scholarly journals Homogenization of fully nonlinear rod lattice structures: on the size of the RVE and micro structural instabilities

2021 ◽  
Author(s):  
Ludwig Herrnböck ◽  
Paul Steinmann
Keyword(s):  
Large Deformations ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Volume Element ◽  
Lattice Structures ◽  
Micro Scale ◽  
Macro Scale ◽  
Unit Cells ◽  
Structural Instabilities

AbstractThis work investigates the possibility of applying two-scale computational homogenization to rod lattice structures emerging, for instance, from additive manufacturing. The influence of the number of unit cells within the representative volume element (RVE), thus, the RVE’s size on the homogenized mechanical response is studied for occurring microscopic structural instabilities. Therein, the macro-scale, described in terms of three-dimensional continuum mechanics, is coupled to the micro-scale described by geometrically exact rods, enabling arbitrary large deformations and rotations. A special feature of the presented framework is that the rods building the lattice structures are not restricted to deform purely elastically but may deform inelastically. The mechanical response of lattice structures is investigated by applying the developed homogenization method to an exemplary lattice. Under special loads the structure reaches an instable state and may buckle. The appearance of instabilities depends on the geometric properties of the lattice’s underlying rods and the RVE’s size.

scholarly journals On the Two-Scale Modelling of Elastohydrodynamic Lubrication in Tilted-Pad Bearings

Lubricants ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 78 ◽  
Author(s):  
Gregory de Boer ◽  
Andreas Almqvist
Keyword(s):  
Surface Topography ◽  
Load Capacity ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Multiscale Methods ◽  
Operating Conditions ◽  
Real Surface ◽  
Micro Scale ◽  
Macro Scale ◽  
Heterogeneous Multiscale

A two-scale method for modelling the Elastohydrodynamic Lubrication (EHL) of tilted-pad bearings is derived and a range of solutions are presented. The method is developed from previous publications and is based on the Heterogeneous Multiscale Methods (HMM). It facilitates, by means of homogenization, incorporating the effects of surface topography in the analysis of tilted-pad bearings. New to this article is the investigation of three-dimensional bearings, including the effects of both ideal and real surface topographies, micro-cavitation, and the metamodeling procedure used in coupling the problem scales. Solutions for smooth bearing surfaces, and under pure hydrodynamic operating conditions, obtained with the present two-scale EHL model, demonstrate equivalence to those obtained from well-established homogenization methods. Solutions obtained for elastohydrodynamic operating conditions, show a dependency of the solution to the pad thickness and load capacity of the bearing. More precisely, the response for the real surface topography was found to be stiffer in comparison to the ideal. Micro-scale results demonstrate periodicity of the flow and surface topography and this is consistent with the requirements of the HMM. The means of selecting micro-scale simulations based on intermediate macro-scale solutions, in the metamodeling approach, was developed for larger dimensionality and subsequent calibration. An analysis of the present metamodeling approach indicates improved performance in comparison to previous studies.

scholarly journals Non-Auxetic Mechanical Metamaterials

Materials ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 635 ◽  
Author(s):  
Christa de Jonge ◽  
Helena Kolken ◽  
Amir Zadpoor
Keyword(s):  
Mechanical Properties ◽  
Yield Stress ◽  
Fatigue Behavior ◽  
Analytical Data ◽  
Three Dimensional ◽  
Mechanical Metamaterials ◽  
Macro Scale ◽  
Unit Cells ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The concept of “mechanical metamaterials” has become increasingly popular, since their macro-scale characteristics can be designed to exhibit unusual combinations of mechanical properties on the micro-scale. The advances in additive manufacturing (AM, three-dimensional printing) techniques have boosted the fabrication of these mechanical metamaterials by facilitating a precise control over their micro-architecture. Although mechanical metamaterials with negative Poisson’s ratios (i.e., auxetic metamaterials) have received much attention before and have been reviewed multiple times, no comparable review exists for architected materials with positive Poisson’s ratios. Therefore, this review will focus on the topology-property relationships of non-auxetic mechanical metamaterials in general and five topological designs in particular. These include the designs based on the diamond, cube, truncated cube, rhombic dodecahedron, and the truncated cuboctahedron unit cells. We reviewed the mechanical properties and fatigue behavior of these architected materials, while considering the effects of other factors such as those of the AM process. In addition, we systematically analyzed the experimental, computational, and analytical data and solutions available in the literature for the titanium alloy Ti-6Al-4V. Compression dominated lattices, such as the (truncated) cube, showed the highest mechanical properties. All of the proposed unit cells showed a normalized fatigue strength below that of solid titanium (i.e., 40% of the yield stress), in the range of 12–36% of their yield stress. The unit cells discussed in this review could potentially be applied in bone-mimicking porous structures.

