Development of a large strain strategy for topology optimization

Development of an algorithm for topology optimization in a large strain settin

A finite element reduced-order model based on adaptive mesh refinement and artificial neural networks

This is the accepted version of the following article: [ Baiges, J, Codina, R, Castañar, I, Castillo, E. A finite element reduced‐order model based on adaptive mesh refinement and artificial neural networks. Int J Numer Methods Eng. 2020; 121: 588– 601. https://doi.org/10.1002/nme.6235], which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6235.In this work, a reduced-order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The idea is to run a high-fidelity simulation by using an adaptively refined finite element mesh and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced-order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to nonlinear solid mechanics problems, transient quasi-incompressible flows, and a fluid-structure interaction problem. The results of the numerical examples show that the FAN-ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.Peer ReviewedPostprint (author's final draft

Numerical simulation of Fluid–Structure Interaction problems with viscoelastic fluids using a log-conformation reformulation

In this paper the numerical simulation of the interaction between Oldroyd-B viscoelastic fluid flows and hyperelastic solids is approached. The algorithm employed is a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially. A Galerkin finite element approach has been employed for the numerical approximation of the solid, while the flow equations are approximated using a stabilized finite element method based on the Variational Multi-Scale approach to overcome the instabilities of the Galerkin method. To be able to deal with flows with dominant elasticity, a log-conformation reformulation of the constitutive equation can be employed; here this approach is extended to Fluid–Structure Interaction problems. Several numerical examples are presented and discussed to assess the robustness of the proposed scheme and its applicability to problems with viscoelastic fluids in which elasticity is dominant interacting with hyperelastic solids.L. Moreno acknowledges the support received from the project Nemesis, LARE_BIRD2020_01 (id: 33593). I. Castañar gratefully acknowledges the support received from the Agència de Gestió d’Ajuts i de Recerca through the predoctoral FI grant 2019-FI-B-00649. R. Codina gratefully acknowledges the support received through the ICREA, Spain Acadèmia Research Program of the Catalan Government. This work was partially funded through the TOP-FSI: RTI2018-098276-B-I00 project of the Spanish Government. CIMNE is a recipient of a “Severo Ochoa Programme for Centers of Excellence in R&D” grant (CEX2018-000797-S) by the Spanish Ministry of Economy and Competitiveness .Peer ReviewedPostprint (published version

Topology optimization of incompressible structures for fluid-structure interaction problems

