Level-set topology optimization for multimaterial and multifunctional mechanical metamaterials

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Metamaterials are artificially engineered composites designed to have unusual properties. This article will develop a new level-set based topology optimization method for the computational design of multimaterial metamaterials with exotic thermomechanical properties. In order to generate metamaterials consisting of arrays of microstructures under periodicity, the numerical homogenization method is used to evaluate the effective properties of the microstructure, and a multiphase level-set model is used to evolve the boundaries of the multimaterial microstructure. The proposed method will produce material geometries with distinct interfaces and smoothed boundaries, which may facilitate the fabrication of the topologically optimized designs. Several numerical cases are used to demonstrate the effectiveness of the proposed method

A short survey: topological shape optimization of structures using level set methods

This paper will give a short survey about topology optimization of structures. It is particularly focused on topological shape optimization of structures using level-set methods, including the level-set based standard methods and the level-set based alternative methods. The former often directly solve the Hamilton-Jacobi partial differential equation (H-J PDE) to obtain the boundary velocity field using Finite Differential Methods (FDM), and the later commonly employ parametric or equivalent methods to evaluate the velocity field without directly solving the H-J PDE. The unique characteristics of the level-set based topology optimization methods are discussed, and a future perspective and prospects in this research area is also included. A benchmark numerical example is used to showcase the effectiveness of the level-set based methods

Modelling-based design of anisotropic piezocomposite transducers and multi-domain analysis of smart structures

Piezocomposites are attracting widespread interest since they can offer greater flexibility and better performances in specific applications with respect to traditional piezoelectric wafers. Design of piezocomposites requires accurate homogenisation models for the prediction of the equivalent electro-mechanical properties. In macro-scale models of structures with piezocomposite transducers, these properties are adopted in order to avoid the complexity of the piezocomposite microstructure. In the case of smart structures the accurate modelling of the actuation and the response of the structure is of primary importance. If classical structural finite elements are not sufficiently accurate, higher order or solid elements should be adopted. Thanks to adaptation or mixed-dimensional methods, it is possible to adopt computationally expensive higher order or solid elements only in some sub-domains of the structure. In this work, the modelling of smart structures equipped with thin piezoelectric transducers is considered in a multi-scale framework. Micromechanical homogenisation models are developed and employed for the prediction of the equivalent properties of piezocomposites. A micromechanical model based on the concept of inclusion is proposed to investigate the influence of the shape of the inclusions, of the constituent materials and of the polarisation on the equivalent properties. It has been found that fibre-shaped inclusions should be considered in order to obtain piezocomposites with strong piezoelectric effect and to have at the same time high direction-dependence. The equivalent properties of Macro Fiber Composites are determined via the Asymptotic Homogenisation Method (AHM) with an analytical solution and with a numerical solution via FEM which takes into account the effect of the electrodes. AHM analytical solution is adopted to investigate the effect of the material properties of the matrix on the overall piezocomposite. Results indicate that low values of the Young's modulus and of the Poisson's ratio yield high directional dependence in the piezoelectric properties. A laminated design with anisotropic layers and a piezocomposite layer is investigated via UFM. A configuration with maximum directional dependence in terms of equivalent piezoelectric strain constants is proposed, whereas maximum directional dependence in terms of piezoelectric stress constants is proved to be not achievable with such a design. Hierarchical finite elements for structural analyses based on a Unified Formulation (UF) by Carrera are developed and coupled via the Arlequin method proposed by Ben Dhia. Solid, plate and beam finite elements for mechanical and for piezoelectric problems are presented. Via UF, higher order and piezoelectric elements can be formulated straightforwardly. These elements are combined in variable kinematic solutions in the Arlequin framework. Higher-order elements are adopted locally where the stress field is three-dimensional, whereas the remaining parts of the structure are modelled with computationally cheap lower-order elements. Two electro-mechanical coupling operator for the Arlequin method in the context of piezoelectric analyses are proposed. Results are validated towards monomodel solutions and three-dimensional analytical and numerical reference solutions. Accurate solutions are obtained reducing the computational costs

Vibration Energy Harvesting for Wireless Sensors

Kinetic energy harvesters are a viable means of supplying low-power autonomous electronic systems for the remote sensing of operations. In this Special Issue, through twelve diverse contributions, some of the contemporary challenges, solutions and insights around the outlined issues are captured describing a variety of energy harvesting sources, as well as the need to create numerical and experimental evidence based around them. The breadth and interdisciplinarity of the sector are clearly observed, providing the basis for the development of new sensors, methods of measurement, and importantly, for their potential applications in a wide range of technical sectors

Design of mechanical metamaterials using a level-set based topology optimization method