Multi-Scale Stereolithography Using Shaped Beams

2017 ◽  
Author(s):  
Huachao Mao ◽  
Yuen-Shan Leung ◽  
Yuanrui Li ◽  
Pan Hu ◽  
Wei Wu ◽  
...  
Keyword(s):  
Laser Beam ◽  
Tool Path ◽  
Three Dimensional ◽  
Laser Exposure ◽  
Micro Scale ◽  
Multi Scale ◽  
Good Surface ◽  
Single Scale ◽  
Macro Scale ◽  
Micro Patterns

Current Stereolithography (SL) can fabricate three-dimensional (3D) objects in a single scale level, e.g. printing macro-scale or micro-scale objects. However, it is difficult for the SL printers to fabricate a 3D macro-scale object with micro-scale features. In the paper a novel SL-based multi-scale fabrication method is presented to address such a problem. The developed SL process can fabricate multi-scale features by dynamically changing the shape and size of a laser beam. Different shaped beams are realized by switching apertures with different micro-patterns. The laser beam without using any micro-patterns is used to fabricate the macro-scale features, while the shaped laser beams with smaller sizes are used to fabricate micro-patterned features. Accordingly, the tool path planning method for the multi-scale fabrication process are developed so that macro-scale and micro-scale features can be built by using different layer thicknesses, laser exposure time, and scanning paths. Compared with the conventional SL process based on a fixed laser beam size, our process can fabricate multi-scale features in a 3D object. It also has fast fabrication speed and good surface quality.

Homogenization of Vibrating Periodic Lattice Structures

2005 ◽  
Author(s):  
Stefano Gonella ◽  
Massimo Ruzzene
Keyword(s):  
Smart Materials ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Periodic Pattern ◽  
Periodic Lattice ◽  
Lattice Structures ◽  
Equivalent Representation ◽  
Detailed Model ◽  
Wide Range ◽  
Unit Cells

The paper describes a homogenization technique for periodic lattice structures. The analysis is performed by considering the irreducible unit cell as a building block that defines the periodic pattern. In particular, the continuum equivalent representation for the discrete structure is sought with the objective of retaining information regarding the local properties of the lattice, while condensing its global behavior into a set of differential equations. These equations can then be solved either analytically or numerically, thus providing a model which involves a significantly lower number of variables than those required for the detailed model of the assembly. The methodology is first tested by comparing the dispersion relations obtained through homogenization with those corresponding to the detailed model of the unit cells and then extended to the comparison of exact and approximate harmonic responses. This comparison is carried out for both one-dimensional and two-dimensional assemblies. The application to three-dimensional structures is not attempted in this work and will be approached in the future without the need for substantial conceptual changes in the theoretical procedure. Hence the presented technique is expected to be applicable to a wide range of periodic structures, with applications ranging from the design of structural elements of mechanical and aerospace interest to the optimization of smart materials with attractive mechanical, thermal or electrical properties.

scholarly journals Micro- and Macro-Scale Measurement of Flow Velocity in Porous Media: A Shadow Imaging Approach for 2D and 3D

Optics ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Reza Sabbagh ◽  
Mohammad Amin Kazemi ◽  
Hirad Soltani ◽  
David S. Nobes
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flow Pattern ◽  
Flow Measurement ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Detailed Knowledge ◽  
Micro Scale ◽  
Macro Scale

Flow measurement in porous media is a challenging subject, especially when it comes to performing a three-dimensional (3D) velocimetry at the micro scale. Volumetric flow measurement techniques such as defocusing and tomographic imaging generally involve rigorous procedures, complex experimental setups, and multi-part data processing procedures. However, detailed knowledge of the flow pattern at the pore and subpore scales is important in interpreting the phenomena that occur inside the porous media and understanding the macro-scale behaviors. In this work, the flow of an oil inside a porous medium is measured at the pore and subpore scales using refractive index matching (RIM) and shadowgraph imaging techniques. At the macro scale, flow is measured using the particle image velocimetry (PIV) method in two dimensions (2D) to confirm the volumetric nature of the flow and obtain the overall flow pattern in the vicinity of the flow entrance and at the far field. At the micro scale, the three-dimensional (3D) flow within an arbitrary volume of the porous medium was quantified using 2D particle-tracking velocimetry (PTV) utilizing the law of conservation of mass. Using the shadowgraphy method and a single camera makes the flow measurement much less complex than the approaches using laser light sheets or multiple cameras with multiple viewing angles.

scholarly journals Three-dimensional laser printing of macro-scale glass objects at a micro-scale resolution

2020 ◽  
Author(s):  
Peng Wang ◽  
Wei Chu ◽  
Xiaolong Li ◽  
Zijie Lin ◽  
Jian Xu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Micro Scale ◽  
Laser Printing ◽  
Macro Scale

Fabrication defects and limitations of AlSi10Mg lattice structures manufactured by selective laser melting

