Deformable Obstacle Research Articles

Impact damage testing based on high-speed continuous water jet aircraft coatings

When an aircraft passes through a rainy area at high speed, the coating on the front edge of the fuselage will be continuously eroded by raindrops, causing the coating to wear, crack or even peel off. This paper uses carbon fiber T300 material as the base material, and at the different impact speeds and impact numbers, water cutting equipment was used to simulate the erosion of the coating caused by the continuous impact of water droplets. The damage morphology of samples at different damage stages was observed by digital microscope and Scanning Electron Microscope (SEM), and the damage evolution curve was established to analyze and reveal the damage behavior and damage mechanism of rain erosion. The results show that the degree of damage experienced an increasing trend with the increase of impact numbers and speed, until circular peel damage was formed; no damage occurred during the incubation period, and the curvature of the damage evolution curve increased significantly after the expansion period and eventually showed a stable expansion trend. The mechanical properties of the coating material were the main influencing factors of its rain corrosion resistance. Moreover, the axially symmetric unsteady contact problem of droplets impacting the surface of a solid deformable body was studied. And the contact area was determined based on the iterative algorithm boundary positioning method. A mathematical model and closed mathematical formula describing the unsteady interaction between a droplet and a solid deformable obstacle were proposed.

Machine-Learning-Accelerated Simulations for the Design of Airbag Constrained by Obstacles at Rest.

Predicting airbag deployment geometries is an important task for airbag and vehicle designers to meet safety standards based on biomechanical injury risk functions. This prediction is also an extraordinarily complex problem given the number of disciplines and their interactions. State-of-the-art airbag deployment geometry simulations (including time history) entail large, computationally expensive numerical methods such as finite element analysis (FEA) and computational fluid dynamics (CFD), among others. This complexity results in exceptionally large simulation times, making thorough exploration of the design space prohibitive. This paper proposes new parametric simulation models which drastically accelerate airbag deployment geometry predictions while maintaining the accuracy of the airbag deployment geometry at reasonable levels; these models, called herein machine learning (ML)-accelerated models, blend physical system modes with data-driven techniques to accomplish fast predictions within a design space defined by airbag and impactor parameters. These ML-accelerated models are evaluated with virtual test cases of increasing complexity: from airbag deployments against a locked deformable obstacle to airbag deployments against free rigid obstacles; the dimension of the tested design spaces is up to six variables. ML training times are documented for completeness; thus, airbag design explorers or optimization engineers can assess the full budget for ML-accelerated approaches including training. In these test cases, the ML-accelerated simulation models run three orders of magnitude faster than the high-fidelity multi-physics methods, while accuracies are kept within reasonable levels within the design space.

Оцінка динамічної навантаженості екіпажів моторвагонного поїзда з сис-темою пасивної безпеки при його зіткненні з великим транспортним засо-бом

