Protocols for the Optimal Design of Multi‐Functional Cellular Structures: From Hypersonics to Micro‐Architected Materials

Cellular materials with periodic architectures have been extensively investigated over the past decade for their potential to provide multifunctional solutions for a variety of applications, including lightweight thermo-structural panels, blast resistant structures, and high-authority morphing components. Stiffer and stronger than stochastic foams, periodic cellular materials lend themselves well to geometry optimization, enabling a high degree of tailorability and superior performance benefits. This article reviews a commonly established optimal design protocol, extensively adopted at the macro-scale for both single and multifunctional structures. Two prototypical examples are discussed: the design of strong and lightweight sandwich beams subject to mechanical loads and the combined material/geometry optimization of actively cooled combustors for hypersonic vehicles. With this body of literature in mind, we present a motivation for the development of micro-architected materials, namely periodic multiscale cellular materials with overall macroscopic dimensions yet with features (such as the unit cell or subunit cell constituents) at the micro- or nano-scale. We review a suite of viable manufacturing approaches and discuss the need for advanced experimental tools, numerical models, and optimization strategies. In analyzing challenges and opportunities, we conclude that the technology is approaching maturity for the development of micro-architected materials with unprecedented combinations of properties (e.g., specific stiffness and strength), with tremendous potential impact on a number of fields.

[1]  D. Gall,et al.  High‐Temperature Tribological Behavior of CrN‐Ag Self‐lubricating Coatings , 2006 .

[2]  Julia R. Greer,et al.  Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients , 2005 .

[3]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[4]  F. Melchels,et al.  A review on stereolithography and its applications in biomedical engineering. , 2010, Biomaterials.

[5]  Norman A. Fleck,et al.  Fabrication and structural performance of periodic cellular metal sandwich structures , 2003 .

[6]  D. Dimiduk,et al.  Sample Dimensions Influence Strength and Crystal Plasticity , 2004, Science.

[7]  Lorenzo Valdevit,et al.  Structural performance of near-optimal sandwich panels with corrugated cores , 2006 .

[8]  N. Fleck,et al.  Strain gradient plasticity , 1997 .

[9]  M. Ashby,et al.  Micro-architectured materials: past, present and future , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  Julia R Greer,et al.  Transition from a strong-yet-brittle to a stronger-and-ductile state by size reduction of metallic glasses. , 2010, Nature materials.

[11]  J. D. De Hosson,et al.  Strength of submicrometer diameter pillars of metallic glasses investigated with in situ transmission electron microscopy , 2009 .

[12]  C. Thompson.  The yield stress of polycrystalline thin films , 1993 .

[13]  J. Banhart.  Manufacture, characterisation and application of cellular metals and metal foams , 2001 .

[14]  Salvatore Torquato,et al.  Optimal and Manufacturable Two-dimensional, Kagomé-like Cellular Solids , 2002 .

[15]  Scott William Godfrey.  Optimal design of orthotropic fiber-composite corrugated-core sandwich panels under axial compression , 2010 .

[16]  M. Kunz,et al.  Fabrication, structure and mechanical properties of indium nanopillars , 2010 .

[17]  A. Mouritz,et al.  A mechanistic interpretation of the comparative in-plane mechanical properties of 3D woven, stitched and pinned composites , 2010 .

[18]  Anthony G. Evans,et al.  A microbend test method for measuring the plasticity length scale , 1998 .

[19]  Vikram Deshpande,et al.  The impulsive response of sandwich beams: analytical and numerical investigation of regimes of behaviour , 2006 .

[20]  L. Valdevit,et al.  Optimal active cooling performance of metallic sandwich panels with prismatic cores , 2006 .

[21]  A. Ngan,et al.  Breakdown of Schmid’s law in micropillars , 2008 .

[22]  G. Pharr,et al.  Small-scale mechanical behavior of intermetallics and their composites , 2008 .

[23]  J. Greer,et al.  The in-situ mechanical testing of nanoscale single-crystalline nanopillars , 2009 .

