Indentation Mechanics Of Heterogeneous Materials

Understanding the correlation between the microstructures and properties ofheterogeneous materials is of both technical and scientific importance, and hasreceived considerable attention of the scientists and engineers from variousdisciplines. Indentation is a promising tool to probe the mechanical properties ofheterogeneous materials at different length scales. A number of issues relevant to theindentation of heterogeneous materials have been addressed in this thesis.First, we explore the possibility to evaluate the minimum representative volumeelement (or representative volume) of heterogeneous materials using indentation tests.Determination of the representative volume of heterogeneous materials represents acentral issue for long time in mechanics of heterogeneous materials. Considering thatthe the size of contact region can across several length scales in a single indentationtest, it is possible to probe the representative volume of heterogeneous materialsbased on the effects of microstructures on the indentation responses. To justify thisconjecture, we develop micromechanical models based on both finite element andboundary element method to simulate indentation tests. Our analysis shows that atleast for two-phase composites, the critical contact region at which the indentationmodulus approaches a constant may be used to estimate the representative volume.The results given by the proposed method match the theoretical solutions in theliterature well, indicating that indentation could be a promising tool to evaluate therepresentative volume.Second, we investigate the indentation of viscoelastic composites. Thecomposite is assumed to consist of two phases, i.e., the filler and the matrix, whichare linear elastic and linear viscoelastic material, respectively. Two cases areinvestigated:1). hard fillers are scattered in a very soft matrix;2). the matrix is muchharder than the fillers. Particular attention is paid to the correlation between theindentation relaxation loads and the material and geometric parameters of thecomposite 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 reducedrelaxation modulus of the matrix with the indentation relaxation load. This result onone hand indicates that for the two cases under study the relaxation feature of theindentation load is determined by the reduced relaxation modulus of the matrix. Onthe other hand, the result shows that the reduced relaxation modulus of the matrix ofthe composites may be simply determined from the indentation relaxation loadwithout invoking the knowledge of both the indenter geometry and the profile ofindented solids.Finally, we explore indentation triggered microstructural instability inelastomeric cellular solids through combined experimental, numerical and theoreticalefforts. The results demonstrate that when the indentation depth is greater than acritical value, local instability occurs and further propagates into a rectangular regionbeneath the indenter. The width of the rectangular region scales with the contactwidth, and we propose a simple scaling relation to estimate the maximum depth towhich the instability can propagate based on the elastic contact theory. The resultsreported here may find such applications as in the integrity evaluation of soft cellularmaterials and structures and the development of advanced functional materials withnovel optical, acoustic and wetting properties.