Metamaterials are a family of artificially engineered materials consisting of an array of periodically arranged microstructures, offering unusual material properties that may not be easily found in nature. This paper will propose a new topological shape optimization method for the design of mechanical metamaterials with negative Poisson’s ratios, by integrating the numerical homogenization method with a powerful level set method. The homogenization method is used to calculate the effective properties of the microstructure, and the level set method is utilized to implement shape and topology optimization of the microstructure until the desired material properties are obtained. The proposed method can retain the unique features of the level set methods, while avoid unfavourable numerical issues occurred in the conventional level set methods. Several typical numerical examples are used to showcase the effectiveness of the proposed design method

Engineering 3D architected metamaterials for enhanced mechanical properties and functionalities.

Compared with conventional materials, architected metamaterials have shown unprecedented mechanical properties and functionalities applications. Featured with controlled introduction of porosity and different composition, architected metamaterials have demonstrated unprecedent properties not found in natural materials. Such design strategies enable researchers to tailor materials and structures with multifunctionalies and satisfy conflicting design requirements, such as high stiffness and toughness; high strength with vibration mitigation properties, etc. Furthermore, with the booming advancement of 3D printing technologies, architected materials with precisely defined complex topologies can be fabricated effortlessly, which in turn promotes the research significantly. The research objectives of this dissertation are to achieve the enhanced mechanical properties and multifunctionalities of architected metamaterials by integrative design, computational modeling, 3D printing, and mechanical testing. Phononic crystal materials are capable of prohibiting the propagation of mechanical waves in certain frequency ranges. This certain frequency ranges are represented by phononic band gaps. Formally, band gaps are formed through two main mechanisms, Bragg scattering and local resonance. Band gaps induced by Bragg scattering are dependent on periodicity and the symmetry of the lattice. However, phononic crystals with Bragg-type band gaps are limited in their application because they do not attenuate vibration at lower frequencies without requiring large geometries. It is not practical to build huge models to achieve low frequency vibration mitigation. Alternatively, band gaps formed by local resonance are due to the excitation of resonant frequencies, and these band gaps are independent of periodicity. Therefore, lower frequency band gaps have been explored mostly through the production of phononic metamaterials that exploit locally resonant masses to absorb vibrational energy. However, despite research advances, the application of phononic metamaterials is sill largely hindered by their limited operation frequency ranges. Designing lightweight phononic metamaterials with low-frequency vibration mitigation capability is still a challenging topic. On the other hand, conventional phononic crystals usually exhibit very poor mechanical properties, such as low stiffness, strength, and energy absorption. This could largely limit their practical applications. Ideally, multifunctional materials and structures with both vibration mitigation property and high mechanical performance are demanded. In this work, we propose architected polymer foam material to overcome the challenges. Beside altering the topological architecture of metamaterials, tailoring the composition of materials is another approach to enhance the mechanical properties and realize multifunctionalities. Natural materials have adopted this strategy for long period of time. Biological structural materials such as nacre, glass sea sponges feature unusual mechanical properties due to the synergistic interplay between hard and soft material phases. These exceptional mechanical performance are highly demanded in engineering applications. As such, intensive efforts have been devoted to developing lightweight structural composites to meet the requirements. Despite the significant advances in research, the design and fabrication of low-cost structural materials with lightweight and superior mechanical performance still represent a challenge. Taking inspiration from cork material, we propose a new type of multilayered cellular composite (MCC) structure composed of hard brittle and soft flexible phases to tackle this challenge. On the other hand, piezoelectric materials with high sensitivity but low energy absorption have largely limited their applications, especially during harsh environment where external load could significantly damage the materials. Enlightened by the multiphase composite concept, we apply this design motif to develop a new interpenetrating-phased piezoelectric materials by combining PZT material as skeleton and PDMS material as matrix. By using a facial camphene-templated freeze-casting method, the co-continuous composites are fabricated with good quality. Through experiment and simulation studies, the proposed composite demonstrates multifunction with exceptional energy absorption and high sensitivity. Based on the above experimental studies, we further propose to use topology optimization framework to obtain the composites with the best performance of multifunctionalities. Specifically, we will use the solid isotropic material with penalization (SIMP) approach to optimize the piezoelectric materials with multi-objectives of 1) energy absorption and 2) electric-mechanical conversion property. The materials for the optimization design will be elastic PZT as skeleton and elatic material PDMS as matrix. To enable the gradient search of objective function efficiently, we will use adjoint method to derive the shape sensitivity analysis