[24]  Haydn N. G. Wadley,et al.  On the performance of truss panels with Kagomé cores , 2003 .

[25]  L. Valdevit,et al.  A Materials Selection Protocol for Lightweight Actively Cooled Panels , 2008 .

[26]  P. S. Bulson,et al.  Background to buckling , 1980 .

[27]  Tian Jian Lu,et al.  Institute of Physics Publishing Journal of Micromechanics and Microengineering Mems Actuators and Sensors: Observations on Their Performance and Selection for Purpose , 2022 .

[28]  N. Fleck,et al.  Collapse of truss core sandwich beams in 3-point bending , 2001 .

[29]  D. Dimiduk,et al.  Effects of Focused Ion Beam Induced Damage on the Plasticity of Micropillars , 2009 .

[30]  Joshua R. Smith,et al.  First principles based predictions of the toughness of a metal/oxide interface , 2010, International Journal of Materials Research.

[31]  C. Schuh,et al.  Nanoscale shape-memory alloys for ultrahigh mechanical damping. , 2009, Nature nanotechnology.

[32]  Zhenyu Xue,et al.  Constitutive model for quasi‐static deformation of metallic sandwich cores , 2004 .

[33]  W. Nix.  Elastic and plastic properties of thin films on substrates : nanoindentation techniques , 1997 .

[34]  E. Arzt,et al.  Loss of pseudoelasticity in nickel-titanium sub-micron compression pillars , 2007 .

[35]  Blythe G. Clark,et al.  On the plasticity of small-scale nickel–titanium shape memory alloys , 2010 .

[36]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[37]  Natasha Vermaak.  Thermostructural design tools for hypersonic vehicles , 2010 .

[38]  B. Derby,et al.  A universal scaling law for the strength of metal micropillars and nanowires , 2009 .

[39]  Meijie Tang,et al.  Athermal mechanisms of size-dependent crystal flow gleaned from three-dimensional discrete dislocation simulations , 2008 .

[40]  A. Needleman,et al.  Plasticity size effects in tension and compression of single crystals , 2005 .

[41]  Michael D. Uchic,et al.  Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples , 2007 .

[42]  Haydn N. G. Wadley,et al.  Cellular metal lattices with hollow trusses , 2005 .

[43]  J. R. Patel,et al.  A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction , 2008 .

[44]  Norman A. Fleck,et al.  A reformulation of strain gradient plasticity , 2001 .

[45]  J. Greer,et al.  Size-dependent mechanical properties of molybdenum nanopillars , 2008 .

[46]  Tian Jian Lu,et al.  Optimal Design of a Novel High Authority SMA Actuator , 2005 .

[47]  Julia R. Greer,et al.  Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale , 2009 .

[48]  Jun Sun,et al.  Strong crystal size effect on deformation twinning , 2010, Nature.

[49]  Peter Gumbsch,et al.  Dislocation sources and the flow stress of polycrystalline thin metal films , 2003 .

[50]  T. Saif,et al.  Mechanical Testing at the Micro/Nanoscale , 2008 .

[51]  C. Motz,et al.  Micro-compression testing: A critical discussion of experimental constraints , 2009 .

[52]  M. Ashby.  The deformation of plastically non-homogeneous materials , 1970 .

[53]  D. Lloyd.  Particle reinforced aluminium and magnesium matrix composites , 1994 .

[54]  John W. Hutchinson,et al.  The mechanics of size-dependent indentation , 1998 .

[55]  G. Pharr,et al.  Effects of focused ion beam milling on the nanomechanical behavior of a molybdenum-alloy single crystal , 2007 .

[56]  H. Wadley,et al.  Quasistatic deformation and failure modes of composite square honeycombs , 2008 .

[57]  Reinhard Pippan,et al.  A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples , 2008 .

[58]  C. Schuh,et al.  Superelasticity and Shape Memory in Micro‐ and Nanometer‐scale Pillars , 2008 .

