Computational homogenization of fibrous piezoelectric materials

Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational modeling to understand the influence that microscale geometry and constitutive variables exert on the macroscopic behavior, a numerical approach is developed here for multiscale and multiphysics modeling of thin piezoelectric sheets made of aligned arrays of polymeric nanofibers, manufactured by electrospinning. At the microscale, the representative volume element consists in piezoelectric polymeric nanofibers, assumed to feature a piezoelastic behavior and subjected to electromechanical contact constraints. The latter are incorporated into the virtual work equations by formulating suitable electric, mechanical and coupling potentials and the constraints are enforced by using the penalty method. From the solution of the micro-scale boundary value problem, a suitable scale transition procedure leads to identifying the performance of a macroscopic thin piezoelectric shell element.Comment: 22 pages, 13 figure

A multiscale-multiphysics strategy for numerical modeling of thin piezoelectric sheets

Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational modeling to understand the influence that microscale geometry and constitutive variables exert on the macroscopic behavior, a numerical approach is developed here for multiscale and multiphysics modeling of piezoelectric materials made of aligned arrays of polymeric nanofibers. At the microscale, the representative volume element consists in piezoelectric polymeric nanofibers, assumed to feature a linear piezoelastic constitutive behavior and subjected to electromechanical contact constraints using the penalty method. To avoid the drawbacks associated with the non-smooth discretization of the master surface, a contact smoothing approach based on B\'ezier patches is extended to the multiphysics framework providing an improved continuity of the parameterization. The contact element contributions to the virtual work equations are included through suitable electric, mechanical and coupling potentials. From the solution of the micro-scale boundary value problem, a suitable scale transition procedure leads to the formulation of a macroscopic thin piezoelectric shell element.Comment: 11 pages, 6 pages, 21 reference

A segmentation-free isogeometric extended mortar contact method

This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed, which leads to an unbiased formulation and, when applied to the mortar setting, has the additional advantage that the mortar coupling term is no longer present in the contact forces. As a result, the computationally expensive segmentation at overlapping master-slave element boundaries, usually required in mortar methods (although often simplified with loss of accuracy), is not needed from the outset. For the numerical integration of general contact problems, the so-called refined boundary quadrature is employed, which is based on adaptive partitioning of contact elements along the contact boundary. The contact patch test shows that the proposed formulation passes the test without using either segmentation or refined boundary quadrature. Several numerical examples are presented to demonstrate the robustness and accuracy of the proposed formulation.Comment: In this version, we have removed the patch test comparison with the classical mortar method and removed corresponding statements. They will be studied in further detail in future work, so that the focus is now entirely on the new IGA mortar formulatio

Interfacial stress analysis for thin plates bonded to curved substrates

This paper is focused on analytical and numerical modeling of the interface between a rigid substrate with simple curvature and a thin bonded plate. The interfacial behavior is modeled by independent cohesive laws in the normal and tangential directions. The analytical model makes use of appropriate simplifying assumptions. In the numerical model the interface is modeled by zero-thickness node-to-segment contact elements. In this paper the first results and comparisons between predictions of the two models are presented

The contact patch test for linear contact pressure distributions

It is well known that the classical one-pass node-to-segment algorithms for the enforcement of contact constraints fail the contact patch test. This implies that solution errors may be introduced at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method, but the situation is even worse with the penalty method. In a recent study, the authors proposed a modified one-pass node-to-segment algorithm which is able to pass the contact patch test also in conjunction with the penalty method. In a general situation, the pressure distribution transferred across a contact surface is non-uniform. Hence, even for a contact element which passes the contact patch test under a uniform distribution of the contact pressures, the transfer of a non-uniform state of stress may give rise to disturbances related to the discretization, which affect the accuracy of the analysis. This paper, following up to the previous study, develops an enhanced node-to-segment formulation able to pass a modified version of the contact patch test whereby a linear distribution of pressures has to be transmitted across the contact surface. The proposed formulation is illustrated and some numerical examples demonstrate the good patch test performance of the enhanced contact element

Cooperativity in the enhanced piezoelectric response of polymer nanowires

We provide a detailed insight into piezoelectric energy generation from arrays of polymer nanofibers. For sake of comparison, we firstly measure individual poly(vinylidenefluoride-co-trifluoroethylene) (P(VDF-TrFe)) fibers at well-defined levels of compressive stress. Under an applied load of 2 mN, single nanostructures generate a voltage of 0.45 mV. We show that under the same load conditions, fibers in dense arrays exhibit a voltage output higher by about two orders of magnitude. Numerical modelling studies demonstrate that the enhancement of the piezoelectric response is a general phenomenon associated to the electromechanical interaction among adjacent fibers, namely a cooperative effect depending on specific geometrical parameters. This establishes new design rules for next piezoelectric nano-generators and sensors.Comment: 31 pages, 11 figures, 1 tabl

A debonding model for superficial reinforcements under inclined loading

This paper presents a numerical model of the interface between a quasi-brittle substrate and a thin elastic adherend subjected to mixed-mode loading. The interface is modeled by zero-thickness contact elements, which describe both debonding and contact within a unified framework using the node-to-segment contact strategy. Uncoupled cohesive interface constitutive laws are adopted in the normal and tangential directions. The formulation is implemented and tested using the finite element code FEAP. The model is able to predict the response of the bonded joint as a function of the main parameters, which are identified through dimensional analysis. The main objective is to compute the debonding load and the effective bond length of the adherend, i.e. the value of bond length beyond which a further increase of bond length has no effect on the debonding load, as functions of the peel angle