-plastic adhesion constitutive model. Variational autoencoder-based principal component ordering is employed by PartsNet to reduce the high-dimensional dynamic response and extract critical parameters along with their weights. Gated recurrent units are combined with a novel sparse multi-head attention mechanism to process sequential data. The fusion information is delivered by residual multilayer perceptron, achieving the association between sequential response and model parameters. The errors in response data generated by calibrated parameters are quantified by PartsNet based on adaptive differentiation and Taylor expansion. Remarkable calibration capabilities are exhibited by PartsNet across six evaluation indicators, surpassing seven other deep learning approaches in the ablation test. The calibration accuracy of PartsNet reaches 91.29%, and MSE loss converges to 0.000934. The validation experiments and regression analysis confirmed the generalization capability of PartsNet in the calibration of wet sand. The improved sparse attention mechanism optimizes multi-head attention, resulting in a convergence speed of 21.25%. PartsNet contributes to modeling and simulating the precise mechanical properties of complex elastoplastic systems and offers valuable insights for diverse engineering applications.

Phản ứng động đất của các hệ nhị tuyến tính đàn - dẻo và tự tâm định dưới tác dụng của các chuyển động nền do động đất xa và gần

This study presents seismic response of single degree of freedom (SDOF) elasto-plastic and self-centering systems under far and near-fault ground motions. These parameters was conducted to determine the influence on SDOF structure response in term of ductility, absolute acceleration, absorbed energy, strength ratio and strength reduction factor. It was found that maximum ductility for bilinear elasto-plastic systems was qualitatively similar to self-centering hysteretic systems, by adjusting the value of α and β, a self-centering hysteretic systems could be made qualitatively better than bilinear elasto-plastic systems in term of ductility. With respect to the absorbed energy, the self-centering hysteretic systems always less than comparable bilinear elasto-plastic systems. A three 3-story steel frame Self-Centering Brace Frame (SCBF) was designed according AISC seismic provison to validate of response of single degree of freedom self centering systems. 20 far field earthquake groundmotion are used for analysing of three 3-story steel frame SCBF under DBE (Design Based Earthquake) and MCE (Maximum Considerded Earthquake) level by using computer program PISA3D. The maxmimun value of interstory drift are under 1% and 2%, while residual drift are small.

A projection‐based reduced‐order model for parametric quasi‐static nonlinear mechanics using an open‐source industrial code

AbstractWe propose a projection‐based model order reduction procedure for a general class of parametric quasi‐static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code codeaster. Model order reduction aims to lower the computational cost of engineering studies that involve the simulation to a costly high‐fidelity differential model for many different parameters, which correspond, for example to material properties or initial and boundary conditions. We develop an adaptive algorithm based on a POD‐Greedy strategy, and we develop an hyper‐reduction strategy based on an element‐wise empirical quadrature in order to speed up the assembly costs of the reduced‐order model by building an appropriate reduced mesh. We introduce a cost‐efficient error indicator which relies on the reconstruction of the stress field by a Gappy‐POD strategy. We present numerical results for a three‐dimensional elastoplastic system in order to illustrate and validate the methodology.

Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media

For a stable numerical solution of the system of equations governing an elastoviscoplastic continuous medium model, a second-order explicit-implicit scheme is proposed. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations containing a small relaxation time parameter in the denominator of the nonlinear free terms. A second-order implicit approximation for isotropic and anisotropic elastoviscoplastic models is constructed to match the orders of approximation of the explicit elastic and implicit adjustment steps. Refined formulas for correcting the stress deviators after the elastic step are derived for various viscosity function representations. The resulting solutions of the second-order implicit approximation for the stress deviators of the elastoviscoplastic equations admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of the numerical solutions to the elastoplastic systems.