Advances in combined architecture, plant, and control design

The advancement of many engineering systems relies on novel design methodologies, design formulations, design representations, and other advancements. In this dissertation, we consider three broad design domains: architecture, plant, and control. These domains cover most of the potential design decision elements in an actively-controlled engineering system. In this dissertation, strategic aspects of this combined problem are addressed. The task of representing and generating candidate architectures is addressed with methods developed based on colored graphs built by enumerating all perfect matchings of a specified catalog of components. The proposed approach captures all architectures under specific assumptions. General combined plant and control design (or co-design) problems are examined. Previous work in co-design theory imposed restrictions on the type of problems that could be posed. Here many of those restrictions are lifted. The problem formulations and optimality conditions for both the simultaneous and nested solution strategies are given along with a detailed discussion of the two methods. Direct transcription is also discussed as it enables the solution of general co-design problems by approximating the problem. Motivated primarily by the need for efficient methods to solve certain control problems that emerge using the nested co-design method, an automated problem generation procedure is developed to support easy specification of linear-quadratic dynamic optimization problems using direct transcription and quadratic programming. Pseudospectral and single-step methods (including the zero-order hold) are all implemented in this unified framework and comparisons are made. Three detailed engineering design case studies are presented. The results from the enumeration and evaluation of all passive analog circuits with up to a certain number of components are used to synthesize low-pass filters and circuits that match a certain magnitude response. Advantages and limitations of enumerative approaches are highlighted in this case study, along with comparisons to circuits synthesized via evolutionary computation; many similarities are found in the topologies. The second case study tackles a complex co-design problem with the design of strain-actuated solar arrays for spacecraft precision pointing and jitter reduction. Nested co-design is utilized along with a linear-quadratic inner loop problem to obtain solutions efficiently. A simpler, scaled problem is analyzed to gain general insights into these results. This is accomplished with a unified theory of scaling in dynamic optimization. The final case study involves the design of active vehicle suspensions. All three design domains are considered in this problem. A class of architecture, plant, and control design problems which utilize linear physical elements is discussed. This problem class can be solved using the methods in this dissertation

Modelling-based design of anisotropic piezocomposite transducers and multi-domain analysis of smart structures

Piezocomposites are attracting widespread interest since they can offer greater flexibility and better performances in specific applications with respect to traditional piezoelectric wafers. Design of piezocomposites requires accurate homogenisation models for the prediction of the equivalent electro-mechanical properties. In macro-scale models of structures with piezocomposite transducers, these properties are adopted in order to avoid the complexity of the piezocomposite microstructure. In the case of smart structures the accurate modelling of the actuation and the response of the structure is of primary importance. If classical structural finite elements are not sufficiently accurate, higher order or solid elements should be adopted. Thanks to adaptation or mixed-dimensional methods, it is possible to adopt computationally expensive higher order or solid elements only in some sub-domains of the structure. In this work, the modelling of smart structures equipped with thin piezoelectric transducers is considered in a multi-scale framework. Micromechanical homogenisation models are developed and employed for the prediction of the equivalent properties of piezocomposites. A micromechanical model based on the concept of inclusion is proposed to investigate the influence of the shape of the inclusions, of the constituent materials and of the polarisation on the equivalent properties. It has been found that fibre-shaped inclusions should be considered in order to obtain piezocomposites with strong piezoelectric effect and to have at the same time high direction-dependence. The equivalent properties of Macro Fiber Composites are determined via the Asymptotic Homogenisation Method (AHM) with an analytical solution and with a numerical solution via FEM which takes into account the effect of the electrodes. AHM analytical solution is adopted to investigate the effect of the material properties of the matrix on the overall piezocomposite. Results indicate that low values of the Young's modulus and of the Poisson's ratio yield high directional dependence in the piezoelectric properties. A laminated design with anisotropic layers and a piezocomposite layer is investigated via UFM. A configuration with maximum directional dependence in terms of equivalent piezoelectric strain constants is proposed, whereas maximum directional dependence in terms of piezoelectric stress constants is proved to be not achievable with such a design. Hierarchical finite elements for structural analyses based on a Unified Formulation (UF) by Carrera are developed and coupled via the Arlequin method proposed by Ben Dhia. Solid, plate and beam finite elements for mechanical and for piezoelectric problems are presented. Via UF, higher order and piezoelectric elements can be formulated straightforwardly. These elements are combined in variable kinematic solutions in the Arlequin framework. Higher-order elements are adopted locally where the stress field is three-dimensional, whereas the remaining parts of the structure are modelled with computationally cheap lower-order elements. Two electro-mechanical coupling operator for the Arlequin method in the context of piezoelectric analyses are proposed. Results are validated towards monomodel solutions and three-dimensional analytical and numerical reference solutions. Accurate solutions are obtained reducing the computational cost

