A C0 interior penalty Finite Element Method for flexoelectricity

This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-021-01613-wWe propose a C0 Interior Penalty Method (C0-IPM) for the computational modelling of flexoelectricity, with application also to strain gradient elasticity, as a simplified case. Standard high-order C0 finite element approximations, with nodal basis, are considered. The proposed C0-IPM formulation involves second derivatives in the interior of the elements, plus integrals on the mesh faces (sides in 2D), that impose C1 continuity of the displacement in weak form. The formulation is stable for large enough interior penalty parameter, which can be estimated solving an eigenvalue problem. The applicability and convergence of the method is demonstrated with 2D and 3D numerical examples.This work was supported by the European Research Council (StG679451 to Irene Arias), Agencia Estatal de Investigaci´on (RTI2018-101662-B-I00), Ministerio de Econom´ıa y Competitividad (CEX2018-000797-S) and Generalitat de Catalunya (2017- SGR-1278)Peer ReviewedPostprint (author's final draft

Topology optimization of flexoelectric metamaterials with apparent piezoelectricity

The flexoelectric effect, coupling polarization and strain gradient as well as strain and electric field gradients, is universal to dielectrics, but, as compared to piezoelectricity, it is more difficult to harness as it requires field gradients and it is a small-scale effect. These drawbacks can be overcome by suitably designing metamaterials made of a non-piezoelectric base material but exhibiting apparent piezoelectricity. We develop a theoretical and computational framework to perform topology optimization of the representative volume element of such metamaterials by accurately modeling the governing equations of flexoelectricity using a Cartesian B-spline method, describing geometry with a level set, and resorting to genetic algorithms for optimization. We consider a multi-objective optimization problem where area fraction competes with four fundamental piezoelectric functionalities (stress/strain sensor/ actuator). We computationally obtain Pareto fronts, and discuss the different geometries depending on the apparent piezoelectric coefficient being optimized. In general, we find competitive estimations of apparent piezoelectricity as compared to reference materials such as quartz and PZT ceramics. This opens the possibility to design devices for sensing, actuation and energy harvesting from a much wider, cheaper and effective class of materials

Mathematical and computational modeling of flexoelectricity

We first revisit the mathematical modeling of the flexoelectric effect in the context of continuum mechanics at infinitesimal deformations. We establish and clarify the relation between the different formulations, point out theoretical and numerical issues related to the resulting boundary value problems, and present the natural extension to finite deformations. We then present a simple B-spline based computational technique to numerically solve the associated boundary value problems, which can be extended to handle unfitted meshes, hence allowing for arbitrarily-shaped geometries. Several numerical examples illustrate the flexoelectric effect in simple benchmark setups, as well as in new flexoelectric devices and metamaterials engineered for sensing or actuation.Peer ReviewedPostprint (author's final draft

Weak enforcement of interface continuity and generalized periodicity in high-order electromechanical problems

This is the peer reviewed version of the following article: Barcelo, J. [et al.]. Weak enforcement of interface continuity and generalized periodicity in high-order electromechanical problems. "International journal for numerical methods in engineering", 28 Febrer 2022, vol. 123, núm. 4, p. 901-923, which has been published in final form at DOI10.1002/nme.6882. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.We present a formulation for the weak enforcement of continuity conditions atmaterialinterfacesinhigh-orderproblemsbymeansofNitsche’smethod,whichis particularly suited for unfitted discretizations. This formulation is extendedto impose generalized periodicity conditions at the unit cell boundaries of peri-odic structures. The formulation is derived for flexoelectricity, a high-orderelectromechanical coupling between strain gradient and electric field, mathe-matically modeled as a coupled system of fourth-order PDEs. The design of flex-oelectricdevicesrequiresthesolutionofhigh-orderboundaryvalueproblemsoncomplex material architectures, including general multimaterial arrangements.ThiscanbeefficientlyachievedwithanimmersedboundaryB-splinesapproach.Furthermore, the design of flexoelectric metamaterials also involves the anal-ysis of periodic unit cells with generalized periodicity conditions. Optimalhigh-order convergence rates are obtained with an unfitted B-spline approxi-mation, confirming the reliability of the method. The numerical simulationsillustrate the usefulness of the proposed approach toward the design of func-tional electromechanical multimaterial devices and metamaterials harnessingthe flexoelectric effect.Departament d'Universitats, Recerca i Societat de la Informació, 2017-SGR-1278; ICREA Academia; H2020 European Research Council, StG-679451; Secretaría de Estado de Investigación, Desarrollo e Innovación, CEX2018-000797-S; RTI2018-101662-B-I00.Peer ReviewedPostprint (author's final draft

