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Finite strain poro-hyperelasticity: an asymptotic multi-scale ALE-FSI approach supported by ANNs Dehghani, Hamidreza ; Zilian, Andreas in Computational Mechanics (2023) This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their ... [more ▼] This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their characteristic multi-scale and multi-physics parameters. In the present work this is achieved by formulating a non-dimensionalised fluid–solid interaction problem (FSI) at the pore level using an arbitrary Lagrange–Euler description (ALE). The resulting coupled systems of PDEs on the reference configuration are expanded and analysed using the asymptotic homogenisation technique. This approach yields three partially novel systems of PDEs: the macroscopic/effective problem and two supplementary microscale problems (fluid and solid). The latter two provide the microscopic response fields whose average value is required in real-time/online form to determine the macroscale response (a concurrent multi-scale approach). In order to overcome the computational challenges related to the above multi-scale closure, this work introduces a surrogate approach for replacing the direct numerical simulation with an artificial neural network. This methodology allows for solving finite strain (multi-scale) porohyperelastic problems accurately using direct automated differentiation through the strain energy. Optimal and reliable training data sets are produced from direct numerical simulations of the fully-resolved problem by including a simple real-time output density check for adaptive sampling step refinement. The data-driven approach is complemented by a sensitivity analysis of the RVE response. The significance of the presented approach for finite strain poro-elasticity/poro-hyperelasticity is shown in the numerical benchmark of a multi-scale confined consolidation problem. Finally, to show the robustness of the method, the system response is dimensionalised using characteristic values of soil and brain mechanics scenarios. [less ▲] Detailed reference viewed: 32 (3 UL)Optimal electrode coverage based on a new criterion for piezoelectric energy harvesters Shang, Lan ; ; Zilian, Andreas in Energy Conversion and Management (2023), 284 Piezoelectric energy harvesters (PEHs) are a promising alternative to conventional electrochemical batteries with the advantage of being self-powered and maintenance-free, but their application is ... [more ▼] Piezoelectric energy harvesters (PEHs) are a promising alternative to conventional electrochemical batteries with the advantage of being self-powered and maintenance-free, but their application is severely restricted by the low electric power output. It has been reported that the power output of PEHs can be enhanced by well-designed electrode coverage. A common design criterion for beam-like PEHs is based on the strain node to avoid electrode charge cancellation. This criterion, however, is not feasible for PEHs subject to complex spatio-temporal excitation patterns, where strain nodes change their position. This work proposes a new design criterion for optimal electrode coverage of beam-like PEHs based on the closed-form solution of the circuit equation that expresses voltage as a function of the beam’s dynamic response, specifically the cross-section rotation. The new criterion maximizes the averaged curvature of the beam segment covered by the electrode using data on the instantaneous rotation field. The improved physical significance and reliability of the presented criterion are discussed. The associated electrode optimization procedure is then exemplified for PEHs driven by fluid flow, which helps to realize a complex excitation pattern. Two numerical studies, both including a variety of combinations of fluid densities and inlet velocities, are performed to demonstrate that an optimal electrode configuration can be obtained with the proposed criterion. Comparison of different electrode configurations in above studies finally leads to useful conclusions on the power output and electrode configuration. [less ▲] Detailed reference viewed: 32 (0 UL)Nonlinear local solver Habera, Michal ; Zilian, Andreas Scientific Conference (2022, August) Many engineering applications require solution of a global finite element problem coupled with nonlinear equations of local nature. Local in the sense, that for a known global state the local solution ... [more ▼] Many engineering applications require solution of a global finite element problem coupled with nonlinear equations of local nature. Local in the sense, that for a known global state the local solution could be found on cell-by-cell basis. Examples include plastic deformation problems, static condensation (hybridization) of displacement-stress formulation or just a simple nonlinear constitutive laws to be satisfied at each quadrature point. These types of problems either required special libraries and extensions in order to be solved with FEniCS (and FEniCS-X) tools, or lead to very slow implementations due to hacks and tricks needed to achieve the solution (e.g. monolithic schemes which increase the matrix problem size). In this talk a unified approach tailored for the current state of FEniCS-X interfaces is presented. The approach computes consistent global tangent operator