Recently, the DEM has been extensively applied to the simulation of heterogeneous solids to study their dynamic deformation behaviour and fracture problems. It could be stated, however, that a unified approach consistent with classical (non-rotational) continuum concept is still at the stage of development.

The paper addresses the development of the lattice-type DE model for planar classical continuum by combining it with the finite element technique.

In the framework of the developed combined approach, their computation is based on the analogy between structural and continuum variables in the triangle, employing the natural concept of finite element method (FEM) suggested by Argyris at al. [2].

The above concept considerably modifies the lattice-type DEM model. As opposed to the extensive developments exploring a lattice with central interaction as suggested by Griffiths and Mustoe [3], we arrive at the model with angular interaction [4], expressed, however, in the alternative form.

Unlike earlier developments based on a separate shear stiffness concept [3], here, shear stiffness works only in combination with axial stiffness. Consequently, the model demonstrates higher diversity of the Poisson's ratio. Secondly, it is not related to particular triangle shapes and may be extended to various meshes composed of triangles and to three-dimensional.

From the physical point of view, mutual interaction is extended to the neighbouring particles, while the new approach requires modification of the algorithm and the DEM code. The developed DEM model was implemented into the original DEM code DEMMAT [5] and validated by simulating the dynamic behaviour of the plane stress problem against the 'exact' FE results. Brittle cracking with randomly distributed tensile strength properties of the material is also considered as an application.

1

P.A. Cundall, O.D.L. Strack, "A discrete numerical model for granular assemblies", Geotechnique, 29(1), 47-65, 1979.

2

J. Argyris, H. Balmer, J.St. Doltsinis, P.C. Dunne, M. Haase, M. Kleiber, G.A. Malejannakis, H.-P., Mlejnek, M. Müller, D.W. Sharpf, "Finite Element Method - the Natural Approach", Comp. Meth. Appl. Mech. Engrg., 17/18, 1-107, 1979. doi:10.1016/0045-7825(79)90083-5

3

D.V. Griffiths, G.G.W. Mustoe, "Modelling of elastic continua using a grillage of structural elements based on discrete element concepts", Int. J. Numer. Meth. Engng, 50, 1759-1775, 2001. doi:10.1002/nme.99

4

M. Ostoja-Sttarzewski, "Lattice models in micromechanics", Appl. Mech. Rev., 55(1), 2002. doi:10.1115/1.1432990

5

R. Balevicius, A. Dziugys, R. Kacianauskas, A. Maknickas, K. Vislavicius, "Investigation of performance of programming approaches and languages used for numerical simulation of granular material by the discrete element method", Comp. Phys. Comm., 175, 404-415, 2006. doi:10.1016/j.cpc.2006.05.006

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