[59]  Hilary Bart-Smith,et al.  Influence of imperfections on the performance of metal foam core sandwich panels , 2002 .

[60]  Zhenyu Xue,et al.  Crush dynamics of square honeycomb sandwich cores , 2006 .

[61]  J. Greer,et al.  Tensile deformation of electroplated copper nanopillars , 2011 .

[62]  A. Minor,et al.  The deformation of Gum Metal through in situ compression of nanopillars , 2010 .

[63]  Anders Klarbring,et al.  An Introduction to Structural Optimization , 2008 .

[64]  Neville Reid Moody,et al.  COMMENT: Trapping of hydrogen to lattice defects in nickel , 1995 .

[65]  G. Dehm,et al.  On the importance of sample compliance in uniaxial microtesting , 2009 .

[66]  Tian Jian Lu,et al.  Optimal design of a flexural actuator , 2001 .

[67]  M. Jenko,et al.  FIB damage of Cu and possible consequences for miniaturized mechanical tests , 2007 .

[68]  Haydn N. G. Wadley,et al.  Titanium alloy lattice truss structures , 2009 .

[69]  J. Greer,et al.  Nanoscale gold pillars strengthened through dislocation starvation , 2006 .

[70]  M. Ashby,et al.  Effective properties of the octet-truss lattice material , 2001 .

[71]  E. Lilleodden.  Microcompression study of Mg (0 0 0 1) single crystal , 2010 .

[72]  Paolo Colombo,et al.  Cellular Ceramics: Structure, Manufacturing, Properties and Applications , 2005 .

[73]  T. Akin,et al.  A resonant tuning fork force sensor with unprecedented combination of resolution and range , 2011, 2011 IEEE 24th International Conference on Micro Electro Mechanical Systems.

[74]  J. Greer,et al.  Microstructure versus size: mechanical properties of electroplated single crystalline Cu nanopillars. , 2010, Physical review letters.

[75]  A. G. Evans,et al.  Structural performance of metallic sandwich panels with square honeycomb cores , 2005 .

[76]  Blythe G. Clark,et al.  Size effect on strength and strain hardening of small-scale [111] nickel compression pillars , 2008 .

[77]  H. Espinosa,et al.  Dislocation-source shutdown and the plastic behavior of single-crystal micropillars. , 2008, Physical review letters.

[78]  G. Pharr,et al.  Effects of focused ion beam milling on the compressive behavior of directionally solidified micropillars and the nanoindentation response of an electropolished surface , 2009 .

[79]  J. Hutchinson,et al.  Sandwich Plates Actuated by a Kagome Planar Truss , 2004 .

[80]  O. Kraft,et al.  Plasticity in Confined Dimensions , 2010 .

[81]  Natasha Vermaak,et al.  Influence of Configuration on Materials Selection for Actively Cooled Combustors , 2010 .

[82]  M. Baskes,et al.  Modified embedded-atom potentials for cubic materials and impurities. , 1992, Physical review. B, Condensed matter.

[83]  Hilary Bart-Smith,et al.  Experimental analysis of deformation mechanisms in a closed-cell aluminum alloy foam , 2000 .

[84]  Vikram Deshpande,et al.  Concepts for enhanced energy absorption using hollow micro-lattices , 2010 .

[85]  Huajian Gao,et al.  Indentation size effects in crystalline materials: A law for strain gradient plasticity , 1998 .

[86]  Antonio Rinaldi,et al.  Sample-size effects in the yield behavior of nanocrystalline nickel , 2008 .

[87]  Michael D. Uchic,et al.  Size-affected single-slip behavior of pure nickel microcrystals , 2005 .

[88]  N. Moody,et al.  Quantitative adhesion measures of multilayer films: Part I. Indentation mechanics , 1999 .

[89]  T. Bui-Thanh,et al.  An active concept for limiting injuries caused by air blasts , 2010 .

[90]  Andrew M. Minor,et al.  Nanomechanical Testing of Gum Metal , 2010 .

