Related papers: A Hybrid-High Order method for fracture modelling
In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes.…
We devise a Hybrid High-Order (HHO) method for the coupling between the acoustic and elastic wave equations in the time domain. A first-order formulation in time is considered. The HHO method can use equal-order and mixed-order settings…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…
Geological settings with reservoir characteristics include fractures with different material and geometrical properties. Hence, numerical simulations in applied geophysics demands for computational frameworks which efficiently allow to…
The problem of hydraulic fracture propagation is considered by using its recently suggested modified formulation in terms of the particle velocity, the opening in the proper degree, appropriate spatial coordinates and…
Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and…
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…
In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method,…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
We develop a method for numerical time-domain wave propagation based on the model order reduction approach. The method is built with high-performance computing (HPC) implementation in mind that implies a high level of parallelism and…
This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in…
Waves scattering from unbounded structures are always complicated problems for numerical simulations. For the case that the non-periodic incident field scattered by (locally perturbed) periodic surfaces, with the help of the Bloch…
We present a phase field modeling framework for hydrogen assisted cracking. The model builds upon a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, and a hydrogen-dependent fracture energy…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…
We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the…
We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…
Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…