Simulation of crack propagation based on eigenerosion in brittle and ductile materials subject to finite strains

In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. 10.1002/nme.4352) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented.

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

We present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

A general, implicit, finite-strain FE$$^2$$ framework for the simulation of dynamic problems on two scales

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$$^2$$ 2 methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible dynamic effects arising from micro heterogeneities. A finite-strain formulation is adapted to account for geometrical nonlinearities enabling the study of e.g. plasticity or fiber pullout, which may be associated with large deformations. A consistent kinematic scale link is established as displacement constraint on the whole representative volume element. The consistent macroscopic material tangent moduli are derived including micro inertia in closed form. These can easily be calculated with a loop over all microscopic finite elements, only applying existing assembly and solving procedures. Thus, making it suitable for standard finite element program architectures. Numerical examples of a layered periodic material are presented and compared to direct numerical simulations to demonstrate the capability of the proposed framework. In addition, a simulation of a split Hopkinson tension test showcases the applicability of the framework to engineering problems.

Finite Strain Modelling for Multiphase Flow in Dual Scale Porous Media During Resin Infusion Process

Resin infusion is a pressure-gradient-driven composite manufacturing process in which the liquid resin is driven to flow through and fill in the void space of a porous composite preform prior to the heat treatment for resin solidification. It usually is a great challenge to design both the infusion system and the infusion process meeting the manufacturing requirements, especially for large-scale components of aircraft and wind turbine blades. Aiming at addressing the key concerns about flow fronts and air bubble entrapment, the present study proposes a modelling framework of the multiphase flow of resin and air in a dual scale porous medium, i.e. a composite preform. A finite strain formulation is discussed for the fluid–solid interaction during an infusion process. The present study bridges the gap between the microscopic observation and the macroscopic modelling by using the averaging method and first principle method, which sheds new light on the high-fidelity finite element modelling.

Microstructure-Based Computational Analysis of Deformation and Fracture in Composite and Coated Materials Across Multiple Spatial Scales

A multiscale analysis is performed to investigate deformation and fracture in the aluminum-alumina composite and steel with a boride coating as an example. Model microstructure of the composite materials with irregular geometry of the matrix-particle and substrate-coating interfaces correspondent to the experimentally observed microstructure is taken into account explicitly as initial conditions of the boundary value problem that allows introducing multiple spatial scales. The problem in a plane strain formulation is solved numerically by the finite-difference method. Physically-based constitutive models are developed to describe isotropic strain hardening, strain rate and temperature effects, Luders band propagation and jerky flow, and fracture. Local regions experiencing bulk tension are found to occur during compression that control cracking of composites. Interrelated plastic strain localization in the steel substrate and aluminum matrix and crack origination and growth in the ceramic coating and particles are shown to depend on the strain rate, particle size and arrangement, as well as on the loading direction: tension or compression.

Fecal Recovery of Probiotics Administered as a Multi-Strain Formulation during Antibiotic Treatment

The present study aimed to investigate whether probiotic recovery is affected when consumed together with antibiotics. Fecal samples were collected from an earlier antibiotic associated diarrhea, randomized, placebo-controlled study with a product consisting of a combination of Lactobacillus acidophilus NCFM, Lactobacillus paracasei Lpc-37, and Bifidobacterium lactis Bi-07, B. lactis Bl-04 at equal numbers and at a total dose of 1010 CFU. Fecal samples were collected during the screening visit (T0), i.e., at the time of antibiotic prescription, and then on the last day of the antibiotic treatment (T1) as well as seven days after the subject had stopped taking the antibiotic treatment (T2) and at two weeks after completing antibiotic treatment and one week after probiotic/placebo consumption stopped (T3). Samples were analyzed for the presence of the four administered strains. The study was registered at clinicaltrials.gov as NCT01596829. Detection levels of all four strains were significantly increased from T0 to T1 and returned to baseline level from T2 to T3. There were also significantly more subjects with detectable levels of L. paracasei Lpc-37, B. lactis Bi-07, and B. lactis Bl-04 at T1 and T2 compared to T0 and T3, and compared to placebo. Each of the four strains could be detected in the feces of patients apparently unaffected by the simultaneous consumption of antibiotics.