Constitutive Modelling and Multiphysics

Deformation in Homogeneized and Discrete Model for Hexagonal Lattice

Deformation in Homogeneized and Discrete Models for Hexagonal Lattice

Large Warping in Body Center Cube Lattice

Large Warping in Body Center Cube Lattice


In a microtruss, the assembly of members in a defined configuration controls the macroscopic response of the material. If the characteristic length of its constituent elements is at least 1 order of magnitude smaller than the macroscopic length of the component, then the lattice can be treated as a material with homogenized properties. The cell geometry of a lattice governs not only the structural response but also a range of physical properties, such as wave propagation, energy absorption, toughness, diffusivity, coefficient of thermal expansion and electrical conductivity.

In the publications below, we have developed refined constitutive models that can capture the multiscale mechanics of two and three-dimensional lattices with any arbitrary topology, as well as with open and closed cell. Such models enable to treat a lattice component as a homogeneous medium and predict also non-linear structural responses, i.e. deformation mechanisms induced by both geometric and material non-linearity. Besides modelling, we are working on the design optimization of the lattice microarchitecture for single and multiple functional requirements.

Relevant publications

Xu H, Farag A, Ma R, Pasini D, Thermally actuated hierarchical lattices with large linear and rotational expansion, Special Issue on Architectured Materials, ASME Journal of Applied Mechanics, Vol. 86 / 111011, pp. 1-12, 2019. PDF_logo

Xu H, Farag A, Pasini D, Routes to program thermal expansion in three-dimensional lattice metamaterials built from tetrahedral building blocks, Journal of the Mechanics and Physics of Solids, Vol. 117, pp. 54-87, 2018. PDF_logo

Xu H, Farag A, Pasini D, Multilevel hierarchy in bi-material lattices with high specific stiffness and unbounded thermal expansion, Acta Materialia, Vol. 134,  pp. 155-166, 2017. PDF_logo

Akbarzadeh AH, Fu JW, Liu L, Chen ZT, Pasini D, Electrically Conducting Sandwich Cylinder with a Planar Lattice Core under Prescribed Eigenstrain and Magnetic Field, Composite Structures, 153: 632-644, 2016. PDF_logo

Vigliotti A, Deshpande VS, Pasini D, Non linear constitutive models for lattice materials, Journal of the Mechanics and Physics of Solids 64: 44-60, 2014. PDF_logo

Arabnejad S, Pasini D, Mechanical properties of planar lattice materials via asymptotic homogenization and comparison with alternative homogenization methods, International Journal of Mechanical Science 77: 249-262, 2013.  PDF_logo

Vigliotti A, Pasini D, Mechanical properties of hierarchical lattices, Mechanics of Materials 62: 32-43, 2013. PDF_logo

Vigliotti A, Pasini D, Stiffness and Strength of Tridimensional Periodic Lattices, Computer Methods in Applied Mechanics and Engineering 229-232: 27-43, 2012. PDF_logo

Vigliotti A, Pasini D, Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials, Mechanics of Materials 46: 57-68, 2012. PDF_logo

Elsayed M, Pasini D, Analysis of the Elastostatic Specific Stiffness of 2D Stretching-Dominated Lattice Materials, Mechanics of Materials 42 (7): 709-725, 2010. PDF_logo

Elsayed M, Pasini D, Multiscale Structural Design of Columns made of Regular Octet-Truss Lattice Material, International Journal of Solids and Structures 47 (14-15): 1764-1774, 2010. PDF_logo