for nonlinear problems. In addition, local equations are formulated symbolically in UFL, and their derivatives are therefore computed automatically. Several low-level examples (incl. plasticity with symbolic yield surface, nonlinear static condensation and materials with implicit constitutive laws) that demonstrate the main concepts are presented. Finally, high-level wrappers for this functionality are presented. These come as a part of package `dolfiny` (https://github.com/michalhabera/dolfiny). [less ▲] Detailed reference viewed: 30 (5 UL)Nonlinear analysis of thin-walled structures based on tangential differential calculus with FEniCSx Zilian, Andreas ; Habera, Michal Scientific Conference (2022, August) We present an approach to implement the Tangential Differential Calculus (TDC) for a variety of thin-walled structures (beams, membranes, shells) in the framework of nonlinear kinematics and/or material ... [more ▼] We present an approach to implement the Tangential Differential Calculus (TDC) for a variety of thin-walled structures (beams, membranes, shells) in the framework of nonlinear kinematics and/or material behaviour. In contrast to classical formulations the TDC describes kinematics, equilibrium and constitutive relation of the thin structure (as two-dimensional manifold) on the basis of a full three-dimensional deformation state. This allows to introduce the undeformed configuration of e.g. a shell directly in terms of a mesh of topological dimension 2 and geometrical dimension 3. Of particular interest is the use of finite elements of higher-order geometrical order to capture the (interpolated) curvature of the manifold with high accuracy. Numerical examples and reference implementations of this work to support nonlinear stress and post-buckling analyses (using a realisation of the classical arc-length method in FEniCSx) will be provided as a part of the package dolfiny (https://github.com/michalhabera/dolfiny). [less ▲] Detailed reference viewed: 38 (3 UL)AI-supported Modelling of Brain tissue as Soft Multiscale Multiphysics (Poroelastic) medium Dehghani, Hamidreza ; Zilian, Andreas Presentation (2022, January) Detailed reference viewed: 12 (2 UL)Stochastic porous media, towards a digital meniscus Obeidat, Anas ; Zilian, Andreas in Bulletin of the American Physical Society (2022) Detailed reference viewed: 22 (0 UL)Modeling and simulation of thin-walled piezoelectric energy harvesters immersed in flow using monolithic fluid–structure interaction Shang, Lan ; ; Zilian, Andreas in Finite Elements in Analysis and Design (2022), 206 Detailed reference viewed: 23 (1 UL)Thermo-mechanical modelling for metal additive manufacturing Mashhood, Muhammad ; ; et al Scientific Conference (2021, October 27) [1] Alnaes, M. S. Blechta, J. Hake, J. Johansson, A. Kehlet, B. Logg, A. Richardson, C. Ring, J.Rognes, M. E. and Wells, G. N. The FEniCS Project Version 1.5. Archive of Numerical Software(2015), Vol. 3 ... [more ▼] [1] Alnaes, M. S. Blechta, J. Hake, J. Johansson, A. Kehlet, B. Logg, A. Richardson, C. Ring, J.Rognes, M. E. and Wells, G. N. The FEniCS Project Version 1.5. Archive of Numerical Software(2015), Vol. 3., 100:9–23. [2] Carraturo, M. and Kollmannsberger, S. and Reali, A. and Auricchio, F. and Rank, E. An immersed boundary approach for residual stress evaluation in SLM processes. [less ▲] Detailed reference viewed: 33 (1 UL)AI-aided, incremental numerical approach for fi nite strain poroelasticity: On the brain tissue deformation Dehghani, Hamidreza ; Zilian, Andreas Scientific Conference (2021, May 21) Detailed reference viewed: 53 (3 UL)Data science meets computational mechanics Dehghani, Hamidreza ; Zilian, Andreas Report (2021) Detailed reference viewed: 83 (4 UL)Frictional interactions for non-localised beam-to-beam and beam-inside-beam contact ; Lengiewicz, Jakub ; Zilian, Andreas et al in International Journal for Numerical Methods in Engineering (2021), 122(7), 1706-1731 This contribution presents the extensions of beam-to-beam and beam-inside-beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams’ true surfaces ... [more ▼] This contribution presents the extensions of beam-to-beam and beam-inside-beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams’ true surfaces (instead of surfaces implicitly deduced from the beams’ centroid lines), the presented enhancements are not only able to account for frictional sliding in the beams’ axial directions, but also in the circumferential directions. Both the frictional beam-to-beam approach as well as the frictional beam-inside-beam approach are applicable to shear-deformable and shear-undeformable beams, as well as to beams with both circular and elliptical cross-sections (although the cross-sections must be rigid). A penalty formulation is used to treat unilateral and frictional contact constraints. FE implementation details are discussed, where automatic differentiation techniques are used to derive the implementations. Simulations involving large sliding displacements and large deformations are presented for both beam-to-beam and beam-inside-beam schemes. All simulation results are compared to those of the frictionless schemes. [less ▲] Detailed reference viewed: 383 (7 UL)dolfiny: Convenience wrappers for DOLFINx Zilian, Andreas ; Habera, Michal Scientific Conference (2021, March 23) With the increased flexibility of DOLFINx