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A quasistatic unilateral frictionless contact problem for a rigid axisymmetric indenter pressed into a homogeneous, linearly elastic and transversely isotropic elastic layer bonded to a homogeneous, linearly elastic and transversely…

For cylindrical indentation of elastic half-space the relationship between the depth of indentation delta and the applied force F is nonlinear, in contrast to the linear relationship between the height of the contact zone delta_0 and the…

The classical problem of indentation on an elastic substrate has found new applications in the field of the Atomic Force Microscopy. However, linearly elastic indentation models are not sufficiently accurate to predict the…

Surface tension is a prominent factor for the deformation of solids at micro-/nano-scale. This paper investigates the effects of surface tension on the two-dimensional contact problems of an elastic layer bonded to the rigid substrate.…

An indentation experiment involves five variables: indenter shape, material behavior of the substrate, contact size, applied load and indentation depth. Only three variable are known afterwards, namely, indenter shape, plus load and depth…

The force of adhesion of a rotationally symmetric indenter and an elastic half-space is analyzed analytically and numerically using an extension of the method of dimensionality reduction (MDR) for superimposed normal/tangential adhesive…

Indentation tests are largely exploited in experiments to characterize the mechanical and fracture properties of the materials from the resulting crack patterns. This work proposes an efficient theoretical and computational framework, whose…

Application of the principle of energy balance to a rigid indenter in contact with elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more…

Within a model where micrometer-size soft colloidal particles are viewed as liquid drops, we theoretically study the contact interaction between them. We compute the exact deformation energy across a broad range of indentations and for…

The determination of the contact area is a key step to derive mechanical properties such as hardness or an elastic modulus by instrumented indentation testing. Two families of procedures are dedicated to extracting this area: on the one…

In this article, we extended our approach, that is mentioned in part 1, to model the indentation of an adhesive beam by a rigid cylindrical punch. We considered clamped and simply supported beams for this study. We first modeled these beams…

We investigate the interaction between an infinite cylinder and a free fluid-fluid interface governed only by its surface tension. We study the deformation of an initially flat interface when it is deformed by the presence of a cylindrical…

Pressurized elastic shells are ubiquitous in nature and technology, from the outer walls of yeast and bacterial cells to artificial pressure vessels. Indentation measurements simultaneously probe the internal pressure and elastic properties…

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the…

Load-depth relation is the fundamental requisite in nanoindentation tests for thin layers, however, the effects of surface tension are seldom included. This paper concerns micro-/nano-sized indentation of a bonded elastic layer by a rigid…

Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without…

In this paper, adhesive contact of a rigid cylinder on an elastic power-law graded half-space is studied analytically with the theory of weakly singular integral equation and orthogonal polynomial method. Emphasis is placed on the coupling…

Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single…

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere, or compression between two plates. Previously, different theoretical approaches have been developed to retrieve material parameters (e.g.…

We consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter ("line contact") with account of the surface tension of the layer. First, it is shown that the boundary condition for the…