•A phase-field model for fluid–structure interaction is developed.•The model can handle freely moving objects, topological changes, contact dynamics and adhesion.•The model is validated by energy ...variation, asymptotic analysis and numerical studies.
In this paper, we develop a novel phase-field model for fluid–structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to a wall. The model is based on a fully Eulerian description of the velocity field in both, the fluid and the elastic domain. Viscous and elastic stresses in the Navier–Stokes equations are restricted to the corresponding domains by multiplication with their characteristic functions. The solid is described as a hyperelastic neo-Hookean material and the elastic stress is obtained by solving an additional Oldroyd-B – like equation. Thermodynamically consistent forces are derived by energy variation. The convergence of the derived equations to the traditional sharp interface formulation of fluid–structure interaction is shown by matched asymptotic analysis. The model is evaluated in a challenging benchmark scenario of an elastic body traversing a fluid channel. A comparison to reference values from Arbitrary Lagrangian Eulerian (ALE) simulations shows very good agreement. We highlight some distinct advantages of the new model, like the avoidance of re-triangulations and the stable inclusion of surface tension. Further, we demonstrate how simple it is to include contact dynamics into the model, by simulating a ball bouncing off a wall. We extend this scenario to include adhesion of the ball, which to our knowledge, cannot be simulated with any other FSI model. While we have restricted simulations to fluid–structure interaction, the model is capable to simulate any combination of viscous fluids, visco-elastic fluids and elastic solids.
In this paper, the cell-based smoothed finite element using quadrilateral elements (CS-FEM) is used for 2D contact problems which are converted into linear complementarity problems (LCPs), which can ...be solved efficiently using the Lemke method. The modified Coulomb friction contact model with tangential strength and normal adhesion is considered, which models sticking-slipping, contacting-departing, and bonding-debonding processes, in a unified formulation. Smoothed Galerkin weak-form with contact boundary is deduced, in which the stiffness is implemented using the CS-FEM with 1 smoothing domain (1SD), 2SD, 3SD, 4SD, 8SD, and 16SD for each element. Contact interface equations are discretized through contact point-pairs that are constructed using a master-slave surface algorithm. Intensive numerical examples are given to investigate the effects of contact parameters on contact behaviors and examine the effectiveness of the proposed approach. The numerical results of CS-FEM models are compared with that of FEM-Q4 model, which demonstrates that all CS-FEM models are softer than FEM-Q4 model. The strain energy solutions, obtained using several CS-FEM models, are monotonically decreasing with the number of the SDs for each element increasing. The upper bound solutions in strain energy can be obtained using a CS-FEM-1SD model in our examples, while the lower bound solutions are obtained using CS-FEM-16SD model or FEM-Q4, with FEM-Q4 solution being the lowest.
Microscale beam-like structures are standard components of micromechanical systems in many devices. However, the small dimensionality affects their deformation characteristics and leads to ...misinterpretations of the results. Presenting such size dependency is possible with advanced continuum descriptions via introducing additional variables compared to the classical one. Hence, the problems where contact occurs require the readjustment of boundary conditions considering these extra parameters. That burdens the already challenging task of contact problem calculations and restricts most demonstration examples to two-dimensional problems and geometrical linearity. The resolution of the imposed restrictions within finite element modeling further emphasizes the usage of advanced media in design and facilitates its application to various problems, which is the aim of this paper. The delivery of that task is as follows. Firstly, we present the kinematics and material descriptions for the micropolar media. The authors propose to use a newly developed continuum-based micropolar beam formulation to avoid an overwhelming computational burden and, at the same time, deal with nonlinear stress–strain relations. Secondly, the work develops a contact approach within the micropolar theory from two-dimensional to three-dimensional elasticity, although the contact is considered frictionless. Finally, it compares two existing contact formulations, including the developed one, for the contact beam problems, using the examples of two collinear sliding beams’ bending.
•Presented two known contact formulations within the micropolar theory.•Developed one of the contact approaches to three-dimensional elasticity.•Considered a practical problem of bending two-layered cantilever beam. .
This paper is devoted to a study of the numerical solution of elliptic hemivariational inequalities with or without convex constraints by the finite element method. For a general family of elliptic ...hemivariational inequalities that facilitates error analysis for numerical solutions, the solution existence and uniqueness are proved. The Galerkin approximation of the general elliptic hemivariational inequality is shown to converge, and Céa's inequality is derived for error estimation. For various elliptic hemivariational inequalities arising in contact mechanics, we provide error estimates of their numerical solutions, which are of optimal order for the linear finite element method, under appropriate solution regularity assumptions. Numerical examples are reported on using linear elements to solve sample contact problems, and the simulation results are in good agreement with the theoretically predicted linear convergence.
We consider a static contact problem between an elastic body and an absolutely rigid foundation with Signorini contact conditions and Coulomb friction law. The problem can be formulated as a ...quasi-variational inequality in which the normal stress is proportional with the friction coefficient to the friction force in the contact zone. In this case, the normal stress itself depends on the desired solution, and the existence of a solution to the problem reduces to the existence of a fixed point of a certain mapping. Consideration of Coulomb friction naturally leads to the non-differentiability of the objective functional in the auxiliary problem of the method of successive approximations and, thereby, to a significant complication of the algorithms for solving the constrained minimization problem. We propose a method of solving an auxiliary problem with given friction, which is based on the Uzawa algorithm and modified Lagrange functionals. The main advantage of the proposed method is that it allows to effectively solve auxiliary problems and to prove the theoretical convergence of the method of successive approximations to a fixed point. Numerical experiments are carried out to demonstrate the efficiency of the proposed method.