A topical problem of the home railway transport is motor-car train renewval, speed increase, and safety improvement in accordance with the Ukrainian State Standards DSTU EN 12633 and DSTU EN 15227, which specify the passenger car crashworthiness and passive safety, respectively, in emergency collisions with various obstacles. Relying on the world experience, researchers of the institute of Technical Methanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine developed a passive protection concept for home high-speed passenger trains in emergency collisions according to the DSTU EN 15227 requirements, proposals on the passive propection of a home motor-car train head car, lower- and upper-level honeycomb energy-absorbing devoces (EAD 1 and UL EAD, respectively) for the head car front part, and EAD 2 and EAD 3 low-level devices to be installed in intercar connecteions. The upper- and lower-level protective devices for home motor-car trains were developed based on finite-element simulation results using previous experience in the development of a passive protection device for a high-speed passenger locomotive and the results of a successful crash test of its proptotype. For Scenario 3, which chraracterizes a collision of a reference motor-car train at 110 km/h with a 15 t large road vehicle at a railway crossing, a model of a large deformable obstacle (LDO) was developed in compliance with the DSTU EN 15227 requirements. Finite-element models were developed to determine the force characteristics of interaction between the proposed head car passive protection devices and an LDO. The aim of this paper is to determine dynamic loads on a motor-car train equipped with passive protection devices in its collision with a large road vehicle. Based on a mathematical collision model for identical motor-car trains, a mathematical model was developed for a collision of a reference train with a large road vehicle at a railway crossing (Scenario 3) with account for the determined force characteristics of obstacle ? two EAD 1 low-level devices and obstacle ? two UL EAD upper-level devices interaction and the in-collision work of the head car structure. Dynamic loads on the cars of a reference train with a passive safety system (a head car mass of 80 t and intermediate car masses of 50 t or 64 t) were analyzed for its collision by Scenario 3. Two EAD layouts in the head car front part were studied. It was found that the proposed passive protection of the reference train cars meets the DSTU EN 15227 criteria for Scenario 3 for both EAD layouts and the determined variants of lower- and upper-level EAD use according to the intermediate car masses. The proposed mathematical model of dynamic loads on a passenger train with a passive safety system in its collision with a large road vehicle and the results obtained may be used in designing an up-to-date high-speed motor-car train to the DSTU EN 15227 requirements.

Визначення силової характеристики взаємодії системи пасивної безпеки головного вагона з великим транспортним засобом при зіткненні

One of the priorities of the National Economic Strategy of Ukraine for the Period up to 2030 is the development of the transport sector, in particular railway vehicle renewal, the introduction of high-speed railway passenger transport, and railway traffic safety improvement. The home motor-car trains must be renewed in compliance with new home standards harmonized with European ones, among which one should mention the Ukrainian State Standard DSTU EN 15227, which specifies the passive safety of a passenger train in its emergency collisions with different obstacles. New car designs must provide not only effective up-to-date braking systems to prevent emergency collisions, but also passive safety systems with energy-absorbing devices. The main purpose of these devices is to reduce the longitudinal forces in the intercar connections and the car accelerations to an acceptable level for the three collision scenarios specified in the DSTU EN 15227. The Department of Statistical Dynamics and Multidimensional Mechanical Systems Dynamics, Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, developed a passive protection concept for home high-speed passenger trains in emergency collisions by the DSTU EN 15227 scenarios, proposals on the passive protection of a motor-car train head car, and honeycomb designs of lower- and upper-level energy-absorbing devices (EAD 1 and UL EAD, respectively), which are integrated into the head car front part and serve to damp the major part of the impact energy in front collisions with obstacles. This paper considers DSTU EN 15227 Scenario 3: a collision of a reference motor-car train at a speed of 110 km/h at a railway crossing with a large 15 t road vehicle, which is simulated as a large-size deformable obstacle (LSDO). The aim of the paper is to determine the force characteristic of the interaction of energy-absorbing devices mounted on the head car front part with a large road vehicle in a collision to assess the compliance of the proposed passive protection with the normative requirements. Finite-element models were constructed to analyze the plastic deformation of the elements of the EAD 1 – LSDO, UL EAD – LSDO, and EAD 1 – UL EAD –LSDO systems in a collision with account for geometric and physical nonlinearities, steel dynamic hardening as a function of the impact speed, and varying contact interaction between the elements of the systems considered. The studies conducted made it possible to determine the force characteristics of energy-absorbing device – obstacle interaction and the total characteristic of the contact force between two lower-level devices and two upper-level ones as a function of the obstacle center of mass displacement in a collision. The proposed mathematical models and the calculated force characteristics may be used in the study of the dynamics of a reference motor-car train – large road vehicle collision with the aim to assess the compliance of the passive protection of the home head car under design with the DSTU EN 15227 requirements.

