Failure analysis of elasto-plastic material models on dierent levels of observation Ellen Kuhl a , Ekkehard Ramm a , Kaspar Willam b, * a Institute of Structural Mechanics, University of Stuttgart, Pfaenwaldring 7, D-70550 Stuttgart, Germany b Department of Civil, Environmental and Architectural Engineering ± CEAE Department, University of Colorado at Boulder, Campus Box 428, Boulder, CO 80309-0428, USA Received 6 October 1999; in revised form 23 January 2000 Abstract This paper aims at characteristic failure mechanisms of cohesive frictional materials at two levels of observation: (a) at the macroscale of continuum elastoplasticity, and (b) at the microscale of active microplanes with arbitrary orien- tation. Thereby, the criteria for the loss of uniqueness and the loss of ellipticity will be discussed for a macroscopic as well as a microplane-based anisotropic plasticity formulation. In addition, conditions for shear dilatancy will be de- veloped at the two scales which illustrate the necessity to couple normal and shear components at each micro- plane. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Elastoplastic failure analysis; Microplane level; Extended Drucker±Prager model 1. Introduction The prediction of failure caused by the deterioration of material properties is of great interest not only for material scientists but also for various practical engineering applications. Especially, the behavior of cohesive frictional materials like soils, concrete or rock which exhibit an entirely dierent response at in- creasing levels of con®nement, is not yet fully understood and thus cannot be simulated properly. In contrast to metals, cohesive-frictional materials are characterized by a large contrast of tensile and com- pressive strength values due to strong pressure sensitivity. Consequently, their possible failure modes cover the wide range from purely decohesive failure in tension to ductile sliding failure in shear and compression. Moreover, the granular action of the aggregate causes frictional eects, which induce dilatational defor- mation as pointed out already by Reynolds (1885) as early as 1885. The suppression of shear dilatancy and concomitant con®nement leads to ductile failure modes of the shear-compression type even in shear dominated loading situations. Material deterioration usually starts at the microscopic level manifesting itself in the formation of microdefects such as microcracks or microvoids. Under progressive loading, the coalescence of these International Journal of Solids and Structures 37 (2000) 7259±7280 www.elsevier.com/locate/ijsolstr * Corresponding author. Fax: +1-303-492-7317. E-mail address: willam@bechtel.colorado.edu (K. Willam). 0020-7683/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII:S0020-7683(00)00198-0