DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists of a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field in composite continua.

DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists in a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field in composite continua.

DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists in a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field into composite continua.

DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

This paper deals with a DEM (Discrete Element Method) approach of the Cell Method (CM), useful for providing a multiscale modeling of composite materials. The new numerical model, called DECM, combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in a continuum, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field into composite continua.

Numerical prediction of dynamic stability loss of a flexible cylindrical shell in a granular medium

The paper presents an application of the discrete element method for an analysis of dynamical stability loss of the flexible cylindrical shell section interacting with a model granular medium. The main scope was to investigate the forms of dynamical stability loss, considering finite displacements. The granular medium weight and additional external load transmitted from the surface were considered with different backfill height over the cylindrical shell. Application of a discrete model enables to consider random imperfections in the granular medium structure. It is shown that imperfections of a granular soil structure occurring in a close surrounding of the shell have an essential impact on the shell deformations. Numerical modelling, using the discrete element method, enables to obtain solutions of dynamic interaction by investigating finite two dimensional deformations. Keywords: discrete element method, cylindrical shell, granular medium, stability

2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV

Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

2-D finite displacements and finite strain from PIV analysis of plane-strain tectonic analogue models

Image correlation techniques have provided new ways to analyze the distribution in space and time of deformation in analogue models of tectonics. Here we demonstrate how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also calculate the finite displacements and finite strain tensor. We illustrate, using synthetic images, the ability of the algorithm to produce maps of the velocity gradients, small-strain tensor components, but also incremental or instantaneous principal strains and maximum shear. The incremental displacements can then summed up using a Eulerian or a Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state, and decomposed into the finite rigid-body rotation and left or right finite stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterization of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data, and help produce conceptual mechanical models.