Concepedia

Hill-mandel Condition

The Hill-Mandel Condition is a fundamental homogenization principle in micromechanics that requires the volume average of the virtual work performed by microscopic stresses and strains over a Representative Volume Element to equal the virtual work associated with macroscopic stresses and strains, thereby ensuring energetic consistency between microscale heterogeneity and macroscale continuum behavior.

33

Publications

1.8K

Citations

71

Authors

32

Institutions

Publications per year

2017–2026

13

Variants

Hill-mandel Macrohomogeneity ConditionHill-mandel Principle

Parents

Publications

33

Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme

V.G. Kouznetsova, M.G.D. Geers, W.A.M. Brekelmans · International Journal for Numerical Methods in Engineering · 2002 · 801 citations

, , +17

Hill condition and overall properties of composites

S. Hazanov · Archive of Applied Mechanics · 1998 · 98 citations

, , +14

A second‐order homogenization procedure for multi‐scale analysis based on micropolar kinematics

Ragnar Larsson, Stefan Diebels · International Journal for Numerical Methods in Engineering · 2006 · 87 citations

, , +17

On the size of representative volume element for Darcy law in random media

Xiangdong Du, Martin Ostoja‐Starzewski · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2006 · 83 citations

, , +17

The solid phase stress tensor in porous media mechanics and the Hill–Mandel condition

William G. Gray, Bernhard A. Schrefler, Francesco Pesavento · Journal of the Mechanics and Physics of Solids · 2008 · 79 citations

, , +16

1–5 of 33

Authors

71

  1. MO
    Martin Ostoja‐Starzewski

    University of Illinois Urbana-Champaign, United States

    6 publications · 142 citations

    6

    h-index

  2. DM
    Danial Molavitabrizi

    Uppsala University, Sweden

    2 publications · 43 citations

    2

    h-index

  3. VK
    V.G. Kouznetsova

    Eindhoven University of Technology, Netherlands

    2 publications · 872 citations

    2

    h-index

  4. SD
    Stefan Diebels

    Saarland University, Germany

    1 publications · 87 citations

    1

    h-index

  5. PP
    Panayiotis Papadopoulos

    University of California, Berkeley, United States

    1 publications · 21 citations

    1

    h-index

1–5 of 71

Institutions

32

  1. University of Illinois Urbana-Champaign

    Urbana, United States

    5 h-index

    14 publications

    151 citations

  2. Eindhoven University of Technology

    Eindhoven, The Netherlands

    3 h-index

    7 publications

    2.6K citations

  3. Uppsala University

    Uppsala, Sweden

    3 h-index

    6 publications

    139 citations

  4. Chalmers University of Technology

    Gothenburg, Sweden

    2 h-index

    5 publications

    143 citations

  5. University of Naples Federico II

    Naples, Italy

    1 h-index

    1 publications

    22 citations

  6. University of California, Berkeley

    Berkeley, United States

    1 h-index

    3 publications

    63 citations

  7. Southern Methodist University

    Dallas, United States

    1 h-index

    2 publications

    30 citations

  8. Google (United States)

    Mountain View, United States

    1 h-index

    2 publications

    166 citations

1–8 of 32

Venues

  1. 4

    h-index

  2. 4

    h-index

  3. Archive of Applied Mechanics

    2 publications · 111 citations

    2

    h-index

  4. 2

    h-index

  5. Journal of the Mechanics and Physics of Solids

    2 publications · 150 citations

    2

    h-index

1–5