Design of three dimensional isotropic microstructures for maximized stiffness and conductivity

The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The optimization objective is to maximize a linear combination of the effective bulk modulus and conductivity of the composite. Composites with the Schwartz primitive and diamond minimal surfaces as the phase interface have been shown to have maximal bulk modulus and conductivity. Since these composites are not elastically isotropic their stiffness under uniaxial loading varies with the direction of the load. An isotropic composite is presented with similar conductivity which is at least 23% stiffer under uniaxial loading than the Schwartz structures when loaded uniaxially along their weakest direction. Other new near-optimal isotropic composites are presented, proving the capablities of the level-set method for microstructure design.     

Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization

We compute Pareto fronts that estimate the upper bounds of the bulk modulus and fluid permeability cross-property space for periodic porous materials over a range of porosities. The fronts are generated numerically using topology optimization, which is a systematic, free-form design algorithm for optimizing material layouts. The presented microstructures demonstrate the trade-off between the bulk modulus and fluid permeability achievable with a multifunctional porous material and will be useful for designers of materials for which both stiffness and permeability are important. Our results suggest that the range of achievable stiffness and permeability properties is significantly restricted when considering elastic isotropy, as compared to cubic elastic symmetry. The estimated bounds are of practical importance given the lack of microstructure-independent theoretical cross-property bounds.     

The MLPG applied to porous materials with variable stiffness and permeability

Two-dimensional (2-d) and axisymmetric consolidation problems are treated with a meshless local Petrov–Galerkin approach. The porous continuum is modeled with Biot’s theory, where the solid displacements and the pore pressure are chosen as unknowns (u-p-formulation). These unknowns are approximated with independent spatial discretizations using the moving least-squares scheme. The method is validated by a comparison with an 1-d analytical solution. Studies with graded material data show that a variable permeability has a strong influence on the consolidation process. The example of a disturbed zone around a borehole shows as well the importance of graded material data.     

Optimizing a fin ray for stiffness

We optimize the elastic constants of the supporting structure in flexible fish fins—the fin ray—to obtain the least deflection under loading. We first solve the problem numerically for rays with shear layers of uniform thickness. The optimal distributions of bending and shear moduli are nonzero on disjoint regions. The numerical solution suggests the form of the analytical solution, which we obtain using calculus of variations on two intervals with continuity conditions at the interface. The deflection of the optimal ray is less than half that of the uniform ray. When the shear layer thickness is allowed to vary, we find a tapered thickness distribution which gives zero deflection for a given positive loading.     

Optimum design of phononic crystal perforated plate structures for widest bandgap of fundamental guided wave modes and maximized in-plane stiffness

This paper presents a topology optimization of single material phononic crystal plate (PhP) to be produced by perforation of a uniform background plate. The primary objective of this optimization study is to explore widest exclusive bandgaps of fundamental (first order) symmetric or asymmetric guided wave modes as well as widest complete bandgap of mixed wave modes (symmetric and asymmetric). However, in the case of single material porous phononic crystals the bandgap width essentially depends on the resultant structural integration introduced by achieved unitcell topology. Thinner connections of scattering segments (i.e. lower effective stiffness) generally lead to (i) wider bandgap due to enhanced interfacial reflections, and (ii) lower bandgap frequency range due to lower wave speed. In other words higher relative bandgap width (RBW) is produced by topology with lower effective stiffness. Hence in order to study the bandgap efficiency of PhP unitcell with respect to its structural worthiness, the in-plane stiffness is incorporated in optimization algorithm as an opposing objective to be maximized. Thick and relatively thin Polysilicon PhP unitcells with square symmetry are studied. Non-dominated sorting genetic algorithm NSGA-II is employed for this multi-objective optimization problem and modal band analysis of individual topologies is performed through finite element method. Specialized topology initiation, evaluation and filtering are applied to achieve refined feasible topologies without penalizing the randomness of genetic algorithm (GA) and diversity of search space. Selected Pareto topologies are presented and gradient of RBW and elastic properties in between the two Pareto front extremes are investigated. Chosen intermediate Pareto topology, even not extreme topology with widest bandgap, show superior bandgap efficiency compared with the results reported in other works on widest bandgap topology of asymmetric guided waves, available in the literature. Finally, steady state and transient frequency response of finite thin PhP structures of selected Pareto topologies are studied and validity of obtained bandgaps is confirmed.     

Nonlinear dynamics and stability of microstructures in a lattice model for ferroelastic materials

With the view of understanding how precise macroscopic properties of a material emerge from the underlying physics of homogeneous microstructures, a lattice model which can describe complex non-linear patterns made of elastic domains and interfaces is proposed. On the basis of a two-dimensional lattice model involving non-linear and competing interactions the dynamics of microstructure formation is examined. The emphasis is placed especially on an instability mechanism of a strain band producing localized domains. The influence of applied forces and dissipative effects on the dynamics of two perpendicular strain bands is studied. The results are interpreted as a microtwinning in crystalline alloys. The physical conjectures are checked by means of numerical simulations performed directly on the microscopic system.

