@article {300,
	title = {Scratch hardness-strength solutions for cohesive-frictional materials},
	journal = {International Journal for Numerical and Analytical Methods in Geomechanics},
	volume = {36},
	year = {2014},
	month = {Feb-25-2014},
	pages = {307 - 326},
	abstract = {<p>In this paper we develop analytical solutions for scratch hardness\&ndash;strength relations for cohesive-frictional materials of the Mohr\&ndash;Coulomb and Drucker\&ndash;Prager type. Based on the lower bound yield design approach, closed-form solutions are derived for frictionless scratch devices, and validated against computational upper bound and elastoplastic finite element solutions. The influence of friction at the blade\&ndash;material interface is also investigated, for which a simple computational optimization is proposed. Illustrated for scratch tests on cement paste, we show that the proposed solutions provide a convenient way to determine estimates of cohesion and friction parameters from scratch data, and may serve as a benchmark to identify the relevance of strength models for scratch test analysis. Copyright \&copy; 2011 John Wiley \&amp; Sons, Ltd.</p>
},
	doi = {10.1002/nag.1008},
	author = {Bard, Romain and Franz-Josef Ulm}
}
