This paper presents a local constitutive model for modelling the linear and non linear behavior of soft and hard cohesive materials with the discrete element method (DEM). We present the results obtained in the analysis with the DEM of cylindrical samples of cement, concrete and shale rock materials under a uniaxial compressive strength test, different triaxial tests, a uniaxial strain compaction test and Electronic supplementary material The online version of this article (

The Discrete Element Method (DEM) has been used for modeling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear elastic behavior of a continuum modelled via the classical force-displacement relationships at the contact interfaces between particles. In this work we propose a new way for computing the contact forces between discrete particles. The newly proposed forces take into account the surroundings of the contact, not just the contact itself. This brings in the missing terms that provide an accurate approximation to an elastic continuum, and avoids calibration of the DEM parameters for the purely linear elastic range.

This work investigates the failure patterns of ice cakes and oe-ice when loaded by a moving and sloping structure (ice-breaking ships and cones).In the paper we introduce the most frequently encountered ice-infested scenarios, the main characteristics of ice-breaking ships and the predicted failure modes of oe-ice depending on the loading conditions, the structure type and the ice feature dimensions and thickness. For the simulations, a local bonded Discrete Element Method (DEM) is used to model sea ice and its fractures. The packing of bonded spherical particles which reproduce the ice continuum can break due to ship-ice interactions and the failure modes are studied. A set of validation simulations are rst carried out. A level ice sheet breaking against an installed ice-breaking cone with dierent slope angles is studied and the results are compared with other DEM simulations. Then, a group of bonded DEM simulations are performed to predict the dierent failure modes produced when an ice-breaking ship bow contacts with ice cakes and oe-ice of dierent dimensions and thickness, typical in broken ice elds. Finally, the study of breaking a continuous level ice sheet is carried out by modeling with the bonded DEM an innite large domain of sea ice and loaded by a Single Degree of Freedom model of an ice-breaking ship.

In this chapter we present recent advances in the Discrete Element Method (DEM) and in the coupling of the DEM with the Finite Element Method (FEM) for solving a variety of problems in non linear solid mechanics involving damage, plasticity and multifracture situations.