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Sommario Si propone un modello reticolare che può descrivere complessi arrangiamenti fatti di domini elastici ed interfacce. Sulla base di un modello bidimensionale in cui sono presenti interazioni contrastanti e nonlineari si esamina la dinamica della formazione di microstrutture. L'accento è posto sui meccani'smi di instabilità che determinano bande di deformazione localizzata. Si studia l'influenza delle forze applicate e degli effetti dissipativi sulla dinamica di due bande perpendicolari e si interpretano i risultati come un microtwinning in leghe cristalline. Si verificano le congetture fisiche per mezzo di simulazioni numeriche del modello microscopico.

     

轻质高强点阵材料及其力学性能研究进展

点阵材料是一种新型轻质高强材料, 同时具备形状控制、致动、能量吸收和传热等多种功能. 文章综述了点阵材料的拉伸主导型设计原则、点阵构型和制备工艺. 拉伸主导型点阵材料的比强度和比刚度明显强于一般胞元材料, 在低密度时质量效率更加突出. 根据材料的基本构型特征主要介绍了三维八角点阵以及夹层点阵材料, 比较分析了熔模铸造法和冲压折叠成型工艺的特点. 总结了研究点阵材料力学性能的理论方法和试验研究成果, 研究表明缺陷对点阵材料力学性能的影响明显小于一般胞元材料. 对点阵材料在形状控制与致动、传热和数值计算方面的应用研究成果进行了介绍. 文中归纳了作者近期在炭纤维点阵复合材料方面的工作, 给出了制备炭纤维隐身点阵格栅的探索性工作. 主要包括炭纤维点阵复合材料的三维编织工艺和二维点阵格栅的嵌锁工艺以及隐身点阵格栅反射率试验测试结果.      

Prediction of elastic properties of heterogeneous materials with complex microstructures

The phase-field microelasticity (PFM) is adapted into a homogenization process to predict all the effective elastic constants of three-dimensional heterogeneous materials with complex microstructures. Comparison between the PFM approach and the Hashin-Shtrikman variational approach is also given. Using 3D images of two-phase heterogeneous media with regular and irregular microstructures, results indicate that the PFM approach can accurately take into account the effects of both elastic anisotropy and inhomogeneity of materials with arbitrary microstructure geometry, such as complex porous media with suspended inclusions.     

On the permeability of fibre-reinforced porous materials

Biological tissues can be considered as composite materials comprised of a porous matrix filled with interstitial fluid and reinforced by impermeable collagen fibres. Motivated by studies on fluid flow in articular cartilage, we would like to quantify the undeformed configuration permeability of fibre-reinforced composite materials. If there is a sufficient scale separation between the internal structure of the porous matrix and the arrangement of the fibres, the matrix can be taken as a porous continuum at the fibre scale. In this case, the fibres can be treated as inclusions in a porous continuum, and the overall permeability of the composite can be evaluated using homogenisation procedures. For an isotropic homogeneous matrix, the symmetry of the system is governed by the orientation of the fibres. Here, we propose to retrieve the overall permeability through geometrical considerations and directional averaging methods. The special case of transverse isotropy is discussed in detail, with particular attention to the sub-cases of aligned fibres and fibres lying on a plane.     

Effective permeability of cracked unsaturated porous materials

This study focuses on a theoretical estimation of the effective permeability of unsaturated cracked porous media. The closed-form flow solution around and in a superconductive crack, embedded in an infinite porous matrix under a far-field condition, is recalled first. Then the solution of flow around a completely unsaturated (empty) crack that is considered as an obstruction against the flow is determined. The flow solution for partially saturated crack in special configurations is obtained by superposition of the two basic solutions for superconductive and empty cracks. The contribution of an unsaturated crack, with a given saturation degree, to the effective permeability is estimated by using dilute upscaling scheme. Numerical results obtained by Finite Elements Method, are in good agreement with the theoretical results for weak crack densities but show the additional effect of cracks interaction for higher densities.     

Unconventional phase field simulations of transforming materials with evolving microstructures

Transforming materials with evolving microstructures is one of the most important classes of smart materials that have many potential technological applications,and an unconventional phase field approach based on the characteristic functions of transforming variants has been developed to simulate the formation and evolution of their microstructures.This approach is advantageous in its explicit material symmetry and energy well structure,minimal number of material coefficients,and easiness in coupling multiple physical processes and order parameters,and has been applied successfully to study the microstructures and macroscopic properties of shape memory alloys,ferroelectrics,ferromagnetic shape memory alloys,and multiferroic magnetoelectric crystals and films with increased complexity.In this topical review,the formulation of this unconventional phase field approach will be introduced in details,and its applications to various transforming materials will be discussed.Some examples of specific microstructures will also be presented.     

