JKR adhesive contact for a transversely isotropic layer of finite thickness

Abstract

Commonsense reasoning patterns such as interpolation and a fortiori inference have proven useful for dealing with gaps in structured knowledge bases. An important di culty in applying these reasoning patterns in practice is that they rely on fine-grained knowledge of how di↵erent concepts and entities are semantically related. In this paper, we show how the required semantic relations can be learned from a large collection of text documents. To this end, we first induce a conceptual space from the text documents, using multi-dimensional scaling. We then rely on the key insight that the required semantic relations correspond to qualitative spatial relations in this conceptual space. Among others, in an entirely unsupervised way, we identify salient directions in the conceptual space which correspond to interpretable relative properties such as 'more fruity than' (in a space of wines), resulting in a symbolic and interpretable representation of the conceptual space. To evaluate the quality of our semantic relations, we show how they can be exploited by a number of commonsense reasoning based classifiers. We experimentally show that these classifiers can outperform standard approaches, while being able to provide intuitive explanations of classification decisions. A number of crowdsourcing experiments provide further insights into the nature of the extracted semantic relations.

Boundary element method for nonadhesive and adhesive contacts of a coated elastic half-space

“…In the opposite limiting case of the contact radius being small compared to the thickness of the layer, analytical solutions exist in form of asymptotic series 26 in dimensionless parameter ɛ=a/h << 1 …”

“…The dependencies (42) and (43) for F and d depend on the following adhesion parameter 24,26 Numerically we carried out the pull-off simulation with five different adhesion parameters ranging from 0.1 to 15, where the constant parameters are set as E 1 ¼ 10 9 Pa, E 2 ¼ e 100 Pa (which means 1, corresponding to the limiting case of rigid foundation), 1 ¼ 0:3, h ¼ 2 mm, Á ¼ 100 J=m 2 and is varied by changing the radius of curvature R of the indenter. The results are shown in Figure 5 in the same dimensionless coordinates as given by equations (40) and (41).…”

“…Curves for different values of adhesion parameter α are shown. Dashed lines depict the dependencies(20) and(21)for the case of a h  . Dash-dot and solid lines are given by expressions(22)and (23) for the case of a h  .…”

Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory

“…Nevertheless the asymptotic approaches were mainly developed for the integral equation or equations of similar structure (see, e.g. [1,3,5,6,31,32,48]).…”

Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials

“…Overall, it is typical to represent the solutions of more complex contact problems in the form of parametric functions, in which both the external load and the indenter displacement depend on the contact radius as the parameter [34]. Among numerous examples of this kind, one can find asymptotic mathematical models of JKR-type contact for layered and coated medium [83][84][85][86], implementations of the Maugis theory [87,88], or the double-Hertz theory [89]. These models have complex mathematical form of parametric functions that cannot be exactly reduced to explicit or implicit ones.…”