DEFORMABLE OBJECT REMOVAL VIA EXEMPLAR-BASED ALGORITHM FOR 3D MODEL OF HERITAGE STRUCTURES

Heritage structures are important for tourism and for learning about nations’ history. Historical sites around the world are in damaged conditions due to various factors from the environment, man-made activities or natural calamities. To ensure safety and avoid further deterioration, digital re- construction of heritage sites can be used to create 3D virtual models of these structures for archiving and for inspection purpose. This paper presents a technique to reconstruct a high-quality image-based 3D model of a heritage structure. An exemplar-based inpainting algorithm was used for removing deformable obstacles such as trees in 2D images since such obstacles are unwanted in a final 3D model. They also create noise in the 3D modeling process, which makes the final 3D model less accurate. In this paper, an inpainting algorithm is applied to generate implied texture to fill holes that occurred from removing objects so that the generated 3D model does not contain any hole and becomes watertight. The modified exemplar-based inpainting algorithm was implemented on 2D images to remove unwanted objects, and then the image-based 3D modeling technique was applied to create a 3D model that did not contain any unwanted objects. The results show that the final 3D model is more accurate when applied the object removal process and the model provides better visualization for heritage structures.

Підвищення рівня безпеки залізничних пасажирських та вантажних перевезень

In 2020, the Ukrainian Government conducted an audit of the Ukrainian economy for nearly 30 years of independence and decided on the vectors of economic development aimed at European and Euro-Atlantic integration. The audit of the Ukrainian railways showed that most of the railway assets are critically worn. The audit and the vectors became a starting point for the development of the National Economic Strategy of Ukraine up to 2030, which was approved on March 3, 2021. One of the priorities of this strategy is the development of the transport sector by a succession of steps, including railway track and vehicle renewal, the introduction of high-speed passenger transport, and increasing railway traffic safety and environment safety on the Urrainian railways. The aim of this paper is to work out recommendations on increasing the safety of passenger and freight traffic in Ukraine. The paper generalizes the experience gained over the years of Ukrainian independence in the fundamental and applied transport-oriented reseach conducted at the Department of Sttistical Dynamics and Multidimensional Mechanical Systems, Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine. This experience may be useful in the implementation of the above steps on the way to the sustainable development of the Ukrainian railway transport. In the paper, emphasis is on new investigations into the passive propection of the cars of a motor car train in emergency collisions whose scenarios are specified by Ukrainian State Standard DSTU EN 15227. Based on a mathematical model of a collision of identical motor car trains, a mathematical model was developed to simulate a collision of a motor car train with a large vehicle at a crossing with account for a specified force characteristic of interaction of the leading car equipped with a passive safety system with a deformable obstacle. The model developed was used in analyzing dynamic loads on the cars of a motor car train with a passive safety system in its collision at 110 km/h with a 15 t large vehicle at a railway crossing. With consideration for the results of previous investigations into the dynamics of emergency collisions of a motor car train with an identical train and a fright car, recommendations were worked out on the passive protection of a home-made leading car in accordance with the requirements of normative documents. The proposed mathematical models and designs of energy-absorbing devices, the research results, and the practical recommendations worked out may be used in designing new motor car train vehicles for the Ukrainian railways in accordance with the DSTU EN 15227 requirements for passive protection in emergency collisions.

Analysis of a contact problem for a viscoelastic Bresse system

In this paper, we consider a contact problem between a viscoelastic Bresse beam and a deformable obstacle. The well-known normal compliance contact condition is used to model the contact. The existence of a unique solution to the continuous problem is proved using the Faedo-Galerkin method. An exponential decay property is also obtained defining an adequate Liapunov function. Then, using the finite element method and the implicit Euler scheme, a finite element approximation is introduced. A discrete stability property and a priori error estimates are proved. Finally, some numerical experiments are performed to demonstrate the decay of the discrete energy and the numerical convergence.