Development of a lattice Boltzmann model to investigate the interaction mechanism of surface acoustic wave on a sessile droplet

This study focuses on the development of a three dimensional numerical model, based on the lattice Boltzmann method (LBM), for two-phase fluid flow dynamics employing a multiple-relaxation-time (MRT) pseudopotential scheme. The numerical model is applied in the investigation of acoustic interactions with microscale sessile droplets (1- 10 µl), under surface acoustic wave (SAW) excitation, through the introduction of additonal forcing terms in the LBM scheme. In the study, a range of resonant frequencies (61.7 - 250.1 MHz) are studied and quantatively compared to existing studies and experimental findings to verify the proposed model. The modelling predictions on the roles of forces (SAW, interfacial tension, inertia and viscosity) on the dynamics of mixing, pumping and jetting of a droplet are in good agreement with observations and experimental data. Further examination of the model, through parameter study, identified that the relaxation parameters considered free to tune in the MRT, play an important role in model stability, providing large reductions in spurious velocities, in both the liquid and gas phases, when the values are specified correctly. It has also been discovered that employing a dynamic contact angle hysteresis model increased the adhesion between the liquid droplet and the substrate, improving the agreement with experimental findings by up to 20%. Lastly, an investigation of various equation of state implementations revealed some fascinating differences in droplet dynamics and behaviours, owing primarily to the physical underpinning of which each is based upon. The developed model is successfully applied in the examination of various scenarios including SAW-droplet interactions on an inclined slope, droplet impact on flat (horizontal) and inclined surfaces with and without SAW interactions, and dual SAW interactions on a droplet at several configurations. The findings indicate the importance of applied SAW power, especially in inclined slope scenarios, to overcome the inertia and gravitational forces which act to counteract the droplet motion initiated by the acoustic wave direction of travel. Furthermore, a new multi-component multi-phase multi-pseudopotential (MCMP MPI) LB model is proposed. The study details initial model development and verification for classical benchmark cases, comparing to both the single-component (SCMP MPI) and publicised data. Similar to its SCMP MPI counterpart, the model displays excellent stability, even at high density ratios, and thermodynamic consistency. Comparison to the SCMP MPI model reveals lower spurious velocities are generated in the proposed MCMP model, approximately one order of magnitude lower. Close inspection of the interaction force implementation shows they are analogous whilst similar surface tension values are presented for both models. The proposed scheme signifies a new class of MPI model capable of simulating realistic fluid compositions for use in applications of scientific and engineering interest

Adjoint-based optimization for inkjet printing

In this thesis the flow inside inkjet printhead microchannels is analysed using a two- parameter low Mach number expansion of the compressible Navier–Stokes equations and a reduced order model for the free surface flow inside the inkjet nozzle. The channel flow is separated into equations for an incompressible flow with no acoustic oscillations and equations for thermoviscous acoustic oscillations with no mean flow. This thesis concerns two types of optimal control problems. The optimal control problem of the first type is finding a velocity profile of the piezo-electric actuator that eliminates residual oscillations after a droplet is ejected. The cost function is the sum of the acoustic energy in the channel and the surface energy of the spherical cap of ink at the end of the nozzle at a given time. This problem is approached by obtaining the sensitivity of the total energy inside an inkjet microchannel with respect to boundary forcing using the adjoint method. Using gradient-based optimization algorithms, optimal waveforms are found that minimize the objective value at various final times and for geometries with increasing complexity. Physical interpretation to the optimal waveforms profiles is provided, and the exploited mechanisms are revealed. The optimal control problem of the second type is finding a shape of the inkjet printhead channel that maximises dissipation of the acoustic oscillations, without increasing the pressure drop required to drive the steady flow. Similarly, the adjoint approach is used to obtain the sensitivity of the acoustic flow eigenvalues with respect to boundary deformations in Hadamard form. Knowing the shape sensitivity of the incompressible flow viscous dissipation, the constrained optimization problem is solved to find a design that has the same viscous dissipation for the steady flow but a 40% larger decay rate for the oscillating flow. The final shape is not straightforward and would have been difficult to achieve through physical insight or trial and error. It could be improved further by adapting the parameters that describe the shape, but in this case the improvement would be small. The method is general and could be applied to many different applications in microfluidics. In summary, the methods in this thesis are promising techniques in the design and optimization of inkjet printheads. The discussed numerical techniques and the gained physical understanding can be used to automatically find the optimal design parameters, or, at a minimum, accelerate the experimental trial and error processes.This project has received funding from the European Unions Horizon 2020 research and innovation programme under Grant Agreement No. H2020-MSCA-ITN-2015