(English) Topology optimization of incompressible structures, in which the loads on the structure come from the stresses exerted by a surrounding fluid, is a highly complex problem. This work presents a compilation of the research conducted to reproduce such complex phenomena. Firstly, two stabilized mixed finite element methods for finite strain solid dynamics are developed. These stabilized methods are stable for any interpolation spaces of the unknowns. On the one hand, a two-field mixed displacement/pressure formulation capable of dealing with nearly and fully incompressible hyperelastic material behavior is presented. On the other hand, so as to be able to tackle the incompressible limit and at the same time, to obtain a higher accuracy in the computation of stresses, a three-field mixed displacement/pressure/deviatoric stress formulation is proposed. Stability, mesh convergence analysis and nonlinear iteration convergence analysis are performed together with several numerical examples for both formulations. It is shown that both formulations appropriately deal with the incompressibility constraint, but the three-field formulation exhibits higher accuracy in the stress field, even for very coarse meshes. Secondly, we develop algorithms for topology optimization problems based on the topological derivative concept. To deal with incompressible materials, mixed formulations must be considered, but also a new decomposition of the well-known Polarization tensor is required for linear elastic materials. In the finite strain hyperelasticity assumption, an approximation of the topological derivative in combination with the mixed formulations previously presented is considered to deal with incompressibility. Several numerical examples are presented and discussed to assess the robustness of the proposed algorithms and their applicability to topology optimization problems for incompressible elastic solids. Then, we analyze the numerical simulation of the interaction between viscoelastic fluid flows and hyperelastic solids. The fluid-structure interaction problem is solved sequentially. Flow equations are approximated using two stabilized three-field finite element formulations. To address flows with dominant elasticity, a log-conformation reformulation of the constitutive equation is employed. Several numerical examples are presented and discussed to assess the robustness of the proposed scheme and its applicability to problems with viscoelastic fluids, in which elasticity dominates the interaction with hyperelastic solids. Finally, all numerical tools are combined to reproduce the topology optimization problem of incompressible structures subjected to the interaction with a surrounding fluid.(Català) L'optimització topològica d'estructures incompressibles, en què les càrregues sobre l'estructura provenen de les tensions exercides per un fluid que l'envolta, és un problema d'alta complexitat. Aquest treball presenta una recopilació de la investigació realitzada per reproduir aquests fenòmens complexos. En primer lloc, es desenvolupen dos mètodes d'elements finits estabilitzats per estudiar problemes de deformació finita en dinàmica de sòlids. Aquests mètodes són estables per qualsevol espai d'interpolació de les incògnites. Per una banda, es presenta una formulació mixta de dos camps, on les incògnites són desplaçaments i pressions. Aquesta formulació és capaç de tractar amb materials hiperelàstics que presenten un comportament quasi o totalment incompressible. Per l'altra banda, per ser capaços d'arribar al límit incompressible i, alhora, obtenir una major precisió en la computació del camp de tensions, una formulació mixta de tres camps és desenvolupada on afegim el camp de tensions desviadores com una incògnita més del problema. Anàlisis d'estabilitat, de convergència de malla i de convergència de les iteracions no-lineals són estudiades junt amb l'estudi d'exemples numèrics per ambdues formulacions. Es demostra que ambdues formulacions tracten de forma apropiada la restricció d'incompressibilitat, però, la formulació de tres camps mostra una major precisió en el camp de tensions, inclús per malles molt grolleres. En segon lloc, algoritmes per problemes d’optimització topològica basats en el concepte de la derivada topològica són desenvolupats. Per ser capaços de tractar amb materials incompressibles, hem de considerar no només formulacions mixtes, sinó també, una descomposició del tensor de Polarització en elasticitat lineal. En el cas de la hipòtesi de materials hiperelàstics en deformació finita, requerim d’una aproximació de la derivada topològica en combinació amb les formulacions mixtes prèviament presentades. Es presenten i es discuteixen diversos exemples numèrics per avaluar la robustesa dels algoritmes proposats i la seva aplicabilitat a problemes d’optimització topològica per a sòlids elàstics incompressibles. Seguidament, analitzem la simulació numèrica de la interacció entre fluids viscoelàstics i sòlids hiperelàstics. El problema d’interacció fluid-estructura es resol seqüencialment. Les equacions del flux s’aproximen utilitzant formulacions d’elements finits estabilitzats de dos camps i tres camps. Per abordar fluxos on l’elasticitat és dominant, una reformulació logarítmica de les equacions constitutives és emprada. Es presenten i es discuteixen diversos exemples numèrics per avaluar la robustesa de l’esquema proposat i la seva aplicabilitat a problemes amb fluids viscoelàstics, en els quals l’elasticitat domina la interacció amb sòlids hiperelàstics. Finalment, totes les eines numèriques es combines per reproduir el problema d’optimització topològica d’estructures incompressibles sotmeses a la interacció amb un fluid circumdant.DOCTORAT EN ENGINYERIA CIVIL (Pla 2012

Development of a large strain strategy for topology optimization

Development of an algorithm for topology optimization in a large strain settin

Development of a large strain strategy for topology optimization

Development of an algorithm for topology optimization in a large strain settin

A stabilized mixed three-field formulation for stress accurate analysis including the incompressible limit in finite strain solid dynamics

This is the peer reviewed version of the following article: [Castañar, I, Codina, R, Baiges, J. A stabilized mixed three-field formulation for stress accurate analysis including the incompressible limit in finite strain solid dynamics. Int J Numer Methods Eng. 2023; 1- 26. doi: 10.1002/nme.7213], which has been published in final form at https://doi.org/10.1002/nme.7213. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this work a new methodology for finite strain solid dynamics problems for stress accurate analysis including the incompressible limit is presented. In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint in finite strain solid dynamics. To this end, the momentum equation is complemented with a constitutive law for the pressure which emerges from the deviatoric/volumetric decomposition of the strain energy function for any hyperelastic material model. The incompressible limit is attained automatically depending on the material bulk modulus. This work exploits the concept of mixed methods to formulate stable displacement/pressure/deviatoric stress finite elements. The final goal is to design a finite element technology able to tackle simultaneously problems which may involve incompressible behavior together with a high degree of accuracy of the stress field. The variational multi-scale stabilization technique and, in particular, the orthogonal subgrid scale method allows the use of equal-order interpolations. These stabilization procedures lead to discrete problems which are fully stable, free of volumetric locking, stress oscillations and pressure fluctuations. Numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding stabilized mixed displacement/pressure formulation.Peer ReviewedPostprint (author's final draft

A stabilized mixed finite element approximation for incompressible finite strain solid dynamics using a total Lagrangian formulation