2021 ◽  
pp. 146442072110127
Author(s):  
Enrico Ossola ◽  
Andrew A Shapiro ◽  
Andre Pate ◽  
Samad Firdosy ◽  
Eugenio Brusa ◽  
...  
Keyword(s):  
Process Parameters ◽  
Cross Sections ◽  
High Surface ◽  
Three Dimensional ◽  
Lattice Structures ◽  
Unit Cells ◽  
Octet Truss ◽  
Overhang Length ◽  
Fabrication Defects

Additive manufacturing has enabled the production of lattice structures with tailored mechanical properties. However, process limitations still exist, affecting the quality of the struts, practically limiting sizes and types of printable unit cells. Typically, long, thin, unsupported horizontal struts exhibit large deviations from ideal geometries, due to high surface roughness and internal porosity. AlSi10Mg specimens were designed and fabricated by laser powder bed fusion to investigate the role of strut orientation, size, and overhang length using different sets of process parameters. Visual inspection, three-dimensional scanning, and metallographic inspection of the cross-sections were performed. A quality control methodology based on dimensional and geometric tolerances has been defined in order to quantitatively characterize the quality of the struts. Optimized process parameters were selected and used to fabricate octet-truss specimens which were then characterized by compression testing.

Multi-scale modelling of the damage behavior for 3D woven composites with variant structure

2021 ◽  
pp. 152808372110238
Author(s):  
Hua Zhong ◽  
Shuzi Yang
Keyword(s):  
Mechanical Response ◽  
Damage Model ◽  
Three Dimensional ◽  
Tensile Modulus ◽  
Woven Composites ◽  
Scale Model ◽  
Multi Scale ◽  
Macro Scale ◽  
3D Woven Composites ◽  
Variant Structure

In the process of fabricating a three-dimensional (3 D) woven perform, the variant structures introduced during adding and reducing tows, lead to changes of local tow orientation and woven pattern, which affects the mechanical response of 3 D woven composite. In this study, specimens with variant structure were manufactured by adding and reducing tow techniques, and representative unit cells of normal and variant structure were established by topological method. A multi-scale damage model was proposed to analyze the damage behaviors and predict the strength of 3 D woven composites with the user subroutine UMAT of ABAQUS/Standard. The results show that the variation of tensile modulus and strength between the experimental and simulation value were less than 4%. In addition, it is proved that the damage propagation of the macro-scale model with variant structure can be successfully captured.

Three-Dimensional Elastoplastic Contact Analysis of Rough Surface Considering a Micro-Scale Effect

2021 ◽  
Vol 144 (1) ◽  
Author(s):  
Shengyu You ◽  
Jinyuan Tang ◽  
Yuqin Wen
Keyword(s):  
Constitutive Model ◽  
Rough Surface ◽  
Scale Effect ◽  
Three Dimensional ◽  
Nano Indentation ◽  
Micro Scale ◽  
Finite Element Software ◽  
Elastoplastic Contact ◽  
Macro Scale ◽  
Indentation Experiment

Abstract The micro-surface asperity scale of grinding metal parts is within several microns. When two grinding surfaces are in contact, the unevenness of the plastic deformation of the asperities at the micro-scale leads to greater plastic hardening strength of the material. The results of the nano-indentation experiment conducted in this paper confirmed this phenomenon. Based on conventional mechanism-based strain gradient (CMSG) plasticity theory, the micro-scale plastic constitutive equation of materials is given and then is verified by the nano-indentation experiment. Finite element software abaqus and the user-defined element (UEL) subroutine are used to build three-dimensional rough surface elastoplastic contact models. By calculating the grinding rough surface contact in the macro-scale constitutive model based on J2 theory and in the CMSG plasticity constitutive model, the influence law of plastic micro-scale effect on contact performance is obtained.

Micro-Macro Characterization of Granular Materials

2012 ◽  
Vol 598 ◽  
pp. 345-350
Author(s):  
Yan Qiong Zhang ◽  
Xiao Min Xu ◽  
Dao Sheng Ling
Keyword(s):  
Granular Materials ◽  
Strain Tensor ◽  
Volume Element ◽  
Fabric Tensor ◽  
Micro Scale ◽  
Macro Scale ◽  
Intrinsic Complexity ◽  
Force Contact ◽  
Contact Displacement

The intrinsic complexity of granular materials stems from the fact that the characterizing variables at the micro-scale and the macro-scale are of different nature. Macroscopically, tensorial variables (stress tensor, strain tensor, fabric tensor) are commonly used based on Representative Volume Element (RVE), while vectorial variables (contact force, contact displacement, contact normal) are adopted at particle-scale. This paper mainly discusses some basic characterizations for these two scales, as well as their correlations. Numerical simulations using Discrete Element Method (DEM) are then conducted to show the evolutions of both microscopic and macroscopic variables during monotonic loading. It is indicated that the particle reorientations in the dense sample are much more pronounced than that in the loose one during shearing.

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