44 research outputs found
Evolving discontinuities and cohesive fracture
Multi-scale methods provide a new paradigm in many branches of sciences, including applied mechanics. However, at lower scales continuum mechanics can become less applicable, and more phenomena enter which involve discon- tinuities. The two main approaches to the modelling of discontinuities are briefly reviewed, followed by an in-depth discussion of cohesive models for fracture. In this discussion emphasis is put on a novel approach to incorporate triaxi- ality into cohesive-zone models, which enables for instance the modelling of crazing in polymers, or of splitting cracks in shear-critical concrete beams. This is followed by a discussion on the representation of cohesive crack models in a continuum format, where phase-field models seem promising
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
In this paper we consider a multiscale phase-field model for
capillarity-driven flows in porous media. The presented model constitutes a
reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model,
valid in situations where interest is restricted to dynamical and equilibrium
behavior in an aggregated sense, rather than a precise description of
microscale flow phenomena. The model is based on averaging of the equation of
motion, thereby yielding a significant reduction in the complexity of the
underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its
macroscopic dynamical and equilibrium properties. Numerical results are
presented for the representative 2-dimensional capillary-rise problem
pertaining to two closely spaced vertical plates with both identical and
disparate wetting properties. Comparison with analytical solutions for these
test cases corroborates the accuracy of the presented multiscale model. In
addition, we present results for a capillary-rise problem with a non-trivial
geometry corresponding to a porous medium
Bayesian uncertainty quantification for transient heat conduction problems with temperature-dependent conductivity
We present an inverse analysis for the estimation and uncertainty quantification of a temperature dependent thermal conductivity. For that, we consider the one-dimensional problem of a slab made of steel with a temperature-dependent thermal conductivity, to which a constant heat flux is applied at both edges. After defining the mathematical formulation, we can numerically solve the direct problem and derive transient temperature values across the slab. A third-degree polynomial is used to model the temperature-dependence of the conductivity, so the estimation of this physical property is obtained through the estimation of the polynomial's coefficients. We use a Bayesian framework to model the uncertainties involved, consisting of a likelihood and a prior. The likelihood models the temperature measurements and their uncertainties, and is chosen to be a normal distribution with mean at the solution of the direct problem and a standard deviation characterizing the errors. The prior models our pre-existing knowledge about the coefficients that describe the thermal conductivity. To gain insights about the impact of using different priors, we investigate both uniform and normal distributions. The prior and likelihood are combined into a posterior, which describes the coefficients for a given set of temperature measurements. This posterior cannot be computed analytically, and therefore we solve the inverse problem with the Metropolis–Hastings algorithm, a Markov chain Monte Carlo method. Results showed that our approach could deal with all uncertainties involved, and not only provided an estimation of the thermal conductivity curve but also delivered uncertainty quantification using credible intervals. It can furthermore be modified to estimate thermal conductivity values instead of coefficients, allowing for a more physical formulation of the prior
Skeleton-stabilized ImmersoGeometric Analysis for incompressible viscous flow problems
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for
incompressible viscous flow problems with moderate Reynolds number. The
proposed formulation fits within the framework of the finite cell method, where
essential boundary conditions are imposed weakly using a Nitsche-type method.
The key idea of the proposed formulation is to stabilize the jumps of
high-order derivatives of variables over the skeleton of the background mesh.
The formulation allows the use of identical finite-dimensional spaces for the
approximation of the pressure and velocity fields in immersed domains. The
stability issues observed for inf-sup stable discretizations of immersed
incompressible flow problems are avoided with this formulation. For B-spline
basis functions of degree with highest regularity, only the derivative of
order has to be controlled, which requires specification of only a single
stabilization parameter for the pressure field. The Stokes and Navier-Stokes
equations are studied numerically in two and three dimensions using various
immersed test cases. Oscillation-free solutions and high-order optimal
convergence rates can be obtained. The formulation is shown to be stable even
in limit cases where almost every elements of the physical domain is cut, and
hence it does not require the existence of interior cells. In terms of the
sparsity pattern, the algebraic system has a considerably smaller stencil than
counterpart approaches based on Lagrange basis functions. This important
property makes the proposed skeleton-stabilized technique computationally
practical. To demonstrate the stability and robustness of the method, we
perform a simulation of fluid flow through a porous medium, of which the
geometry is directly extracted from 3D scan data