Inspired by manifestations in nature, microengineering and nanoengineering of synthetic materials to achieve superhydrophobicity has been the focus of much work. Generally, hydrophobicity is enhanced ...through the combined effects of surface texturing and chemistry; being durable, rigid materials are the norm. However, many natural and technical surfaces are flexible, and the resulting effect on hydrophobicity has been largely ignored. Here, we show that the rational tuning of flexibility can work synergistically with the surface microtexture or nanotexture to enhance liquid repellency performance, characterized by impalement and breakup resistance, contact time reduction, and restitution coefficient increase. Reduction in substrate areal density and stiffness imparts immediate acceleration and intrinsic responsiveness to impacting droplets (∼350 × g), mitigating the collision and lowering the impalement probability by ∼60% without the need for active actuation. Furthermore, we exemplify the above discoveries with materials ranging from man-made (thin steel or polymer sheets) to nature-made (butterfly wings).
•Enhanced contact model with non-standard contact conditions for a Cosserat continuum.•Contact occurs through rigid microblocks that rotate according to the Cosserat kinematics.•Consistent coupling ...of displacements and microrotations at the contact interface.•Analytical solution for the boundary layers induced by the non-standard contact conditions.•New qualitative features and size effects observed in a 2D Hertz-like contact problem.
Generalized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or for the respective generalized tractions. In this paper, we address several related open problems, namely, how to enhance the classic contact conditions to include the effects of the additional kinematic variables, how to link the enhanced contact model to the underlying microstructure of the solid, and how to do it in a consistent manner. As a first step towards a new class of contact models for generalized continua, a microblock contact model is derived for a Cosserat solid based on simple micromechanical considerations. To illustrate the non-trivial effects introduced by the non-standard boundary conditions, the problem of compression of an infinite strip with nonaligned microblocks is considered, and the analytical solution is derived for the corresponding boundary layers. A Hertz-like contact problem is also solved numerically with the focus on non-standard features of the solution and on the related size effects.
The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the ...discrete fracture-matrix approach. The fracture flow is driven by the cubic law, and the contact conditions prevent fractures from self-penetration. A stable finite element discretization is proposed for the displacement-pressure-flux formulation. The resulting nonlinear algebraic system of equations and inequalities is decoupled using a robust iterative splitting into the linearized flow subproblem, and the quadratic programming problem for the mechanical part. The non-penetration conditions are solved by means of dualization and an optimal quadratic programming algorithm. The capability of the numerical scheme is demonstrated on a benchmark problem for tunnel excavation with hundreds of fractures in 3D. The paper's novelty consists in a combination of three crucial ingredients: (i) application of discrete fracture-matrix approach to poroelasticity, (ii) robust iterative splitting of resulting nonlinear algebraic system working for real-world 3D problems, and (iii) efficient solution of its mechanical quadratic programming part with a large number of fractures in mutual contact by means of own solvers implemented into an in-house software library.
•A numerical method for accurate resolution of flow and mechanics in fractured rock is presented.•Discrete fracture-matrix approach links processes in rock mass and fracture network.•Robust iterative splitting enables solving nonlinear hydro-mechanical problems.•Efficient algorithm for quadratic programming solves non-penetration conditions on fractures.•Parallel implementation is capable of handling complex geometries with hundreds of fractures in 3D.
•Effect of contact stiffness on the impact behaviour.•Modelling contact problem in LS-Dyna.•New factors affecting the contact stiffness.•Scale factors of the penalty contact mechanism.
It is commonly ...understood that the contact stiffness of the two colliding structures/objects is dependent primarily on the material properties. However, there have been experimental and numerical evidences that the contact stiffness is also strongly influenced by other factors. This study experimentally and numerically investigates the effects of contact stiffness on the impact behaviour of RC beams. Reinforced concrete beams were cast and tested under a drop-weight testing apparatus with different contact conditions simulating different contact stiffness. Extensive numerical simulations are carried out to confirm the findings from the experimental results and to perform parametric studies. The experimental and numerical results have shown that the contact stiffness is very sensitive to the actual setup in the experiment and contact condition, leading to a crucial effect on the peak value and duration of the impact force. The contact stiffness however has little effect on the impulse and thus the conversion of the impact energy to the beam and hence the midspan displacement. The magnitude of the inertia resistance is greatly influenced by the contact stiffness, resulting in a significant effect on the dynamic bending moment and shear force distribution along the beam. The contact behaviour needs to be carefully considered when analysing the impact behaviour of RC structures. In addition, advantages and disadvantages of the different contact algorithms in finite element packages, e.g. LS-Dyna, are discussed for a proper use in the simulation. An appropriate contact algorithm and a scale factor are greatly important to ensure the simulation properly reflects the actual contact problems, and they must be selected with extreme caution.
Summary
This paper proposes novel strategies to enable multigrid preconditioners within iterative solvers for linear systems arising from contact problems based on mortar finite element formulations. ...The so‐called dual mortar approach that is exclusively employed here allows for an easy condensation of the discrete Lagrange multipliers. Therefore, it has the advantage over standard mortar methods that linear systems with a saddle‐point structure are avoided, which generally require special preconditioning techniques. However, even with the dual mortar approach, the resulting linear systems turn out to be hard to solve using iterative linear solvers. A basic analysis of the mathematical properties of the linear operators reveals why the naive application of standard iterative solvers shows instabilities and provides new insights of how contact modeling affects the corresponding linear systems. This information is used to develop new strategies that make multigrid methods efficient preconditioners for the class of contact problems based on dual mortar methods. It is worth mentioning that these strategies primarily adapt the input of the multigrid preconditioners in a way that no contact‐specific enhancements are necessary in the multigrid algorithms. This makes the implementation comparably easy. With the proposed method, we are able to solve large contact problems, which is an important step toward the application of dual mortar–based contact formulations in the industry. Numerical results are presented illustrating the performance of the presented algebraic multigrid method.
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