René de Borst
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View article: Integral form of mixed-mode crack opening in the phase field method
Integral form of mixed-mode crack opening in the phase field method Open
Phase-field modelling of cracks has gained popularity in the fracturing analysis recently. Originally developed for brittle fracture, the method has now been extended to cohesive fracture. In the latter case, the crack opening displacement…
View article: An extended isogeometric collocation method for fracture analysis
An extended isogeometric collocation method for fracture analysis Open
A collocation method is developed for discrete fracture models in the context of the partition‐of‐unity method. Spline technologies used in isogeometric analysis (IGA) are exploited to provide a smooth inter‐element transition of gradients…
View article: Phase‐field modelling of cohesive interface failure
Phase‐field modelling of cohesive interface failure Open
A cohesive interface model is proposed in the framework of the phase‐field approach. The discrete interface is transformed into a smeared interface by a regularisation strategy. Nevertheless, the fracture energy is made dependent on the di…
View article: Computation of the crack opening displacement in the phase-field model
Computation of the crack opening displacement in the phase-field model Open
The phase-field model treats discrete cracks in a smeared sense by a regularisation technique. It holds attractive properties: there is no need to consider cracks as geometric discontinuities, and it avoids remeshing around crack tips. The…
View article: A Comparison of Plasticity Regularization Approaches for Geodynamic Modeling
A Comparison of Plasticity Regularization Approaches for Geodynamic Modeling Open
The emergence, geometry and activation of faults are intrinsically linked to frictional rheology. The latter is thus a central element in geodynamic simulations which aim at modeling the generation and evolution of fault zones and plate bo…
View article: Effects of randomness and piezomagnetic coupling on the appearance of stop-bands in heterogeneous magnetorheological elastomers
Effects of randomness and piezomagnetic coupling on the appearance of stop-bands in heterogeneous magnetorheological elastomers Open
Phononic crystals (PCs) consist of a periodic arrangement of inclusions in a matrix material, and have garnered a great deal of interest owing to a phenomenon known as band gap frequencies in which particular frequency ranges are not able …
View article: Fracture and damage in quasi-brittle materials: A comparison of approaches
Fracture and damage in quasi-brittle materials: A comparison of approaches Open
A overview is given of different approaches to simulate and predict crack propagation in quasi-brittle materials, pointing out their merits, disadvantages and complementarity. Discrete crack approaches, smeared crack approaches and Molecul…
View article: Phase-field regularised cohesive zone model for interface modelling
Phase-field regularised cohesive zone model for interface modelling Open
A discrete interface is represented as a smeared interface in the framework of phase field regularisation. Due to the numerical challenge when imposing boundary conditions we prescribe the phase field in the domain using analytical solutio…
View article: Deep learning phase‐field model for brittle fractures
Deep learning phase‐field model for brittle fractures Open
We present deep learning phase‐field models for brittle fracture. A variety of physics‐informed neural networks (PINNs) techniques, for example, original PINNs, variational PINNs (VPINNs), and variational energy PINNs (VE‐PINNs) are utiliz…
View article: Hydraulic fracturing analysis in fluid‐saturated porous medium
Hydraulic fracturing analysis in fluid‐saturated porous medium Open
This paper addresses fluid‐driven crack propagation in a porous medium. Cohesive interface elements are employed to model the behaviour of the crack. To simulate hydraulic fracturing, a fluid pressure degree of freedom is introduced inside…
View article: Analysis of progressive fracture in fluid‐saturated porous medium using splines
Analysis of progressive fracture in fluid‐saturated porous medium using splines Open
Powell‐Sabin B‐splines are employed to model progressive fracturing in a fluid‐saturated porous medium. These splines are defined on triangles and are ‐continuous throughout the domain, including the crack tips, so that crack initiation ca…
View article: Numerical modelling of lithospheric deformations with frictional plasticity
Numerical modelling of lithospheric deformations with frictional plasticity Open
<div><strong><em>Strain localisation is a key process that allows for the emergence of tectonic plates and controls their long-term deformation. Upper crustal levels are relatively cold and their rheology is thus governed…
View article: Direct simulation vs subgrid scale modelling of fluid flow in fractured or fracturing porous media
Direct simulation vs subgrid scale modelling of fluid flow in fractured or fracturing porous media Open
The accuracy and the limits of validity of the discontinuous pressure model, which describes fluid flow inside a fracture using a subgrid scale approach, is assessed by comparing simulation results with those from direct simulation using S…