and its reduction to core functionality, the responsibility for even some basic components of computational analysis is shifted to the user. This presentation ... [more ▼] With the increased flexibility of DOLFINx and its reduction to core functionality, the responsibility for even some basic components of computational analysis is shifted to the user. This presentation provides an overview of the open-source package dolfiny, which provides end-user API interfaces to mesh/meshtags generation and processing, expression list handling, function interpolation and projection as well as the restriction of function spaces to parts of the computational domain. This functionality is consistently considered in interfaces to PETSc/SNES as nonlinear solver and SLEPc as eigensolver backend, both allowing the operation on block and nested operators. In addition, the package provides a convenient approach to incorporate time integration into the UFL formulation of the problem, which is exemplified for the generalised alpha method. The capability of dolfiny is demonstrated in a number of examples, ranging between finite strain structural analysis, plasticity and fluid-structure interaction. [less ▲] Detailed reference viewed: 214 (5 UL)Thermo-mechanical coupling and part-level analysis for additive manufacturing processes Mashhood, Muhammad ; ; Zilian, Andreas et al Scientific Conference (2021, January 13) [1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design ... [more ▼] [1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design (1980-2015), (2013), 52:638–647. [2] Bangerth, W. and Hartmann, R. and Kanschat, G. deal.II – a General Purpose Object Oriented Finite Element Library. ACM Trans. Math. Softw.(2007), Vol. 33., 4:24/1–24/27. [less ▲] Detailed reference viewed: 30 (0 UL)A geometrically nonlinear shear deformable beam model for piezoelectric energy harvesters Shang, Lan ; ; Zilian, Andreas in Acta Mechanica (2021), 232(12), 4847-4866 An electromechanical model for beam-like piezoelectric energy harvesters based on Reissner’s beam theory is developed in this paper. The proposed model captures first-order shear deformation and large ... [more ▼] An electromechanical model for beam-like piezoelectric energy harvesters based on Reissner’s beam theory is developed in this paper. The proposed model captures first-order shear deformation and large displacement/rotation, which distinguishes this model from other models reported in the literature. All governing equations are presented in detail, making the associated framework extensible to investigate various piezoelectric energy harvesters. The weak formulation is then derived to obtain the approximate solution to the governing equations by the finite element method. This solution scheme is completely coupled, and thus allows for two-way interaction between mechanical and electrical fields. To validate this model, extensive numerical examples are implemented in the linear and nonlinear regime. In the linear limit, this model produces results in excellent agreement with reference data. In the nonlinear regime, the large amplitude response of the piezoelectric beam induced by strong base excitation or fluid flow is considered, and the comparison of results with literature data is encouraging. The ability of this nonlinear model to predict limit cycle oscillations in axial flow is demonstrated. [less ▲] Detailed reference viewed: 25 (1 UL)A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs Dehghani, Hamidreza ; Zilian, Andreas E-print/Working paper (2020) We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems ... [more ▼] We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs via ANNs (Artificial Neural Networks). This presented approach allows the selection of a number of locations of interest at which the state variables are expected to fulfil the governing equations associated with a physical problem. Unlike classical PDE approximation methods such as finite differences or the finite element method, there is no need to establish and reconstruct the physical field quantity throughout the computational domain in order to predict the mechanical response at specific locations of interest. The basic idea of MGA-MSGD is the manipulation of the learnable parameters’ components responsible for the error explosion so that we can train the network with relatively larger learning rates which avoids trapping in local minima. The proposed training approach is less sensitive to the learning rate value, training points density and distribution, and the random initial parameters. The distance function to minimise is where we introduce the PDEs including any physical laws and conditions (so-called, Physics Informed ANN). The Genetic algorithm is modified to be suitable for this type of ANN in which a Coarse-level Stochastic Gradient Descent (CSGD) is exploited to make the decision of the offspring qualification. Employing the presented approach, a considerable improvement in both accuracy and efficiency, compared with standard training algorithms such classical SGD and Adam optimiser, is observed. The local displacement accuracy is studied and ensured by introducing the results of Finite Element Method (FEM) at sufficiently fine mesh as the reference displacements. A slightly more complex problem is solved ensuring the feasibility of the methodology [less ▲] Detailed reference viewed: 85 (3 UL)Poroelastic model parameter identification using artificial neural networks: on the effects of heterogeneous porosity and solid matrix Poisson ratio Dehghani, Hamidreza ; Zilian, Andreas in Computational Mechanics (2020), 66 Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests ... [more ▼] Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests for model parameter identification. This problem motivates us to develop a more efficient approach to address complex problems with an acceptable computational cost. In particular, we employ artificial neural network (ANN) for reliable and fast computation of poroelastic model parameters. Based on the strong-form governing equations for the poroelastic problem derived from asymptotic homogenisation, the weighted residuals formulation of the cell problem is obtained. Approximate solution of the resulting linear variational boundary value problem is achieved by means of the finite element method. The advantages and downsides of macroscale properties identification via asymptotic homogenisation and the application of ANN to overcome parameter characterisation challenges caused by the costly solution of cell problems are presented. Numerical examples, in this study, include spatially dependent porosity and solid matrix Poisson ratio for a generic model problem, application in tumour modelling, and utilisation in soil mechanics context which demonstrate the feasibility of the presented framework. [less ▲] Detailed reference viewed: 136 (5 UL)Contact between shear-deformable beams with elliptical cross-sections Magliulo, Marco ; Zilian, Andreas ; Beex, Lars in Acta Mechanica (2020), 231 Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described with a beam. Contact between beams is essential to ... [more ▼] Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described with a beam. Contact between beams is essential to incorporate in mechanical models, but associated contact frameworks are only demonstrated to work for beams with circular cross-sections. Only two studies have shown the ability to treat contact between beams with elliptical cross-sections, but those frameworks are limited to point-wise contact, which narrows their applicability. This contribution presents initial results of a framework for shear-deformable beams with elliptical cross-sections if contact occurs along a line or at an area (instead of at a point). This is achieved by integrating a penalty potential over one of the beams’ surfaces. Simo-Reissner Geometrically Exact Beam (GEB) elements are employed to discretise each beam. As the surface of an assembly of such beam elements is discontinuous, a smoothed surface is introduced to formulate the contact kinematics. This enables the treatment of contact for large sliding displacements and substantial deformations. [less ▲] Detailed reference viewed: 199 (8 UL)Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method ; ; et al in Computational Mechanics (2020), 65(5), 1323-1341 We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto ... [more ▼] We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation allows the flexible utilization of basis functions of different orders as the projection bases. The introduced formulation is much cheaper computationally than the classical $$\bar{B}$$B¯ method. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of $$10^5$$105, and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking with irregular meshes. [less ▲] Detailed reference viewed: 148 (4 UL)Non-localised contact between beams with circular and elliptical cross-sections Magliulo, Marco ; Lengiewicz, Jakub ; Zilian, Andreas et al in Computational Mechanics (2020), 65 The key novelty of this contribution is a dedicated technique to e fficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections ... [more ▼] The key novelty of this contribution is a dedicated technique to e fficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections. The technique consists of parametrizing the surfaces of the two beams in contact, fixing a point on the centroid line of one of the beams and searching for a constrained minimum distance between the surfaces (two variants are investigated). The resulting unilateral (frictionless) contact condition is then enforced with the Penalty method, which introduces compliance to the, otherwise rigid, beams' cross-sections. Two contact integration schemes are considered: the conventional slave-master approach (which is biased as the contact virtual work is only integrated over the slave surface) and the so-called two-half-pass approach (which is unbiased as the contact virtual work is integrated over the two contacting surfaces). Details of the finite element formulation which is suitably implemented using Automatic Di fferentiation techniques are presented. A set of numerical experiments shows the overall performance of the framework and allows a quantitative comparison of the investigated variants. [less ▲] Detailed reference viewed: 181 (50 UL)Data Centric Engineering and Data-Driven Modelling - Computational Engineering Lab Report 2019 Bordas, Stéphane ; Peters, Bernhard ; Viti, Francesco et al Report (2019) https://www.cambridge.org/core/journals/data-centric-engineering Detailed reference viewed: 135 (7 UL) |
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