In this work a new methodology for both the nearly and fully incompressible transient finite strain solid mechanics problem is presented. To this end, the momentum equation is complemented with a constitutive law for the pressure which emerges from the deviatoric/volumetric decomposition of the strain energy function for any hyperelastic material model. The incompressible limit is attained automatically depending on the material bulk modulus. The system is stabilized by means of the Variational Multiscale-Orthogonal Subgrid Scale method based on the decomposition of the unknowns into resolvable and subgrid scales in order to prevent pressure fluctuations. Several numerical examples are presented to assess the robustness and applicability of the proposed formulation.Inocencio Castañar gratefully acknowledges the support received from the Agència de Gestió d’Ajut i de Recerca through the predoctoral FI grant 2019-FI-B-0649. J. Baiges gratefully acknowledges the support of the Spanish Government through the Ramón y Cajal grant RYC-2015-17367. R. Codina gratefully acknowledges the support received through the ICREA Acadèmia Research Program of the Catalan Government. This work was partially funded through the TOP-FSI: RTI2018-098276-B-I00 project of the Spanish Government.Peer ReviewedPostprint (author's final draft

Topological derivative-based topology optimization of incompressible structures using mixed formulations

In this work an algorithm for topological optimization, based on the topological derivative concept, is proposed for both nearly and fully incompressible materials. In order to deal with such materials, a new decomposition of the Polarization tensor is proposed in terms of its deviatoric and volumetric components. Mixed formulations applied in the context of linear elasticity do not only allow to deal with incompressible material behavior but also to obtain a higher accuracy in the computation of stresses. The system is stabilized by means of the Variational Multiscale method based on the decomposition of the unknowns into resolvable and subgrid scales in order to prevent fluctuations. Several numerical examples are presented and discussed to assess the robustness of the proposed formulation and its applicability to Topology Optimization problems for incompressible elastic solids.I. Castañar gratefully acknowledges the support received from the Agència de Gestió d’Ajut i de Recerca through the predoctoral FI grant 2019-FI-B-00649. J. Baiges gratefully acknowledges the support of the Spanish Government through the Ramón Cajal grant RYC-2015-17367. R. Codina gratefully acknowledges the support received through the ICREA Acadèmia Research Program of the Catalan Government, Spain. This work was partially funded through the TOP-FSI, Spain: RTI2018-098276-B-I00 project of the Spanish Government. CIMNE is a recipient of a “Severo Ochoa Programme for Centers of Excellence in R&D” grant (CEX2018-000797-S) by the Spanish Ministry of Economy and Competitiveness .Peer ReviewedPostprint (author's final draft

An accurate approach to simulate friction stir welding processes using adaptive formulation refinement

A novel Adaptive Formulation Refinement (AFR) strategy for Friction Stir Welding (FSW) problems is presented. In FSW, the accurate computation of strains is crucial to correctly predict the highly non-linear material behavior in the stir zone. Based on a posteriori error estimation, AFR switches between two mixed formulations depending on the required accuracy in the different regions of the domain. The higher accuracy formulation is used in the thermo-mechanically affected zone (TMAZ), while a computationally cheaper formulation is used elsewhere. AFR adds to the well-known - (mesh size), - (polynomial degree) and -refinement (spatial distribution) approaches. The considered mixed formulations are the velocity/pressure () and the velocity/pressure/deviatoric strain rate () formulations—both suitable for isochoric material flow. By applying the AFR strategy, the use of linear elements is preserved, the incompressible flow of the material is captured correctly and any remeshing is avoided. Furthermore, the treatment of the interface between refined and unrefined subdomains is straightforward due to the compatibility of variable fields and lack of hanging nodes. The accuracy of the results obtained from the AFR method compares favorably with reference results of the non-adaptive formulation. At the same time, faster build and solve times are achieved.H. Venghaus acknowledges the support by Cimne, a Severo Ochoa Centre of Excellence (2019–2023) under the grant [CEX2018-000797-S], funded by the Research Agency of the Spanish State (AEI, [10.13039/501100011033]), the support from the PriMuS Project (Printing pattern based and MultiScale enhanced performance analysis of advanced Additive Manufacturing components, [PID2020-115575RB-I00]) through the Research Agency of the Spanish State (AEI, [10.13039/501100011033]) as well as the KYKLOS 4.0 project, which has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement [No 872570]. I. Castanar gratefully acknowledges the support received from the Agència de Gestió d’Ajut i de Recerca through the predoctoral FI grant 2019-FI-B-00649.Peer ReviewedPostprint (author's final draft