Meso-scale fracture simulation using an augmented Lagrangian approach

Abstract

A cohesive zone model implemented in an augmented Lagrangian functional is used for simulation of meso-scale fracture problems in this paper. The method originally developed by Lorentz is first presented in a rigorous variational framework. The equivalence between the stationary point of the one field problem and the saddle point of mixed formulation is proved by solving the double inequality of the mixed functional. An adaptation to simulate fracture phenomenon in the meso-scale via mesh modification is also presented as an algorithm to insert zero-thickness interface elements based on Lagrange multipliers, boarding the non-trivial task of the field interpolation for different crack paths (plain and tortuous). A suitable tool to study the matrix fracture and debonding phenomena in composites with strongly different component stiffnesses that avoids ill-conditioning matrices associated with intrinsic cohesive zone models is obtained. The method stability is discussed using a simple patch test. Some numerical applications to fracture problems taking into account the meso-structure and, particularly, the study of transverse failure of longitudinal fiber reinforced epoxy and the fracture in concrete specimens are included in the paper. Comparing the numerical results with the experimental results obtained by other researchers, the paper introduces a discussion about the influence of coarse-aggregate volume in meso-scale fracture mechanism in concrete L-shape specimens.

An adaptive concurrent multiscale model for concrete based on coupling finite elements

“…Table 3 lists the adopted material parameters, which correspond to the same ones assumed by [25]. They were obtained based on the experimental results and are in line with the parameters adopted in previous studies dealing with the same experiment and achieving very satisfactory results in terms of both, crack propagation and macro structural response [48,49]. In the mesoscale modeling of the concrete, the value of the tensile strength adopted to the matrix-matrix interface is twice the value adopted for the ITZ, as described in detail in [26].…”

Modelling progressive failure in multi-phase materials using a phase field method

“…The load-displacement curves for the four different length scale ratios are depicted inFigure 17. The numerical result reported by Nguyen et al[76] and Labanda et al[75] are also provided in the figure. It can be seen that the predicted peak value of the curve decreases with the increasing of the ratio .…”

“…Once the interface nodes are identified, the nodal value of on these nodes should be set to 1 according to equation (9). has also been studied in [74][75][76], and all the above material properties are obtained from them.…”

“…As for load-displacement curve, the results in Figure 17 have shown that the internal length scales have significant influence on it. And through the comparison with the numerical results reported in [75,76], it is recommended that 0 / 1 In this example, a concrete plate as shown in Figure 21 is considered. The size and boundary conditions are also illustrated in the figure.…”

Toward automated identification and quantification of meso-scale damage modes in plain weave glass/epoxy composite laminates

“…Xu et al (2018) used a homogenization approach in a finite element framework to explore the relationship between microscale fiber and matrix constituent stress and mesoscale stress. Labanda et al (2018) used a cohesive zone model to study matrix fracture and fiber-matrix debonding at the meso-length scale.…”