A material point/finite volume method for coupled shallow water flows and large dynamic deformations in seabeds

A hybrid material point/finite volume method for the numerical simulation of shallow water waves caused by large dynamic deformations in the bathymetry is presented. The proposed model consists of coupling the nonlinear shallow water equations for the water flow and a dynamic elastoplastic system for the seabed deformation. As a constitutive law, we consider a linear elastic-non-associative plastic model with the Drucker-Prager yield criterion allowing for large deformations under undrained cases. The transfer conditions between these models are achieved by using forces sampled from the hydraulic pressure and the friction terms along the interface between the seabed soil and shallow water. A detailed description regarding the coupled algorithm for the hybrid material point/finite volume method is presented. Several numerical examples are investigated to demonstrate the performance of the finite volume method for simulations of shallow water flow and the material point method for capturing the large deformation process of the solid phase. We also present numerical simulations of an undrained clay column collapse that induced shallow water waves and a dam-break problem to demonstrate the excellent performance of the proposed hybrid material point/finite volume method.

Elasto-Plastic Short Exoskeleton to Improve the Dynamic and Seismic Performance of Frame Structures

The coupling with external mechanical systems such as oscillating masses working as tuned mass dampers, dynamic mass absorbers, elasto-plastic dampers, and rigid walls is an effective method to reduce the displacements and drifts of structures under external loads. An alternative method is provided by the coupling of the structure with an independent, auxiliary elasto-plastic system. This paper investigates the dynamic and seismic behaviour of a structure rigidly coupled with an auxiliary yielding mechanical system under harmonic and seismic ground excitation. A two-degree-of-freedom model is used to describe the dynamic and seismic behaviour of the main structure rigidly coupled to the yielding system, which is described by a one-degree-of-freedom model. The auxiliary system has an elasto-plastic constitutive behaviour that is modelled by a Bouc-Wen model. The equations of motion of the coupled system are obtained by a direct approach. The coupling with the yielding system is considered beneficial if the displacements of the coupled system reduce with respect to those of the stand-alone frame structure. An extensive parametric analysis is performed to point out the role of the mechanical parameters that describe the elasto-plastic constitutive behaviour of the auxiliary system. Results reveal that in large ranges of the parameters’ values, the coupling with the elasto-plastic system improves the performance of the frame structure.

An improved iterative technique for inelastic time history analysis of single degree of freedom (SDOF) elasto-plastic system

An improved iterative technique for inelastic time history analysis of single degree of freedom (SDOF) elasto-plastic system

Finite-Time Stability of Polyhedral Sweeping Processes with Application to Elastoplastic Systems

We use the ideas of Adly-Attoych-Cabot [Adv. Mech. Math., 12, Springer, 2006] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint (known as polyhedral sweeping processes) of the form $C+c(t).$ We then employ the ideas of Moreau [New variational techniques in mathematical physics, CIME, 1973] to apply our theorem to a system of elastoplastic springs with a displacement-controlled loading. We show that verifying the condition of the theorem ultimately leads to the following two problems: (i) identifying the active vertex ``A'' or the active face ``A'' of the polyhedron that the vector $c'(t)$ points at; (ii) computing the distance from $c'(t)$ to the normal cone to the polyhedron at ``A''. We provide a computational guide to implement steps (i)-(ii) in the case of an arbitrary elastoplastic system and apply the guide to a particular example. Due to the simplicity of the particular example, we can solve (i)-(ii) by the methods of linear algebra and minor combinatorics.

Performance Assessment of RCC Structure Using Nonlinear Analysis

In general, the performance of the structure under earthquake vibrations is not limited to linear analysis. Linear analysis can be done to identify the preliminary parameters like natural frequency and damping ratio of the structure. To understand the structural behaviour beyond the linear elastic region, non-linear analysis is mandatory. Nonlinear analysis reveals the structural performance under the elasto-plastic state. A large deformation in the plastic region alarms the system sustainability under random motions. The quality of ductility is considered for the ratio of yield strength of the linear system to the maximum strength of the elasto-plastic system. The ductility demand versus response reduction factor of the structure is plotted. Design modifications can be done based on the ductility demands for various response reduction factors. Two structures of uniform and non-uniform varying cross-sections are considered in the study. Modal analysis is performed based on approximate and analytical methods to find the fundamental frequencies of the structures. Both the structures are identified at a linear curve of yielding to the ultimate capacity in the pushover curve. Linear time history analysis is performed to identify the performance point of the structure in the pushover curve. Non-linear dynamic analysis is performed to find the response of the structures using the Newmark method of non-linear time history analysis. The results arrived at the linear response which is validated with the linear time history analysis using ETABS. To have the response decay in the structure, peak strength in the elastoplastic range is assumed as the normalized yield strength factor. Based on the yield strength factors, ductility demand in the structure is identified.