[91]  J. Greer,et al.  Size-induced weakening and grain boundary-assisted deformation in 60 nm grained Ni nanopillars , 2011 .

[92]  Julia R. Greer,et al.  Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale , 2009 .

[93]  John W. Hutchinson,et al.  Performance of sandwich plates with truss cores , 2004 .

[94]  Hilary Bart-Smith,et al.  Compressive deformation and yielding mechanisms in cellular Al alloys determined using X-ray tomography and surface strain mapping , 1998 .

[95]  E. Arzt,et al.  Correlation between critical temperature and strength of small-scale bcc pillars. , 2009, Physical review letters.

[96]  K. T. Ramesh,et al.  Microcompression of single-crystal magnesium , 2010 .

[97]  William D. Nix,et al.  The Role of Indentation Depth on the Measured Hardness of Materials , 1993 .

[98]  C. Roper,et al.  Multiobjective optimization for design of multifunctional sandwich panel heat pipes with micro-architected truss cores , 2011 .

[99]  G. Dehm.  Miniaturized single-crystalline fcc metals deformed in tension: New insights in size-dependent plasticity , 2009 .

[100]  M. Ashby,et al.  The topological design of multifunctional cellular metals , 2001 .

[101]  Norman A. Fleck,et al.  Performance of metallic honeycomb-core sandwich beams under shock loading , 2006 .

[102]  H. V. Swygenhoven,et al.  Crystal rotation in Cu single crystal micropillars: In situ Laue and electron backscatter diffraction , 2008 .

[103]  Steven Nutt,et al.  Micro‐scale Truss Structures formed from Self‐Propagating Photopolymer Waveguides , 2007 .

[104]  Satoshi Kawata,et al.  Two-photon photopolymerization and 3D lithographic microfabrication , 2005 .

[105]  S. Nutt,et al.  Vitreous carbon micro-lattice structures , 2011 .

[106]  Steven Nutt,et al.  Compression behavior of micro-scale truss structures formed from self-propagating polymer waveguides , 2007 .

[107]  E. Y. Chen,et al.  Mechanical Properties of Cast Ti‐6Al‐2Sn‐4Zr‐2Mo Lattice Block Structures , 2008 .

[108]  N. Petch,et al.  The Cleavage Strength of Polycrystals , 1953 .

[109]  Tayfun Akin,et al.  MEMS resonant load cells for micro-mechanical test frames: feasibility study and optimal design , 2010 .

[110]  Y. Dufrêne,et al.  Detection and localization of single molecular recognition events using atomic force microscopy , 2006, Nature Methods.

[111]  Anthony G. Evans,et al.  A critical assessment of theories of strain gradient plasticity , 2009 .

[112]  C. Volkert,et al.  Effect of sample size on deformation in amorphous metals , 2008 .

[113]  A. J. Jacobsen,et al.  INTERCONNECTED SELF-PROPAGATING PHOTOPOLYMER WAVEGUIDES : AN ALTERNATIVE TO STEREOLITHOGRAPHY FOR RAPID FORMATION OF LATTICE-BASED OPEN-CELLULAR MATERIALS , 2010 .

[114]  T. Pollock,et al.  Post-fabrication vapor phase strengthening of nickel-based sheet alloys for thermostructural panels , 2008 .

[115]  J. Wang,et al.  Design and demonstration of a high authority shape morphing structure , 2004 .

[116]  Blythe G. Clark,et al.  Size Independent Shape Memory Behavior of Nickel–Titanium , 2010 .

[117]  A. Ngan,et al.  Stochastic nature of plasticity of aluminum micro-pillars , 2008 .

[118]  John W. Hutchinson,et al.  Optimal truss plates , 2001 .

[119]  C. A. Volkert,et al.  Size effects in the deformation of sub-micron Au columns , 2006 .

[120]  L. Valdevit,et al.  Materials Property Profiles for Actively Cooled Panels: An Illustration for Scramjet Applications , 2009 .

[121]  Hilary Bart-Smith,et al.  Measurement and analysis of the structural performance of cellular metal sandwich construction , 2001 .

