International Journal for Numerical Methods in Engineering最新文献

We present a comprehensive model to simulate fracture nucleation and propagation in porous media, incorporating chemical reactions. This model integrates three main processes: fluid flow in porous media, reactive transport, and the mechanical deformation of fractured porous media using a variational phase-field approach. To account for chemical reactions, we use the geochemical package PHREEQC, coupled with a finite-element transport solver (OpenGeoSys), to model reactions in both thermodynamic equilibrium and kinetically, considering changes in porosity. To represent chemical damage, we introduce a variable that ranges from intact material to fully damaged material. This variable accounts for changes in porosity as a result of chemical reactions, separate from the mechanical damage represented by the phase-field variable. We test our model through various examples to showcase its ability to capture fracture nucleation and propagation driven by chemical reactions. Our model is implemented within the open-source finite element framework OpenGeoSys.

A posteriori reduced-order models (ROM), for example, based on proper orthogonal decomposition (POD), are essential to affordably tackle realistic parametric problems. They rely on a trustful training set, that is a family of full-order solutions (snapshots) representative of all possible outcomes of the parametric problem. Having such a rich collection of snapshots is not, in many cases, computationally viable. A strategy for data augmentation, designed for parametric laminar incompressible flows, is proposed to enrich poorly populated training sets. The goal is to include in the new, artificial snapshots emerging features, not present in the original basis, that do enhance the quality of the reduced basis (RB) constructed using POD dimensionality reduction. The methodologies devised are based on exploiting basic physical principles, such as mass and momentum conservation, to construct physically relevant, artificial snapshots at a fraction of the cost of additional full-order solutions. Interestingly, the numerical results show that the ideas exploiting only mass conservation (i.e., incompressibility) are not producing significant added value with respect to the standard linear combinations of snapshots. Conversely, accounting for the linearized momentum balance via the Oseen equation does improve the quality of the resulting approximation and therefore is an effective data augmentation strategy in the framework of viscous incompressible laminar flows. Numerical experiments of parametric flow problems, in two and three dimensions, at low and moderate values of the Reynolds number are presented to showcase the superior performance of the data-enriched POD-RB with respect to the standard ROM in terms of both accuracy and efficiency.

This work presents a micromechanical spectral formulation for obtaining the full-field and homogenized response of elastoplastic micropolar composites. A closed-form radial-return mapping is derived from thermodynamics-based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size-dependent material response and micro-plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.

Cardiocirculatory mathematical models are valuable tools for investigating both physiological and pathological conditions of the circulatory system. To assess an individual's clinical condition, these models must be tailored through parameter calibration. This study introduces a novel calibration method for a lumped-parameter cardiocirculatory model, by leveraging on the correlation matrix between model parameters and outputs to adjust the latter based on observed data. We evaluate the performance of our method, both independently and in combination with the L-BFGS-B optimization algorithm (Limited memory Broyden–Fletcher–Goldfarb–Shanno with Bound constraints), and we compare our results with those of L-BFGS-B alone. Using synthetic data, we show that both the correlation matrix calibration method and the combined one reduce the loss function of the optimization problem more effectively than L-BFGS-B. Moreover, the correlation matrix calibration method exhibits greater robustness to the initial parameter guess than both the combined method and L-BFGS-B. When applied to noisy data, all three calibration methods achieve comparable results. Although the correlation matrix calibration method yields less accurate parameter estimates than L-BFGS-B, in a real-world clinical case, the two new calibration methods provide clinical insights comparable to L-BFGS-B. Notably, the correlation matrix calibration method is three times faster than the other two calibration methods. These findings highlight the effectiveness of our new calibration method for clinical applications.

This article presents the implementation of the canonical Lemaitre and Gurson–Tvergaard–Needleman (GTN) damage models and a more recent phase-field type model within a Lagrangian, geometrically nonlinear, cell-centred finite volume framework. The proposed segregated solution procedure uses Picard-type defect (deferred) outer corrections, where the primary unknowns are cell-centre displacements and pressures. Spurious zero-energy modes (numerical oscillations in displacement and pressure) are avoided by introducing stabilisation (smoothing) diffusion terms to the pressure and momentum equations. Appropriate scaling of the momentum “Rhie–Chow” stabilisation term is shown to be important in regions of plasticity and damage. To accurately predict damage and fracture in wire drawing where hydrostatic pressure is high, novel variants of the Lemaitre model with crack-closure and triaxiality effects are proposed. The developed methods are validated against the notched round bar and flat notched bar experimental cases and subsequently applied to the analysis of axisymmetric wire drawing. It is shown that the proposed finite volume approach provides a robust basis for predicting damage in wire drawing, where the proposed novel Lemaitre model with crack-closure effects was shown to be the most suitable for predicting experimentally observed fracture.

This work proposes a novel approach for coupling non-isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid-filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface-capturing phase-field fracture method and interface-tracking thermo-fluid-structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase-field approach to represent fractures and reconstruct the geometry to frame a thermo-fluid-structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase-field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid-filled fracture with the phase-field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase-field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.