An immersed boundary hierarchical B-spline method for flexoelectricity

© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order nature of the coupled PDE system is addressed by a sufficiently smooth hierarchical B-spline approximation on a background Cartesian mesh. The domain of interest is embedded into the background mesh and discretized in an unfitted fashion. The immersed boundary approach allows us to use B-splines on arbitrary domain shapes, regardless of their geometrical complexity, and could be directly extended, for instance, to shape and topology optimization. The domain boundary is represented by NURBS, and exactly integrated by means of the NEFEM mapping. Local adaptivity is achieved by hierarchical refinement of B-spline basis, which are efficiently evaluated and integrated thanks to their piecewise polynomial definition. Nitsche's formulation is derived to weakly enforce essential boundary conditions, accounting also for the non-local conditions on the non-smooth portions of the domain boundary (i.e. edges in 3D or corners in 2D) arising from Mindlin's strain gradient elasticity theory. Boundary conditions modeling sensing electrodes are formulated and enforced following the same approach. Optimal error convergence rates are reported using high-order B-spline approximations. The method is verified against available analytical solutions and well-known benchmarks from the literature.Peer ReviewedPostprint (author's final draft

Targeting PKC iota-PAK1 signaling pathways in EGFR and KRAS mutant adenocarcinoma and lung squamous cell carcinoma

Introduction: p21-activated kinase 1 (PAK1) stimulates growth and metastasis in non-small cell lung cancer (NSCLC). Protein kinase C iota (PKC iota) is an enzyme highly expressed in NSCLC, regulating PAK1 signaling. In the present study we explored whether the PKC iota-PAK1 signaling pathway approach can be an efficient target in different types of NSCLC cell and mouse models. Methods: The effect of IPA-3 (PAK1 inhibitor) plus auranofin (PKC iota inhibitor) combination was evaluated by cell viability assay, colony formation and western blotting assay, using three types of NSCLC cell lines: EGFR or KRAS mutant adenocarcinoma and squamous cell carcinoma with PAK1 amplification. In addition, for clinical availability, screening for new PAK1 inhibitors was carried out and the compound OTSSP167 was evaluated in combination with auranofin in cell and mice models. Results: The combination of IPA-3 or OTSSP167 plus auranofin showed high synergism for inhibiting cell viability and colony formation in three cell lines. Mechanistic characterization revealed that this drug combination abrogated expression and activation of membrane receptors and downstream signaling proteins crucial in lung cancer: EGFR, MET, PAK1, PKC iota, ERK1/2, AKT, YAP1 and mTOR. A nude mouse xenograft assay demonstrated that this drug combination strongly suppressed tumor volume compared with single drug treatment. Conclusions: Combination of IPA-3 or OTSSP167 and auranofin was highly synergistic in EGFR or KRAS mutant adenocarcinoma and squamous cell carcinoma cell lines and decreased tumor volume in mice models. It is of interest to further test the targeting of PKC iota-PAK1 signaling pathways in EGFR mutant, KRAS mutant and squamous NSCLC patients

Src-Homology 2 Domain-Containing Phosphatase 2 in Resected EGFR Mutation-Positive Lung Adenocarcinoma

Funding: supported by a La Caixa Foundation grant and the Spanish Association Against Cancer (PROYE18012ROSE)EGFR mutation-positive lung adenocarcinoma (LUAD) displays impaired phosphorylation of ERK and Src-homology 2 domain-containing phosphatase 2 (SHP2) in comparison with EGFR wild-type LUADs. We hypothesize that SHP2 expression could be predictive in patients positive with resected EGFR mutation versus patients with EGFR wild-type LUAD. We examined resected LUAD cases from Japan and Spain. mRNA expression levels of AXL, MET, CDCP1, STAT3, YAP1, and SHP2 were analyzed by quantitative reverse transcriptase polymerase chain reaction. The activity of SHP2 inhibitors plus erlotinib were tested in EGFR -mutant cell lines and analyzed by cell viability assay, Western blot, and immunofluorescence. A total of 50 of 100 EGFR mutation-positive LUADs relapsed, among them, patients with higher SHP2 mRNA expression revealed shorter progression-free survival, in comparison with those having low SHP2 mRNA (hazard ratio: 1.83; 95% confidence interval: 1.05-3.23; p = 0.0329). However, SHP2 was not associated with prognosis in the remaining 167 patients with wild-type EGFR. In EGFR -mutant cell lines, the combination of SHP099 or RMC-4550 (SHP2 inhibitors) with erlotinib revealed synergism via abrogation of phosphorylated AKT (S473) and ERK1/2 (T202/Y204). Although erlotinib translocates phosphorylated SHP2 (Y542) into the nucleus, either RMC-4550 alone, or in combination with erlotinib, relocates SHP2 into the cytoplasm membrane, limiting AKT and ERK1/2 activation. Elevated SHP2 mRNA levels are associated with recurrence in resected EGFR mutation-positive LUADs, but not in EGFR wild-type. EGFR tyrosine kinase inhibitors can enhance SHP2 activation, hindering adjuvant therapy. SHP2 inhibitors could improve the benefit of adjuvant therapy in EGFR mutation-positive LUADs