Roman Poya

Bio: Roman Poya is an academic researcher from Swansea University. The author has contributed to research in topics: Finite element method & Elasticity (physics). The author has an hindex of 6, co-authored 7 publications receiving 103 citations. Previous affiliations of Roman Poya include Technische Universität München & UGS Corp..

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

Abstract: The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.

A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers

Abstract: This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (2016) and Ortigosa and Gil (2016) Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications

A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics

Abstract: The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.

On a family of numerical models for couple stress based flexoelectricity for continua and beams

Abstract: A family of numerical models for the phenomenological linear flexoelectric theory for continua and their particularisation to the case of three-dimensional beams based on a skew-symmetric couple stress theory is presented. In contrast to the standard strain gradient flexoelectric models which assume coupling between electric polarisation and strain gradients, we postulate an electric enthalpy in terms of linear invariants of curvature and electric field. This is achieved by introducing the axial (mean) curvature vector as a strain gradient measure. The physical implication of this assumption is many-fold. Firstly, analogous to the standard strain gradient models, for isotropic (non-piezoelectric) materials it allows constructing flexoelectric energies without breaking material’s centrosymmetry. Secondly, unlike the standard strain gradient models, nonuniform distribution of volumetric part of strains (volumetric strain gradients) do not generate electric polarisation, as also confirmed by experimental evidence to be the case for some important classes of flexoelectric materials. Thirdly, a state of plane strain generates out of plane deformation through strain gradient effects. Finally, under this theory, extension and shear coupling modes cannot be characterised individually as they contribute to the generation of electric polarisation as a whole. As a first step, a detailed comparison of the developed couple stress based flexoelectric model with the standard strain gradient flexoelectric models is performed for the case of Barium Titanate where a myriad of simple analytical solutions are assumed in order to quantitatively describe the similarities and dissimilarities in effective electromechanical coupling under these two theories. From a physical point of view, the most notable insight gained is that, if the same experimental flexoelectric constants are fitted in to both theories, the presented theory in general, reports up to 200% stronger electromechanical conversion efficiency. From the formulation point of a view, the presented flexoelectric model is also competitively simpler as it eliminates the need for high order strain gradient and coupling tensors and can be characterised by a single flexoelectric coefficient. In addition, three distinct mixed flexoelectric variational principles are presented for both continuum and beam models that facilitate incorporation of strain gradient measures in to a standard finite element scheme while maintaining the C0 continuity. Consequently, a series of low and high order mixed finite element schemes for couple stress based flexoelectricity are presented and thoroughly benchmarked against available closed form solutions in regards to electromechanical coupling efficiency. Finally, nanocompression of a complex flexoelectric conical pyramid for which analytical solution cannot be established is numerically studied where curvature induced necking of the specimen and vorticity around the frustum generate moderate electric polarisation.

A computational framework for the analysis of linear piezoelectric beams using hp-FEM

Abstract: A new computational framework for 3D linear piezoelectric beams using hp-FEM.Framework suitable for statics, dynamics, actuation and energy harvesting problems.Framework suitable for any anisotropy or electric polarisation orientation.New set of beam equations with new mechanical and electrical cross-sectional area resultants.In order to aid prospective researchers, a new closed-form solution is presented. In this paper, a new computational framework is introduced for the analysis of three dimensional linear piezoelectric beams using hp-finite elements. Unlike existing publications, the framework is very general and suitable for static, modal and dynamic scenarios; it is not restricted to either actuation or energy harvesting applications and, moreover, it can cope with any anisotropy or electric polarisation orientation. Derived from first principles, namely the fundamental equations of continuum piezoelectricity, a new set of beam balance equations is presented based on a Taylor series expansion for the displacement and electric potential across the cross section of the beam. The coupled nature of the piezoelectric phenomenon at a beam level arises via a series of mechanical (and electrical counterparts) stress and strain cross sectional area resultants. To benchmark the numerical algorithm, and in order to aid prospective researchers, a new closed-form solution is presented for the case of cantilever type systems subjected to end tip mechanical/electrical loads. To the best of the authors' knowledge, the analytical solution for this prototypical example has not been previously presented. Finally, some numerical aspects of the hp-discretisation are investigated including the exponential convergence of the hp-refinements and the consideration of linear or quadratic electric potential expansions across the cross section of the beam.

