Design of large composite structures requires understanding the scaling of their mechanical properties, an aspect often overlooked in the literature on composites.This contribution analyzes, experimentally and numerically, the intra-laminar size effect of textile composite structures. Test results of geometrically similar Single Edge Notched specimens made of [0 • ] 8 epoxy/carbon twill 2×2 laminates are reported. Results show that the nominal strength decreases with increasing specimen size and that the experimental data can be fitted well by Bažant's size effect law, allowing an accurate identification of the intra-laminar fracture energy of the material, G f .The importance of an accurate estimation of G f in situations where intra-laminar fracturing is the main energy dissipation mechanism is clarified by studying numerically its effect on crashworthiness of composite tubes. Simulations demonstrate that, for the analyzed geometry, a decrease of the fracture energy to 50% of the measured value corresponds to an almost 42% decrease in plateau crushing load. Further, assuming a vertical stress drop after the peak, a typical assumption of strength-based constitutive laws implemented in most commercial Finite Element codes, results in an strength underestimation of the order of 70%.The main conclusion of this study is that measuring accurately fracture energy and modeling correctly the fracturing behavior of textile composites, including their quasi-brittleness, is key. This can be accomplished neither by strength-or strain-based approaches, which neglect size effect, nor by LEFM which does not account for the finiteness of the Fracture Process Zone.

SUMMARYThe extended finite element method (XFEM) is further improved for fracture analysis of composite laminates containing interlaminar delaminations. New set of bimaterial orthotropic enrichment functions are developed and utilized in XFEM analysis of linear-elastic fracture mechanics of layered composites. Interlaminar crack-tip enrichment functions are derived from analytical asymptotic displacement fields around a traction-free interfacial crack. Also, heaviside and weak discontinuity enrichment functions are utilized in modeling discontinuous fields across interface cracks and bimaterial weak discontinuities, respectively. In this procedure, elements containing a crack-tip or strong/weak discontinuities are not required to conform to those geometries. In addition, the same mesh can be used to analyze different interlaminar cracks or delamination propagation. The domain interaction integral approach is also adopted in order to numerically evaluate the mixed-mode stress intensity factors. A number of benchmark tests are simulated to assess the performance of the proposed approach and the results are compared with available reference results.

The present contribution proposes a general constitutive model to simulate the orthotropic stiffness, pre-peak nonlinearity, failure envelopes, and the post-peak softening and fracture of textile composites. Following the microplane model framework, the constitutive laws are formulated in terms of stress and strain vectors acting on planes of several orientations within the material meso-structure. The model exploits the spectral decomposition of the orthotropic stiffness tensor to define orthogonal strain modes at the microplane level. These are associated to the various constituents at the mesoscale and to the material response to different types of deformation. Strain-dependent constitutive equations are used to relate the microplane eigenstresses and eigenstrains while a variational principle is applied to relate the microplane stresses at the mesoscale to the continuum tensor at the macroscale.Thanks to these features, the resulting spectral stiffness microplane formulation can easily capture various physical inelastic phenomena typical of fiber and textile composites such as: matrix microcracking, micro-delamination, crack bridging, pullout, and debonding. The application of the model to a twill 2×2 shows that it can realistically predict its uniaxial as well as multi-axial behavior. Furthermore, the model shows excellent agreement with experiments on the axial crushing of composite tubes, this capability making it a valuable design tool for crashworthiness applications.The formulation is computationally efficient, easy to calibrate and adaptable to other kinds of composite architectures of great current interest such as 2D and 3D braids or 3D woven textiles.

In this research, the extended finite element method (XFEM) is improved for modeling interfacial cracks between two orthotropic media by new set of orthotropic enrichment functions. New set of bimaterial orthotropic enrichment functions are developed and utilized in XFEM analysis of linear elastic fracture mechanics of layered composites. Interlaminar crack-tip enrichment functions are derived from analytical asymptotic displacement fields around a traction free interfacial crack. In this procedure, elements containing a crack tip or strong/weak discontinuities are not required to conform to those geometries. The domain interaction integral approach is also adopted in order to numerically evaluate the mixed-mode stress intensity factors. A number of benchmark tests are simulated to assess the performance of the proposed approach and the results are compared to available reference results.

This paper deals with the formulation, calibration, and validation of a Lattice Discrete Particle Model (LDPM) for the simulation of the pressure-dependent inelastic response of granular rocks. LDPM is formulated in the framework of discrete mechanics and it simulates the heterogeneous deformation of cemented granular systems by means of discrete compatibility/equilibrium equations defined at the grain scale. A numerical strategy is proposed to generate a realistic microstructure based on the actual grain size distribution of a sandstone and the capabilities of the method are illustrated with reference to the particular case of Bleurswiller sandstone, i.e. a granular rock that has been extensively studied at the laboratory scale. LDPM micromechanical parameters are calibrated based on evidences from triaxial experiments, such as hydrostatic compression, brittle failure at low confinement and plastic behavior at high confinement. Results show that LDPM allows exploring the effect of fine-scale heterogeneity on the inelastic response of rock cores, achieving excellent quantitative performance across a wide range of stress conditions. In addition, LDPM simulations demonstrate its capability of capturing different modes of strain localization within a unified mechanical framework, which makes this approach applicable for a wide variety of geomechanical settings. Such promising performance suggests that LDPM may constitute a viable alternative to existing discrete numerical methods for granular rocks, as well as a versatile tool for the interpretation of their complex deformation/failure patterns and for the development of continuum models capturing the effect of micro-scale heterogeneity.

The extended finite element method is adopted for fracture analysis of delamination problems in fiber-reinforced polymer (FRP) reinforced beams. In this method, the stress singularities near the debonding crack tip are modeled by newly proposed orthotropic bimaterial enrichment functions, while crack faces and the material interface simulated by the Heaviside function and the weak discontinuity enrichment function, respectively. The orthotropic crack tip enrichments are utilized in orthotropic FRP plate and in a reduced isotropic form in the beam. The strain energy release rate is numerically evaluated using mixed-mode stress intensity factors which are evaluated by the means of domain interaction integral approach. The accuracy of this approach is examined through some numerical examples and the results are compared with available reference results.

This paper discusses a continuum approach to track the evolution of permeability in granular rocks by accounting for the combined effect of porosity changes, grain breakage and cement bond damage.To account for such a broad range of microscopic processes under general loading paths, the Breakage Mechanics theory is used and the computed mechanical response is linked with the Kozeny equation, i.e. a permeability model able to evaluate the reduction of the hydraulic conductivity resulting from the simultaneous loss of porosity and growth of surface area. In particular, the evolution of the internal variables of the model has been linked to idealized geometric schemes at particle scale, with the goal to distinguish the contribution of the fines generated by the disaggregation of the cement matrix from that of the broken fragments resulting from the crushing of the skeleton. Compression/flow experiments available in the literature for different granular rocks are used to validate the proposed methodology. The analyses illustrate that the drop of the permeability of damaged rocks would be severely underestimated without an accurate computation of the growth of surface area, as well as that the distributed fragmentation of skeleton particles tends to have stronger implications than the generation of cement fines. These findings, along with the satisfactory agreement between model predictions and experiments, stress the benefits of adopting microstructure-based constitutive laws for the analysis of coupled hydro-mechanical problems.

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