Font Size:

A potential-based particle method for failure modeling in solids

Last modified: 2013-06-27

#### Abstract

Continuum mechanics is typically based on the fundamental notion of a mesoscopic volume

element, whose physical characteristics can be considered as averaged properties over discrete particles, obeying

deterministic relationships. Recent works on granular-like materials have found that a continuum description

may not be appropriate for these cases, since inhomogeneities at the particle level, such as force chains and

microscopic breaking, can occur. The above discussed aspects point out the particle nature of materials and

suggest to use a different approach, namely a discrete one, to describe their mechanical behaviour; moreover

such a new approach can be suitably used for both continuum-like or granular-like materials by properly setting

the nature of the reciprocal forces exerted between particles. Such an approach is usually identified also as the

discrete-element method (DEM). By properly modelling the material as an assemble of small discrete elements,

the mechanical behaviour and the failure evolution of the material under mechanical actions can be properly

described.

In the present paper, a computational discrete element method for continuum or particle-like materials, based

on the concept of potential-based force interaction law for the quantification of the mutual forces exchanged by

small portions of the material interacting each other, is developed. After illustrating the basic concepts related

to the discrete nature of materials and their mechanical modelling, a simple particle based approach is presented

by adopting a Lennard-Jones like potential function to quantify the particles interaction. Finally, an example

related to the failure of a brittle solid is analysed in order to underline the capability of the proposed approach.

element, whose physical characteristics can be considered as averaged properties over discrete particles, obeying

deterministic relationships. Recent works on granular-like materials have found that a continuum description

may not be appropriate for these cases, since inhomogeneities at the particle level, such as force chains and

microscopic breaking, can occur. The above discussed aspects point out the particle nature of materials and

suggest to use a different approach, namely a discrete one, to describe their mechanical behaviour; moreover

such a new approach can be suitably used for both continuum-like or granular-like materials by properly setting

the nature of the reciprocal forces exerted between particles. Such an approach is usually identified also as the

discrete-element method (DEM). By properly modelling the material as an assemble of small discrete elements,

the mechanical behaviour and the failure evolution of the material under mechanical actions can be properly

described.

In the present paper, a computational discrete element method for continuum or particle-like materials, based

on the concept of potential-based force interaction law for the quantification of the mutual forces exchanged by

small portions of the material interacting each other, is developed. After illustrating the basic concepts related

to the discrete nature of materials and their mechanical modelling, a simple particle based approach is presented

by adopting a Lennard-Jones like potential function to quantify the particles interaction. Finally, an example

related to the failure of a brittle solid is analysed in order to underline the capability of the proposed approach.

Full Text:
PDF