Mechanics of Time-Dependent Materials

, Volume 16, Issue 1, pp 1–18 | Cite as

Theoretical and computational modelling of instrumented indentation of viscoelastic composites



In this study, we investigate the indentation of viscoelastic composites. The composite is assumed to consist of two phases, i.e., the filler and the matrix, which are linear elastic and linear viscoelastic material, respectively. Two cases are investigated: (1) hard fillers are scattered in a very soft matrix; (2) the matrix is much harder than the fillers. Particular attention is paid to the correlation between the indentation relaxation loads and the material and geometric parameters of the composite system. To this end, we perform a theoretical analysis which is followed by finite element analysis. Our main result is a simple relation correlating the reduced relaxation modulus of the matrix, E m,r (t), with the indentation relaxation load P(t), i.e., E m,r (t)=P(t)/P(0), where P(0) represents the indentation load at the starting point of the relaxation test. This result on one hand indicates that for the two cases under study the relaxation feature of the indentation load is determined by the reduced relaxation modulus of the matrix. On the other hand, the result shows that the reduced relaxation modulus of the matrix of the composites may be simply determined from the indentation relaxation load without invoking the knowledge of both the indenter geometry and the profile of indented solids.


Indentation Viscoelastic composites Finite element simulation 


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© Springer Science+Business Media, B. V. 2011

Authors and Affiliations

  1. 1.Applied Mechanics Lab, Department of Engineering MechanicsTsinghua UniversityBeijingChina

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