Localisation in a Cosserat continuum under static and dynamic loading conditions

Abstract: Localisation studies have been carried out for an unconstrained, elasto-plastic, strain-softening Cosserat continuum. Because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions. Because of the existence of rotational degrees-of-freedom in a Cosserat continuum additional wave types arise and wave propagation becomes dispersive. This has been investigated analytically and numerically for an elastic Cosserat continuum and an excellent agreement has been found between both solutions.

Flexoelectricity in solids: Progress, challenges, and perspectives

Abstract: The flexoelectricity describes the contribution of the linear couplings between the electric polarization and strain gradient and between polarization gradient and strain to the thermodynamics of a solid and represents the amount of polarization change of a solid arising from a strain gradient. Although the magnitude of the flexoelectric effect is generally small, its contribution to the overall thermodynamics of a solid may become significant or even dominant at the nanometer scale. Recent experimental and computational efforts have led to significant advances in our understanding of the flexoelectric effect and its exploration of potential applications in devices such as sensors, actuators, energy harvesters, and nanoelectronics. Here we review the theoretical development and experimental progress in flexoelectricity including the types of materials systems that have been explored and their potential applications. We discuss the challenges in the experimental measurements and density functional theory computations of the flexoelectric coefficients including understanding the order of magnitude discrepancies between existing experimentally measured and computed values. Finally, we offer a perspective on the future directions for research on flexoelectricity.

Sensitivity and uncertainty analysis for flexoelectric nanostructures

Abstract: In this paper, sensitivity analysis has been applied to identify the key input parameters influencing the energy conversion factor (ECF) of flexoelectric materials. The governing equations of flexoelectricity are modeled by a NURBS-based IGA formulation exploiting their higher order continuity and hence avoiding a complex mixed formulation. The examined input parameters include model and material properties, and the sampling has been obtained using the latin hypercube sampling (LHS) method in the probability space. The sensitivity of the model output to each of the input parameters at different aspect ratios of the beam is quantified by three various common methods, i.e. Morris One-At-a-Time (MOAT), PCE-Sobol’, and Extended Fourier amplitude sensitivity test (EFAST). The numerical results indicate that the flexoelectric constants are the most dominant factors influencing the uncertainties in the energy conversion factor, in particular the transversal flexoelectric coefficient ( h 12 ) . Moreover, the model parameters also show considerable interaction effects of the material properties.

A computational framework for polyconvex large strain elasticity

Abstract: This paper presents a novel computational formulation for large strain polyconvex elasticity. The formulation, based on the original ideas introduced by Schroder et al. (2011), introduces the deformation gradient (the fibre map), its adjoint (the area map) and its determinant (the volume map) as independent kinematic variables of a convex strain energy function. Compatibility relationships between these variables and the deformed geometry are enforced by means of a multi-field variational principle with additional constraints. This process allows the use of different approximation spaces for each variable. The paper extends the ideas presented in Schroder et al. (2011) by introducing conjugate stresses to these kinematic variables which can be used to define a generalised convex complementary energy function and a corresponding complementary energy principle of the Hellinger–Reissner type, where the new conjugate stresses are primary variables together with the deformed geometry. Both compressible and incompressible or nearly incompressible elastic models are considered. A key element to the developments presented in the paper is the new use of a tensor cross product, presented for the first time by de Boer (1982), page 76, which facilitates the algebra associated with the adjoint of the deformation gradient. For the numerical examples, quadratic interpolation of the displacements, piecewise linear interpolation of strain and stress fields and piecewise constant interpolation of the Jacobian and its stress conjugate are considered for compressible cases. In the case of incompressible materials two formulations are presented. First, continuous quadratic interpolation for the displacement together with piecewise constant interpolation for the pressure and second, linear continuous interpolation for both displacement and pressure stabilised via a Petrov–Galerkin technique.