Multiphysics of multifunctional nanofluids based on different oxides nanoparticles and glycerol fluid

Nanofluid (NF) materials consisting of glycerol (Gly) and different inorganic nano oxides (TiO₂, ZnO, Al₂O₃, and SiO₂ for the oxides concentration of 0.01 wt% to the weight of Gly base fluid) were prepared by a two-step method through ultrasonic cavitation process. These nanofluids were investigated by employing an X-ray diffractometer (XRD), ultraviolet–visible (UV–Vis) spectrophotometer, 20 Hz to 1 MHz frequency range dielectric relaxation spectroscopy (DRS), ultrasonic interferometer, and rotational viscometer. The multiphysics of these nanofluids includes structural and optical properties, dielectric permittivity, electrical conductivity, conductivity relaxation, ultrasound velocity, adiabatic compressibility, acoustic impedance, viscosity, density, thermal conductivity, and viscoacoustic relaxation were characterized. The XRD patterns identified monodispersed and stable suspensions of these different characteristic nanoparticles in the hydrogen-bonded 3D supramolecular structure of ultra-high viscous glycerol fluid which were supported by their UV–Vis absorbance analyses. The energy band gap values of the TiO₂ and ZnO containing nanofluids were found primarily ruled by the characteristic optical properties of these oxides nanomaterials. The complex dielectric and various electrical functions studied at 25 °C revealed that the suspension of different oxide nanoparticles in the glycerol fluid increased the static permittivity whereas reduced the direct current electrical conductivity which showed strong conductivity relaxation process dependence. The rheological measurements of the formulated nanofluids were performed over a shear rate range of 0.4–40 s⁻¹ at temperatures of 25–55 °C. The linear relationship between shear rate and shear stress and also the shear rate-independent viscosity revealed the Newtonian behaviour of these nanofluids. The shear viscosity non-linearly decreased with the increase of temperature and exhibited the Arrhenius behaviour for all different oxides containing Gly-based nanofluids. The acoustic parameters of the nanofluids were altered unevenly with types of nano oxides and inferred some structure-property correlations. The promising technologically useable properties of these nanofluids were expected to impact their potential applications in optoelectronics, UV-blocking, sensing, nanodielectrics, energy storing and electric insulation, heat transfer systems, and also in materials processing for the development of innovative soft condensed devices.     

ANCF curvature continuity: application to soft and fluid materials

The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors, particularly in the case of soft and fluid material applications. In this study, the absolute nodal coordinate formulation (ANCF) finite elements are used to define general curvature-continuity conditions that allow for eliminating or minimizing the discontinuity of the position gradients at the element interface. For the ANCF solid element, with four-node surfaces, it is shown that continuity of the gradients tangent to an arbitrary point on a surface is ensured as the result of the continuity of the gradients at the nodal points. The general ANCF continuity conditions are applicable to both reference-configuration straight and curved geometries. These conditions are formulated without the need for using the computer-aided-design knot vector and knot multiplicity, which do not account properly for the concept of system degrees of freedom. The ANCF curvature-continuity conditions are written in terms of constant geometric coefficients obtained using the matrix of position-vector gradients that defines the reference-configuration geometry. The formulation of these conditions is demonstrated using the ANCF fully parameterized three-dimensional solid and tetrahedral elements, which employ a complete set of position gradients as nodal coordinates. Numerical results are presented in order to examine the effect of applying the curvature-continuity conditions on achieving a higher degree of smoothness at the element interfaces in the case of soft and fluid materials.

     

Concepts for structurally robust materials that combine low thermal expansion with high stiffness

A family of robust stretch-dominated bimaterial lattices is introduced which combines low (or zero) thermal expansion with high stiffness, structural robustness over wide temperature ranges and manufacturing facility. This combination of properties is unavailable through any other material solution. The concept uses two constituents configured as adjoining sub-lattices. It accommodates the thermal expansion through rotation of the members of one sub-lattice. Moreover, the lattice exhibits large stiffness to weight because it is fully triangulated and does not rely on rotational resistance at the joints for structural rigidity. A wide range of constituents can be used to build the new lattices enabling many desirable properties to be incorporated, especially high strength and toughness. Examples of both planar and volumetric lattices are presented, and their thermo-mechanical properties derived. The results are verified by conducting experiments and finite element simulations on a lattice fabricated using aluminium and titanium alloy constituents.     

A coupled theory of fluid permeation and large deformations for elastomeric materials

An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model for the free energy based on a Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical-mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. As representative examples of application of the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained, stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii) consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across elastomeric membranes.     

Anisotropic stress state and small strain stiffness in granular materials: RC experiments and DEM simulations

Meccanica - The paper combines experimental and numerical analyses to study the relation between small strain stiffness and micro-structure of an idealized granular material under isotropic and...