Shockwaves in Jammed Ductile Granular Media

Abstract We investigate shock propagation in confined, frictionless granular media using discrete element simulations with an elastoplastic contact law. Depending on the level of confinement and loading, elastoplastic systems exhibit a weak or strong shock propagation response similar to an elastic Hertzian system although the details of the shock development differ markedly from the elastic case. Two modes of dynamic stress propagation are observed based on the shock intensity regime: weak shocks carry the stresses via the initial contact path while strong shocks form new contact networks behind the front. However, unlike for elastic shock propagation, there is an upper bound to the front velocity of strong shocks that depends on the maximum intergranular contact stiffness. Since elastoplastic contact is a dissipative process, results show that dissipation is enhanced with confining pressure in the weak shock regime.

A reliability-based fragility assessment method for seismic pounding between nonlinear buildings

Existing methods to estimate the probability of seismic pounding occurrence of adjacent buildings do not account for nonlinear behavior or only apply to simple lumped mass systems. The present study proposes an efficient method based on subset simulation for fragility and risk assessment of seismic pounding occurrence between nonlinear adjacent buildings neglecting pounding effects with application to finite element models. The proposed method is first applied to adjacent buildings modeled as elastoplastic systems with substantially different dynamic properties for different structural parameters. Seismic pounding fragility and risk of adjacent frame structures with different floor levels is then assessed, paying special attention to modeling the non-linear material behavior in finite element models. Difference in natural periods and impact location are identified to affect the pounding fragility simultaneously. The reliability levels of the minimum code-specified separation distances are also determined. In addition, the incremental dynamic analysis method is extended to assess seismic pounding fragility of the adjacent frame structures, resulting in higher fragility estimates for separation distances larger than the minimum code-specified ones in comparison with the proposed method.

Stabilization of the response of cyclically loaded lattice spring models with plasticity

This paper develops an analytic framework to design both stress-controlled and displacement-controlledT-periodic loadings which make the quasistatic evolution of a one-dimensional network of elastoplastic springs converging to a unique periodic regime. The solution of such an evolution problem is a functiont↦(e(t),p(t)), whereei(t) is the elastic elongation andpi(t) is the relaxed length of springi, defined on [t0,∞) by the initial condition (e(t0),p(t0)). After we rigorously convert the problem into a Moreau sweeping process with a moving polyhedronC(t) in a vector spaceEof dimensiond, it becomes natural to expect (based on a result by Krejci) that the elastic componentt↦e(t) always converges to aT-periodic function ast→∞. The achievement of this paper is in spotting a class of loadings where the Krejci’s limit doesn’t depend on the initial condition (e(t0),p(t0)) and so all the trajectories approach the sameT-periodic regime. The proposed class of sweeping processes is the one for which the normals of anyddifferent facets of the moving polyhedronC(t) are linearly independent. We further link this geometric condition to mechanical properties of the given network of springs. We discover that the normals of anyddifferent facets of the moving polyhedronC(t) are linearly independent, if the number of displacement-controlled loadings is two less the number of nodes of the given network of springs and when the magnitude of the stress-controlled loading is sufficiently large (but admissible). The result can be viewed as an analogue of the high-gain control method for elastoplastic systems. In continuum theory of plasticity, the respective result is known as Frederick-Armstrong theorem.

Second-order work criterion and divergence criterion: a full equivalence for kinematically constrained systems

This paper presents stability results for rate-independent mechanical systems, associated with general tangent stiffness matrices including symmetric and non-symmetric ones. Conservative and nonconservative as well as associate and nonassociate elastoplastic systems are concerned by such a theoretical study. Hill's stability criterion, also called the second-order work criterion, is here revisited in terms of kinematically constrained systems. For piecewise rate-independent mechanical systems (which may cover inelastic and elastic evolution processes), such a criterion is also a divergence Lyapunov stability criterion for any kinematic autonomous constraints. This result is here extended for systems with non-symmetric tangent matrices. By virtue of a new type of variational formulation on the possible kinematic constraints, and thanks to the concept of kinematical structural stability (KISS), both criteria, Hill's stability criterion and the divergence stability criterion under kinematic constraints, are shown to be equivalent.

