DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Mechanical analysis of heterogeneous materials with higher-order parameters

Journal Article · · Engineering with Computers

Abstract Even though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.

Research Organization:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Organization:
USDOE; USDOE Office of Nuclear Energy (NE)
Grant/Contract Number:
NE0008771
OSTI ID:
1835931
Journal Information:
Engineering with Computers, Journal Name: Engineering with Computers Journal Issue: 6 Vol. 38; ISSN 0177-0667
Publisher:
Springer Science + Business MediaCopyright Statement
Country of Publication:
United States
Language:
English

References (75)

Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper journal January 1889
Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme
  • Kouznetsova, V.; Geers, M. G. D.; Brekelmans, W. A. M.
  • International Journal for Numerical Methods in Engineering, Vol. 54, Issue 8 https://doi.org/10.1002/nme.541
journal January 2002
Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . journal January 1929
A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials
  • Lekszycki, T.; dell'Isola, F.
  • ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 92, Issue 6 https://doi.org/10.1002/zamm.201100082
journal March 2012
Homogenized couple stress model of optimal auxetic microstructures computed by topology optimization
  • Ganghoffer, J. F.; Goda, I.; Novotny, A. A.
  • ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 98, Issue 5 https://doi.org/10.1002/zamm.201700154
journal November 2017
A comparison of homogenization and standard mechanics analyses for periodic porous composites journal January 1992
Active and non-active porosity in concrete Part II: Evaluation of existing models journal March 2002
The mechanical properties of cellular solids journal September 1983
Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof journal April 2015
Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients journal October 2015
Material characterization and computations of a polymeric metamaterial with a pantographic substructure journal July 2018
On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity journal October 2020
Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics journal July 2021
Advances in pantographic structures: design, manufacturing, models, experiments and image analyses journal June 2019
Determination of metamaterial parameters by means of a homogenization approach based on asymptotic analysis journal October 2019
A Biot–Cosserat two-dimensional elastic nonlinear model for a micromorphic medium journal November 2019
On the effective properties of foams in the framework of the couple stress theory journal March 2020
Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization journal October 2020
Positive definiteness in coupled strain gradient elasticity journal November 2020
Direct approach-based analysis of plates composed of functionally graded materials journal December 2007
Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities journal September 2016
On effective properties of materials at the nano- and microscales considering surface effects journal July 2015
On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon journal May 2019
Young’s modulus and volume porosity relationships for additive manufacturing applications journal April 2013
Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits journal March 2014
Time-Dependent Evolution of Microstructure and Mechanical Properties of Mortar journal April 2018
Average stress in matrix and average elastic energy of materials with misfitting inclusions journal May 1973
Microstructural effects in elastic composites journal March 1996
A self-consistent mechanics of composite materials journal August 1965
Solutions for effective shear properties in three phase sphere and cylinder models journal August 1979
The differential scheme and its application to cracked materials journal January 1988
The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models journal November 1996
Asymptotic analysis of heterogeneous Cosserat media journal June 2001
Un résultat d'homogénéisation pour un matériau élastique renforcé périodiquement par des fibres élastiques de très grande rigidité journal April 1997
Asymptotic expansion homogenization for heterogeneous media: computational issues and applications journal September 2001
Multi-scale computational homogenization: Trends and challenges journal August 2010
Macroscopic effective mechanical properties of porous dry concrete journal February 2013
Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy journal December 2004
Multiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous Galerkin formulation journal June 2013
Asymptotic homogenisation in linear elasticity. Part I: Mathematical formulation and finite element modelling journal June 2009
A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media journal April 2020
Computation of the effective mechanical properties including nonclassical moduli of 2.5D and 3D interlocks by micromechanical approaches journal August 2016
Pantographic lattices with non-orthogonal fibres: Experiments and their numerical simulations journal June 2017
Dynamical analysis of homogenized second gradient anisotropic media for textile composite structures and analysis of size effects journal February 2017
Establishment of strain gradient constitutive relations by homogenization journal April 2011
Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts journal May 2017
Estimation of material properties for linear elastic strain gradient effective media journal January 2012
A numerical approach for the establishment of strain gradient constitutive relations in periodic heterogeneous materials journal September 2013
A quantitative assessment of the scale separation limits of classical and higher-order asymptotic homogenization journal September 2018
On the asymptotic expansion treatment of two-scale finite thermoelasticity journal April 2012
A variational model based on isogeometric interpolation for the analysis of cracked bodies journal July 2014
A variational approach of homogenization of piezoelectric composites towards piezoelectric and flexoelectric effective media journal January 2021
On natural strain measures of the non-linear micropolar continuum journal February 2009
Establishment of strain gradient constitutive relations by using asymptotic analysis and the finite element method for complex periodic microstructures journal April 2018
Quantitative characterization of porosity and determination of elastic modulus for sintered micro-silver joints journal November 2015
Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation journal October 2008
On nonlinear modeling of an acoustic metamaterial journal January 2020
Homogenized mechanical properties of auxetic composite materials in finite-strain elasticity journal July 2013
Estimating the overall properties of heterogeneous Cosserat materials journal September 1999
Effective Moduli of Solids With Cavities of Various Shapes journal January 1994
Elasticity of Anisotropic Low-Density Lattice Materials journal November 2020
Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients journal February 2003
Mechanical metamaterials: a state of the art journal November 2017
Determination of closed form expressions of the second-gradient elastic moduli of multi-layer composites using the periodic unfolding method journal November 2018
Surface effects of network materials based on strain gradient homogenized media journal October 2019
In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials journal December 2020
On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization journal March 2021
Strain gradient elasticity with geometric nonlinearities and its computational evaluation journal July 2015
Multiscale modeling and optimization of the mechanics of hierarchical metamaterials journal October 2019
Multiscale Homogenization Schemes for the Construction of Second-Order Grade Anisotropic Continuum Media of Architectured Materials journal January 2017
Computational Evaluation of Strain Gradient Elasticity Constants journal January 2004
Linear pantographic sheets: Asymptotic micro-macro models identification journal January 2017
A multiphysics stimulus for continuum mechanics bone remodeling journal January 2018
Grid Convergence Error Analysis for Mixed-Order Numerical Schemes journal April 2003
Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study journal March 2021