Feedback stabilization of a 3D fluid flow by shape deformations of an obstacle

We consider a fluid flow in a time dependent domain Ωf(t)=Ω\Ωs(t)̅⊂ℝ3, surrounding a deformable obstacle Ωs(t). We assume that the fluid flow satisfies the incompressible Navier-Stokes equations in Ωf(t), t > 0. We prove that, for any arbitrary exponential decay rate ω > 0, if the initial condition of the fluid flow is small enough in some norm, the deformation of the boundary ∂Ωs(t) can be chosen so that the fluid flow is stabilized to rest, and the obstacle to its initial shape and its initial location, with the exponential decay rate ω > 0.

Analysis of a contact problem involving thermoelastic mixtures

In this work we study a dynamic contact problem between a thermoelastic mixture and a deformable obstacle. The classical normal compliance condition is used for modeling the contact. The variational formulation of this problem is written as a nonlinear coupled system of three parabolic variational equations. An existence and uniqueness result is proved using the Faedo-Galerkin method. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the decay of the discrete energy and the linear convergence of the algorithm are deduced. Finally, some numerical simulations are presented to show the convergence and the behavior of the solution.

Analysis of a Contact Problem Problem Involving an Elastic Body with Dual-Phase-Lag

In this work we study a contact problem between a thermoelastic body with dual-phase-lag and a deformable obstacle. The contact is modelled using a modification of the well-known normal compliance contact condition. An existence and uniqueness result is proved applying the Faedo–Galerkin method and Gronwall’s inequality. The exponential stability is also shown. Then, we introduce a fully discrete approximation by using the implicit Euler scheme and the finite element method. A discrete stability property and a priori error estimates are obtained, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, some numerical examples are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

AbstractA dynamic contact problem, between a thermoelastic rod with voids and microtemperatures and a deformable obstacle, is numerically investigated in this work. The contact is modelled with a modification of the classical normal compliance contact condition. The mechanical problem consists of a coupled system of two hyperbolic partial differential equations and two parabolic ones. An existence and uniqueness result, and an energy decay property, are stated. Then, fully discrete approximations are introduced to approximate this nonlinear problem by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation and the behaviour of the solution.

Analysis of a dynamic viscoelastic-viscoplastic piezoelectric contact problem

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal compliance contact condition. The variational formulation is written as a nonlinear ordinary differential equation for the stress field, a nonlinear hyperbolic variational equation for the displacement field and a linear variational equation for the electric potential field. An existence and uniqueness result is proved using Gronwall's lemma, adequate auxiliary problems and fixed-point arguments. Then, fully discrete approximations are introduced using an Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some two-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution.

A regularization method for a viscoelastic contact problem

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and a deformable obstacle, the so-called foundation. The material’s behaviour is modelled with a viscoelastic constitutive law with long memory. The contact is frictionless and is defined using a multivalued normal compliance condition. We present a regularization method in the study of a class of variational inequalities involving history-dependent operators. Finally, we apply the abstract results to analyse the contact problem.

On-Chip Quantitative Measurement of Mechanical Stresses During Cell Migration with Emulsion Droplets.

The ability of immune cells to migrate within narrow and crowded spaces is a critical feature involved in various physiological processes from immune response to metastasis. Several in-vitro techniques have been developed so far to study the behaviour of migrating cells, the most recent being based on the fabrication of microchannels within which cells move. To address the question of the mechanical stress a cell is able to produce during the encounter of an obstacle while migrating, we developed a hybrid microchip made of parallel PDMS channels in which oil droplets are sparsely distributed and serve as deformable obstacles. We thus show that cells strongly deform droplets while passing them. Then, we show that the microdevice can be used to study the influence of drugs on migration at the population level. Finally, we describe a quantitative analysis method of the droplet deformation that allows measuring in real-time the mechanical stress exerted by a single cell. The method presented herein thus constitutes a powerful analytical tool for cell migration studies under confinement.