Structurally stable families of periodic solutions in sweeping processes of networks of elastoplastic springs

Networks of elastoplastic springs (elastoplastic systems) have been linked to differential equations with polyhedral constraints in the pioneering paper by Moreau (1974). Periodic loading of an elastoplastic system, therefore, corresponds to a periodic motion of the polyhedral constraint. According to Krejci (1996), every solution of a sweeping process with a periodically moving constraint asymptotically converges to a periodic orbit. Understanding whether such an asymptotic periodic orbit is unique or there can be an entire family of asymptotic periodic orbits (that form a periodic attractor) has been an open problem since then. Since suitable small perturbation of a polyhedral constraint seems to be always capable to destroy a potential family of periodic orbits, it is expected that none of potential periodic attractor is structurally stable. In the present paper we give a simple example to prove that even though the periodic attractor (of non-stationary periodic solutions) can be destroyed by a little perturbation of the moving constraint, the periodic attractor resists perturbations of the physical parameters of the mechanical model (i.e. the parameters of the network of elastoplastic springs).

Multi-physics simulations of lightning strike on elastoplastic substrates

This work is concerned with the numerical simulation of elastoplastic, electromagnetic and thermal response of aerospace materials due to their interaction with a plasma arc under lightning strike conditions. Current approaches treat the interaction between these two states of matter either in a decoupled manner or through one-way coupled ‘co-simulation’. In this paper, a methodology for multiphysics simulations of two-way interaction between lightning and elastoplastic materials is presented, which can inherently capture the non-linear feedback between these two states of matter. This is achieved by simultaneously solving the magnetohydrodynamic and the elastoplastic systems of equations on the same computational mesh, evolving the magnetic and electric fields dynamically. The resulting model allows for the topological evolution and movement of the arc attachment point coupled to the structural response and Joule heating of the substrate. The dynamic communication between the elastoplastic material and the plasma is facilitated by means of Riemann problem-based ghost fluid methods. This two-way coupling, to the best of the authors' knowledge, has not been previously demonstrated. The proposed model is first validated against experimental laboratory studies, demonstrating that the growth of the plasma arc can be accurately reproduced, dependent on the electrical conductivity of the substrate. It is then subsequently evaluated in a setting where the dynamically-evolved properties within the substrate feed back into the plasma arc attachment. Results are presented for multi-layered substrates of different materials, and for a substrate with temperature-dependent electrical conductivity. It is demonstrated that these conditions generate distinct behaviour due to the interaction between the plasma arc and the substrate.

Frictional impact analysis of an elastoplastic multi-link robotic system using a multi-timescale modelling approach

Considering tangential contact compliance, material nonlinearity and contact nonlinearity, an efficient multi-timescale computational approach (MCA) is presented to analyse the contact forces and transient wave propagation generated by the frictional impact of an elastoplastic multi-link robotic system. In the formulation of the MCA, a rigid multibody dynamic equation is derived to calculate the large overall motion without a unilateral contact constraint (large timescale) and the nonlinear finite element dynamic equation, including the penalty function algorithm, is given to calculate the contact force and stress wave propagation (small timescale). An experimental test for a manipulator’s oblique impact against a rough moving plate is also introduced. The accuracy, convergence and efficiency of the MCA are validated by a comparison with the pure finite element method (FEM) solution and experimental data. The error between the MCA and pure FEM solutions for the first peak value of the normal contact force $$F_{\mathrm{n}}$$ is less than 1.5%. The total time cost of the MCA is only 0.705% of the pure FEM. The numerical results also show that the presented MCA can effectively depict the transmission and reflection of the impact-induced waves at the middle hinge. In addition, the influences of the structural compliance, the velocity of plate $$v_{\mathrm{plate}}$$ and the coefficient of friction $$\mu $$ on the transient responses are investigated. The peak value of $$F_{\mathrm{n}}$$ will increase as $$v_{\mathrm{plate}}$$ increases, which has a strong relationship with the so-called dynamic self-locking phenomenon. Due to the large structural compliance of the rod, the “succession collisions” phenomenon (i.e. multiple contacts in a very short time) can be captured during an oblique impact event, and the normal relative motion at the local contact zone may experience two transitions between compression and restitution during a single contact process. The tangential stick-slip motion occurs as a reverse phenomenon. All investigations show that the MCA has sufficient accuracy to analyse the frictional impact of flexible robotic manipulators.

