The increasing use of low‐modulus materials, on which the reinforcement effect of the electrical resistance strain gauge is not negligible, has re‐opened the research interest into this issue. This study deals with the evaluation of stiffness, and of the strain gauge Young's modulus involved in the estimation of both the global and the local reinforcement effect; the relationship between the strain gauge stiffness and the local reinforcement effect is also analysed. In particular, the experimental technique used to determine the stiffness of some commercial strain gauges is described. The results show that the strain gauge stiffness alone does not permit an accurate evaluation of the local reinforcement effect.

We study obstacle problems involving p-Laplace-type operators in non-convex polygons. We establish regularity results in terms of weighted Sobolev spaces. As applications, we obtain estimates for the FEM approximation for obstacle problems in pre-fractal Koch Islands.

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The reinforcement effect of electrical resistance strain gauges is well-described in the literature, especially for strain gauges installed on surface. This paper considers the local reinforcement effect of strain gauges embedded within low Young modulus materials. In particular, by using a simple theoretical model, already used for strain gauges installed on the surface, it proposes a simple formula that allows the user to evaluate the local reinforcement effect of a generic strain gauge embedded on plastics, polymer composites, etc. The theoretical analysis has been integrated by numerical and experimental analyses, which confirmed the reliability of the proposed model. Notation b g Grid width b sg Strain gauge width including the matrix C Correction ratio of the local reinforcement effect of the surface strain gauge C e Correction ratio of the local reinforcement effect of the embedded strain gauge E s Young's modulus of the specimens E sg Average Young's modulus of the strain gauge including the matrix E Ã sg Surface strain gauge sensitivity to the reinforcement effect E *e sg Embedded strain gauge sensitivity to the reinforcement effect L g Grid length of the strain gauge L sg Overall gauge length (including the matrix) SG Strain Gauge t s Thickness of the specimen t sg Total thickness of the strain gauge (including the matrix) ε 0 Strain measured by the strain gauge installed on the surface ε 0 e Strain measured by the embedded strain gauge ε Actual (remote) strain Subscripts: e Embedded g Strain gauge grid s Specimen sg Whole strain gauge (grid and matrix)

We study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary. We perform asymptotic analysis for p → ∞ and n → ∞.