Paradoxical size effects in composite laminates and other heterogeneous materials

Marcus A. Wheel, Jamie C. Frame, Philip E. Riches

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)
24 Downloads (Pure)


Size effects in which there is an apparent increase in stiffness with reducing size scale are forecast in those heterogeneous materials that have constitutive behaviour described by more generalized continuum theories such as couple stress, micropolar or micromorphic elasticity. This short paper considers possibly the simplest heterogeneous material exhibiting such size effects, a two phase composite laminate consisting of alternating layers of stiff and compliant material, and shows that when loaded in bending the nature of the size effect actually depends on the composition of the sample surfaces. The laminate material is apparently capable of exhibiting a diversity of size effects some of which are compatible with the predictions of generalized continuum theories while others are contradictory. Another heterogeneous material consisting of a periodic or regular array of voids within a classically elastic matrix is then considered. Detailed finite element analysis shows that the diversity of size effects encountered in the laminate material may also be observed in this more representative material thereby providing some insight into the contradictory size effects that have sometimes been reported elsewhere in the literature.
Original languageEnglish
Title of host publicationGeneralized Continua as Models for Classical and Advanced Materials
EditorsHolm Altenbach, Samuel Forest
Place of PublicationCham, Switzerland
PublisherSpringer International Publishing AG
Number of pages15
ISBN (Print)9783319317199
Publication statusPublished - 16 Apr 2016

Publication series

NameAdvanced Structural Materials
ISSN (Print)1869-8433


  • generalized continua
  • size effect
  • laminate
  • micropolar (Cosserat) elasticity
  • heterogeneous materials


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