Analysis of the penalized 3D variable viscosity stokes equations coupled to diffusion and transport

The analysis of the penalized Stokes problem, in its variable viscosity formulation, coupled to convection-diffusion equations is presented in this article. It models the interaction between a highly viscous fluid with variable viscosity and immersed moving and deformable obstacles. Indeed, while it is quite common to couple Poisson equations to diffusion-transport equations in plasma physics or fluid dynamics in vorticity formulations, the study of complex fluids requires to consider together the Stokes problem in complex moving geometry and convection-diffusion equations. The main result of this paper shows the existence and the uniqueness of the solution to this equations system with regularity estimates. Then we show that the solution to the penalized problem weakly converges toward the solution to the physical problem. Numerical simulations of fluid mechanics computations in this context are also presented in order to illustrate the practical aspects of such models: lung cells and their surrounding heterogeneous fluid, and porous media flows. Among the main original aspects in the present study, one can highlight the non linear dynamics induced by the coupling, and the tracking of the time-dependence of the domain.

Brownian motion on random dynamical landscapes

We present a study of overdamped Brownian particles moving on a random landscape of dynamic and deformable obstacles (spatio-temporal disorder). The obstacles move randomly, assemble, and dissociate following their own dynamics. This landscape may account for a soft matter or liquid environment in which large obstacles, such as macromolecules and organelles in the cytoplasm of a living cell, or colloids or polymers in a liquid, move slowly leading to crowding effects. This representation also constitutes a novel approach to the macroscopic dynamics exhibited by active matter media. We present numerical results on the transport and diffusion properties of Brownian particles under this disorder biased by a constant external force. The landscape dynamics are characterized by a Gaussian spatio-temporal correlation, with fixed time and spatial scales, and controlled obstacle concentrations.

Numerical simulation of fluid–structure interaction with the volume penalization method

We present a novel scheme for the numerical simulation of fluid–structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid–solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections.

A dynamic viscoelastic contact problem with normal compliance

A dynamic contact problem between a viscoelastic body and a deformable obstacle is numerically considered in this work. The contact is modeled by using the well-known normal compliance contact condition. The variational formulation of this problem is written in terms of the velocity field and it leads to a parabolic nonlinear variational equation. An existence and uniqueness result is stated. Fully discrete approximations are then introduced by using the finite element method to approximate the spatial variable, and a hybrid combination of the implicit and explicit Euler schemes to discretize the time derivatives. An a priori error analysis is recalled. Then, an a posteriori error analysis is provided extending some results already obtained in the study of the heat equation, other parabolic equations and the quasistatic case. Upper and lower bounds are proved. Finally, some two-dimensional numerical simulations are presented to demonstrate the accuracy and the behavior of the error estimators.

A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient

We consider a mathematical model that describes frictionless contact between a viscoplastic body and a deformable obstacle or foundation. The process is quasistatic and contact is modeled with the normal compliance with limited penetration condition, which has been introduced recently. Moreover, the contact stiffness coefficient is allowed to depend on the history of the contact process. We derive a variational formulation of the problem, which is in the form of a strongly nonlinear system coupling an integral equation and a time-dependent variational inequality. Then, we provide the analysis of the problem, which includes its unique weak solvability and the continuous dependence of the solution on the problem data. The proofs are based on results from the theory of history-dependent variational inequalities, on monotonicity and a fixed point argument.

A dynamic contact problem involving a Timoshenko beam model

In this paper, a dynamic contact problem between a viscoelastic beam and a deformable obstacle is considered. The classical Timoshenko beam model is used and the contact is modeled by using the well-known normal compliance contact condition. The variational problem is written as a coupled system composed of a nonlinear variational equation for the displacement field and a linear variational equation for the angular rotation function. The existence of a unique solution is proved by using the Faedo–Galerkin method and employing some a priori estimates and Gronwallʼs inequality. Then, fully discrete approximations are introduced, based on the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, obtaining the linear convergence of the algorithm under an additional regularity condition. Finally, some numerical simulations are presented to show the accuracy of the algorithm and the behavior of the solution.