Abstract

This paper presents a new computational technique for predicting the onset and evolution of fracture in a continuum in a simple manner combining the finite element method (FEM) and the discrete element method (DEM). Once a crack is detected at an element side in the FE mesh, discrete elements are generated at the nodes sharing the side and a simple DEM mechanism is considered to follow the evolution of the crack. The combination of the DEM with simple 3-noded linear triangular elements correctly captures the onset of fracture and its evolution, as shown in several examples of application in two and three dimensions.

Abstract

This paper describes a computation methodology to evaluate the ultimate strength and fracture of concrete samples and structures and its application to four typical tests of experimental laboratories of strength of materials. The tests results are compared and analysed from the experimental and numerical points of view in order to highlight the need for experimental trials to use the information derived from numerical results and, in turn, to validate that numerical models follow the behaviour and physics that occur in laboratory tests This comparison allows to explain the different mechanisms that occur throughout the experiments.

Abstract

The usefulness of using the speckle photography technique in fracture mechanics to check numerical calculations is demonstrated for an internally pressurized cylinder with a surface flaw. A pointwise technique was utilized to measure the opening displacements along the crack line and the Mode I stress-intensity factor was determined by extrapolating these results to the crack tip. Finite element calculations were performed to be compared with experimental data and good agreement was obtained.

Abstract

This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.

Abstract

This paper presents an enhanced coupled approach between the Finite Element Method (FEM) and the Discrete Element Method (DEM) in which an adaptative remeshing technique has been implemented. The remeshing technique is based on the computation of the Hessian of a selected nodal variable, i.e. the mesh is refined where the curvature of the variable field is greater. Once the Hessian is known, a metric tensor is defined node-wise that serves as input data for the remesher (MmgTools) that creates a new mesh. After remeshing, the mapping of the internal variables and the nodal values is performed and a regeneration of the discrete elements on the crack faces of the new mesh is carried out. Several examples of fracturing problems using the enhanced FEM-DEM formulation are presented. Accurate results in comparison with analytical and experimental solutions are obtained.

Abstract

O estudo de fissuras em componentes mecânicos e seu processo de crescimento é estudado pela Mecânica da Fratura. A fadiga provoca a propagação de fissuras em elementos estruturais quando submetidos a esforços mecânicos de tensão constante ou variável. Este trabalho apresenta a proposta de uma nova equação para obtenção da cota superior do método Fast Crack Bounds (FCB) para avaliar o crescimento de trincas com geometria semi-elíptica bidimensional. Este método é aplicado para obter maior eficiência nos tempos de processamento computacional do algoritmo quando comparado aos modelos utilizados para esse fim na área de engenharia. O método FCB não fornece uma solução exata do tamanho da fissura para um determinado ciclo de aplicação de carga. O objetivo é direcionado para a criação de dimensões (superior e inferior) que gerem uma região ajustada graficamente e que internamente tenham o tamanho real da fissura durante o processo de propagação. A lei de Paris-Erdogan é o modelo mais aplicado no estudo da propagação de fissuras, formulado matematicamente com um problema de valor inicial (PVI) e pode ser resolvido com a aplicação de Runge-Kutta de 4ª ordem (RK4). Para avaliar o desempenho das cotas FCB nas estimativas de crescimento de trincas semi-elípticas bidimensionais, foram utilizados 2 testes diferentes, adotando variações dimensionais de placa e trinca; fatores de intensidade de estresse e funções de correção à distância considerando resultados numéricos. Os testes foram baseados em procedimentos publicados na literatura. Os resultados dos tempos computacionais obtidos com as simulações garantiram uma eficiência FCB com uma variação aproximada entre [77 - 365] vezes na análise da propagação da profundidade da fissura e uma variação de [48 - 472] vezes na direção de crescimento de a largura da rachadura. A proposta de tese visa determinar uma nova equação para a cota superior do FCB. Não serão mais necessários os processos de fiscalização realizados em estudos anteriores de aplicação da metodologia de apuração do equacionamento da cota superior.

Abstract

Abstract

This work presents a ZZ-BD a posteriori error estimator tailored for 3-D linear elastic fracture mechanics problems that are approximated by second-order pFEM-GFEM formulations. The proposed error estimator is shown to estimate well discretization errors in the energy norm, with the estimated discretization error converging at the same rate as the exact discretization error. Also, the computed effectivity indexes are close to the optimal value of 1 for a LEFM problem that exhibits 3-D effects.

Abstract

This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method (FEM) and the discrete element method (DEM) approach Zarate2D. Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple 4-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.

Abstract

We present recent developments in the coupling of the finite element method (FEM) and the discrete element method (DEM) for analysis of rock blasting operations in tunnels. The coupled FEM-DEM technique has proven to be an efficient procedure for predicting the multi-fracture of rock induced by the loads generated in blasting situations. The coupled FEM-DEM procedure is applied in the tunnel construction, as well as to gas pressure blasting pyrotechnics situations to break rock for excavation of the tunnel front. In the latter case the effect of gas explosion is modelled by solving with the FEM the equations of gas dynamics in the analysis domain. The effect of the gas forces in the underlying rock mass is modelled via an embedded fluid-structure interaction method. The efficiency of the coupled FEM-DEM technique is demonstrated in several examples of fracture tests and rock blasting problems related to tunnel engineering. The examples presented show that the combination of the DEM with simple 3-noded linear triangular elements (for 2D problems) correctly captures the onset of fractures and their evolution accounting for the penetration of the gas in the failure domain [[#cite-1|[1,2]]].