View article: Modeling Lithospheric Deformation Using a Compressible Visco‐Elasto‐Viscoplastic Rheology and the Effective Viscosity Approach
Modeling Lithospheric Deformation Using a Compressible Visco‐Elasto‐Viscoplastic Rheology and the Effective Viscosity Approach Open
Deformations of the colder regions of the lithosphere mainly occur in the frictional regime. In geodynamic models, frictional plastic deformations are often highly localized (shear bands) and are used as proxies for faults. However, captur…
View article: A regularized continuum model for fault zones with rate and state friction
A regularized continuum model for fault zones with rate and state friction Open
<p>Accurate representation of fault zones is important in many applications in Earth sciences, including natural and induced seismicity. The framework developed here can efficiently model fault zone localization, evolution, and spont…
View article: Stick‐slip like behavior in shear fracture propagation including the effect of fluid flow
Stick‐slip like behavior in shear fracture propagation including the effect of fluid flow Open
Shear‐based fracture propagation in fluid‐saturated porous materials is investigated using a displacement–pressure formulation that includes acceleration and inertial effects of the fluid. Pressure‐dependent plasticity with a nonassociated…
View article: Unequal order T-spline meshes for fracture in poroelastic media
Unequal order T-spline meshes for fracture in poroelastic media Open
Spline-based meshes allow for a higher inter-element continuity. For coupled problems, e.g. poroelasticity, different meshes with different orders of interpolation are normally used for the various fields in order to avoid spurious oscilla…
View article: Convergence in non‐associated plasticity and fracture propagation for standard, rate‐dependent, and Cosserat continua
Convergence in non‐associated plasticity and fracture propagation for standard, rate‐dependent, and Cosserat continua Open
The use of pressure‐dependent plasticity models with a non‐associated flow rule causes a loss of the well‐posedness for sufficiently low hardening rates. Apart from a mesh dependence, this can result in poor convergence, or even divergence…
View article: Modelling lithosphere dynamics with robust rheological implementations: Towards 3D
Modelling lithosphere dynamics with robust rheological implementations: Towards 3D Open
<div>Reliable numerical models of lithospheric deformation require robust solution methods. The latter should account for a complex and realistic rheological model and should also provide convergent and reproducible results.</div&…
View article: Towards coupling fluid flow and rate-and-state friction in compacting visco-poro-elasto-plastic reservoirs
Towards coupling fluid flow and rate-and-state friction in compacting visco-poro-elasto-plastic reservoirs Open
<p>Induced seismicity as a result of natural gas production is a major challenge from both an industrial and a societal perspective. The compaction caused by gas production leads to changes of the effective pressure fields in the res…
View article: Toward Robust and Predictive Geodynamic Modeling: The Way Forward in Frictional Plasticity
Toward Robust and Predictive Geodynamic Modeling: The Way Forward in Frictional Plasticity Open
Strain localization is a fundamental characteristic of plate tectonics. The resulting deformation structures shape the margins of continents and the internal structure of tectonic plates. To model the occurrence of faulting, geodynamic mod…
View article: On viscoplastic regularisation of strain‐softening rocks and soils
On viscoplastic regularisation of strain‐softening rocks and soils Open
Summary Constitutive models for rocks and soils typically incorporate some form of strain softening. Moreover, many plasticity models for frictional materials use a nonassociated flow rule. Strain softening and nonassociated flow rules can…
View article: Finite Thickness of Shear Bands in Frictional Viscoplasticity and Implications for Lithosphere Dynamics
Finite Thickness of Shear Bands in Frictional Viscoplasticity and Implications for Lithosphere Dynamics Open
Permanent deformations in the lithosphere can occur in the brittle as well as in the ductile domain. For this reason, the inclusion of viscous creep and frictional plastic deformation is essential for geodynamic models. However, most curre…
View article: Isogeometric analysis of fracture propagation in saturated porous media due to a pressurised non-Newtonian fluid
Isogeometric analysis of fracture propagation in saturated porous media due to a pressurised non-Newtonian fluid Open
A model has been developed to simulate fractures which are pressurised using a non-Newtonian (power-law) fluid. The flow in the surrounding, deformable porous medium is described with a non-Newtonian fluid as well. The resulting model can …
View article: Implications of single or multiple pressure degrees of freedom at fractures in fluid-saturated porous media
Implications of single or multiple pressure degrees of freedom at fractures in fluid-saturated porous media Open
The physical consequences of modelling the fluid pressure across a fracture using one, two or three degrees of freedom are elucidated. The implications are demonstrated for each model through numerical examples for different boundary value…