ABOUT THE FREE-VIBRATION MODE SHAPES OF ELASTOPLASTIC DISSIPATIVE SYSTEMS

The author presents the conditions of the generalized orthogonality of the free-vibration mode shapes of an elastic dissipative system, for which traditional classical orthogonality conditions are a private case. As opposed to these conditions, the above ratios contain the mass matrix, the damping matrix, and the diagonal form of the spectral characteristics (damping coefficients and mode-shape frequencies). Within the theory of time analysis, free-vibration mode shapes of an elastoplastic system are built on the basis of using a schematized diagram of strain with hardening. The author proposes a design scheme that reduces the process of nonlinear vibrations to a sequence of processes flowing according to a linear scenario within the time intervals called quasilinear. In these intervals, the parameters of the dynamic model (elements of the stiffness matrix and the damping matrix) remain unchanged, all the changes occur only when passing through the critical points. As a result, the author formulated the condition for the nondegenerate state of an elastoplastic dissipative system. According to the condition, local plastic zones characterized by the size, the number and location of the zones on the design scheme of the structure correspond to each quasilinear interval. Since within the intervals, the parameters of the plastic zones are unchanged, the conditions of the generalized orthogonality of the mode shapes of the elastoplastic system are satisfied by analogy with the vibration mode shapes of an elastic dissipative system. The free-vibration motion of a hinged beam with three degrees of freedom are analyzed taking into account local plastic zones with different lengths and the location of zones in different nodes. It is shown that the configuration of the forms of elastoplastic oscillations differs qualitatively from the configuration of the corresponding forms of elastic vibrations.

Numerical modeling of the dynamics of multi-storey buildings with elastoplastic seismic insulators

The work is devoted to the problems of reducing the intensity of seismic impacts on multi-storey buildings. The main difficulties in solving the problems of seismic isolation of buildings and structures lie in the field of creating mathematical models of the dynamic interaction of the systems “foundation - seismic isolation device - construction”. One of the most effective ways to reduce the level of seismic effects on buildings is to equip them with special devices - seismic isolators, a successful way of implementing which is the use of elastoplastic systems. The method of calculation for seismic actions of multi-storey buildings equipped with elastoplastic seismic insulators is proposed. Numerical modelling of the alternating loading of which uses the rheological model of N N Davidenkov. Modelling of dynamic processes is carried out by means of a mathematical description of the dynamics of two linear multidimensional subsystems that approximate the structures located under seismic insulators and above seismic insulators. The dynamics equations are formed on the basis of the D’Alembert principle. Horizontal seismic effects are considered. The presented technique makes it possible to determine the movements of the nodes of the system at any time of the seismic action specified in the form of a digitized seismogram. The above algorithm is implemented as a software module Proxima. The results of calculations are presented on the example of a model of a 24-storey building designed for the conditions of building in the city of Irkutsk.

Mathematical and numerical analysis in thermo-gradient-dependent theory of plasticity

In this paper, we develop new governing equations for thermo-gradient-dependent theory of plasticity. They include the coupled effects of thermal elastic-plastic theory, including balance and constitutive equations. To demonstrate the salient feature of the gradient-dependent model of plasticity, particular attention is addressed to isotropic hardening with second sound effects to eliminate the paradox of infinite speed of thermal signals. The resulting system of partial differential equations formally describes the coupled thermomechanical behavior of the gradient-dependent elasto-plastic system. Then, we develop an appropriate state-space form and, by using the semigroup theory, we prove the well-posedness and the exponential stability of the thermo-gradient-dependent elasto-plastic one-dimensional problem. Finally, we perform numerical simulations to validate the proposed model and to show its capability.

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.