[122]  M. Ashby,et al.  Cellular solids: Structure & properties , 1988 .

[123]  D. Dimiduk,et al.  Estimating the strength of single-ended dislocation sources in micron-sized single crystals , 2007 .

[124]  Franz J. Giessibl,et al.  Advances in atomic force microscopy , 2003, cond-mat/0305119.

[125]  D. Dimiduk,et al.  Dislocation structures and their relationship to strength in deformed nickel microcrystals , 2008 .

[126]  van der Erik Giessen,et al.  Discrete dislocation plasticity: a simple planar model , 1995 .

[127]  Julia R. Greer,et al.  Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale , 2010 .

[128]  G. Pharr,et al.  Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology , 2004 .

[129]  M. Wolcott.  Cellular solids: Structure and properties , 1990 .

[130]  D. Dimiduk,et al.  Scale-Free Intermittent Flow in Crystal Plasticity , 2006, Science.

[131]  M. J. Rost,et al.  Scanning probe microscopy at video-rate , 2008 .

[132]  L. Valdevit,et al.  Active cooling by metallic sandwich structures with periodic cores , 2005 .

[133]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity—II. Analysis , 2000 .

[134]  Julia R. Greer,et al.  Size dependence of mechanical properties of gold at the sub-micron scale , 2005 .

[135]  Blythe G. Clark,et al.  Orientation-independent pseudoelasticity in small-scale NiTi compression pillars , 2008 .

[136]  Transient-Liquid-Phase Bonding of Ceramics , 2011 .

[137]  W. Gerberich,et al.  In situ imaging of μN load indents into GaAs , 1995 .

[138]  H. Moss,et al.  Vitreous , 2012, Neurology.

[139]  S. Torquato,et al.  Design of smart composite materials using topology optimization , 1999 .

[140]  Julia R. Greer,et al.  Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect , 2011 .

[141]  M. Ashby,et al.  Metal Foams: A Design Guide , 2000 .

[142]  N. Moody,et al.  Quantitative adhesion measures of multilayer films: Part II. Indentation of W/Cu, W/W, Cr/W , 1999 .

[143]  Andrew M Minor,et al.  Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. , 2008, Nature materials.

[144]  John W. Hutchinson,et al.  Structurally optimized sandwich panels with prismatic cores , 2004 .

[145]  S. Han,et al.  Uniaxial compression of fcc Au nanopillars on an MgO substrate: The effects of prestraining and annealing , 2009 .

[146]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity— I. Theory , 1999 .

[147]  G. Pharr,et al.  Effects of pre-strain on the compressive stress-strain response of Mo-alloy single-crystal micropillars , 2008 .

[148]  Frank W. Zok,et al.  A protocol for characterizing the structural performance of metallic sandwich panels: application to pyramidal truss cores , 2004 .

[149]  G. Pharr,et al.  An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments , 1992 .

[150]  H. Wadley.  Cellular Metals Manufacturing , 2002 .

[151]  D. Dimiduk,et al.  Plasticity of Micrometer-Scale Single-Crystals in Compression: A Critical Review (PREPRINT) , 2008 .

[152]  Norman A. Fleck,et al.  Kagome plate structures for actuation , 2003 .

[153]  Frank W. Zok,et al.  Design of metallic textile core sandwich panels , 2003 .

[154]  A. Ngan,et al.  Effects of trapping dislocations within small crystals on their deformation behavior , 2009 .

[155]  Steven Nutt,et al.  Micro-scale truss structures with three-fold and six-fold symmetry formed from self-propagating polymer waveguides , 2008 .

[156]  J. Greer,et al.  Size dependence in mechanical properties of gold at the micron scale in the absence of strain gradients , 2007 .

[157]  Kyeongjae Cho,et al.  MEAM study of carbon atom interaction with Ni nano particle , 2009 .

[158]  Martin P. Bendsøe.  Topology Optimization , 2009, Encyclopedia of Optimization.