arXiv subjects

Keita Yoshioka

Publications and source records attributed to Keita Yoshioka.

5 recordsLinked to original sources

arXiv2026

Revisiting the hydromechanical formulation of a micromechanics-based phase-field model for poro-elastoplastic media

Even for tension-dominated fracture propagation, porous materials may deform plastically adjacent to the propagating fracture. As is common for porous materials, existing phase-field models typically employ a non-associative flow rule for plasticity, and a Helmholtz free energy based on strain and fluid pressure. This work revisits the hydromechanically coupled formulation of the phase-field model for fracture in poro-elastoplastic media by analyzing the strength surface and fracture driving force. Our analyses show that these common choices of flow rule and free energy will lead to a discontinuous strength surface across the tension-compression transition. A non-associative flow rule introduces a jump at the strength surface, while treating fluid pressure-rather than fluid content-as the independent variable in the Helmholtz free energy omits a coupling term from the phase-field driving force, also breaking continuity. Incorporating an associative Drucker-Prager flow rule and this omitted coupling term ensures a continuous strength surface and the accurate fracture driving force. The proposed model exhibits improved accuracy in hydromechanical responses when compared against the analytical solution of the Kristianovich-Geertsma-de Klerk hydraulic fracturing benchmark. Numerical simulations of hydraulic fracturing and biaxial compression in poro-elastoplastic media show that the model can reproduce both shear-dominated fractures induced by mechanical disturbance and tension-dominated fractures driven by fluid injection in saturated porous media.

cond-mat.soft↗

arXiv2026

A dual--continuum phase-field model for hydraulic fracturing: Viscosity-dominated regime and fluid lag

The phase-field model regularizes sharp fractures into a diffuse representation, blurring the boundary between the fracture and the intact material. This blurring makes it difficult to capture distinct domain processes in hydraulic fracturing, where Reynolds flow governs the fracture and Darcy flow describes the surrounding porous matrix. Consequently, the blurred delineation artificially smears the pressure field across the fracture--matrix interface, which is acceptable in toughness-dominated hydraulic fracturing regimes where pressure drops within the fracture are negligible. However, in viscosity-dominated regimes, typically for actual subsurface injections due to high injection rates, the fluid pressure drops more drastically, and the fluid front may even lag behind the propagating fracture tip, a phenomenon that a smeared pressure field cannot capture. Despite its relevance, the viscosity-dominated regime has not been addressed by any existing phase-field models to date, likely due to its numerical instability. In this study, we propose a dual--continuum phase-field model based on double-porosity microporomechanics that explicitly separates mesoscale crack pressure from micropore pressure. The framework provides a variationally consistent formulation alongside phase-field--dependent poroelasticity. To ensure the numerical stability of the hydromechanical coupling, a fixed-stress split scheme is modified for two independent fluid pressures, while a variational inequality constraint is applied to reproduce fluid lag. Verified against the closed-form solutions in toughness-dominated, viscosity-dominated, and early-time transitional regimes, the model accurately captures complex fluid flow behavior and transient fluid lag within the fracture, and opens a new frontier for applying phase-field models to realistic viscosity-dominated hydraulic fracturing.

physics.flu-dyn↗

arXiv2024

A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation

This work extends the hydro-mechanical phase-field fracture model to non-isothermal conditions with micromechanics based poroelasticity, which degrades Biot's coefficient not only with the phase-field variable (damage) but also with the energy decomposition scheme. Furthermore, we propose a new approach to update porosity solely determined by the strain change rather than damage evolution as in the existing models. As such, these poroelastic behaviors of Biot's coefficient and the porosity dictate Biot's modulus and the thermal expansion coefficient. For numerical implementation, we employ an isotropic diffusion method to stabilize the advection-dominated heat flux and adapt the fixed stress split method to account for the thermal stress. We verify our model against a series of analytical solutions such as Terzaghi's consolidation, thermal consolidation, and the plane strain hydraulic fracture propagation, known as the KGD fracture. Finally, numerical experiments demonstrate the effectiveness of the stabilization method and intricate thermo-hydro-mechanical interactions during hydraulic fracturing with and without a pre-existing weak interface.

math.NA↗

arXiv2023

On poroelastic strain energy degradation in the variational phase--field models for hydraulic fracture

Though a number of formulations have been proposed for phase--field models for hydraulic fracture, the definition of the degraded poroelastic strain energy varies from one model to another. This study explores previously proposed forms of the poroelastic strain energy with diffused fracture and assesses their ability to recover the explicit fracture opening aperture. We then propose a new form of degraded poroelastic strain energy derived from micromechanical analyses. Unlike the previously proposed models, our poroelastic strain energy degradation depends not only on the phase--field variable (damage) but also on the type of strain energy decomposition. Comparisons against closed form solutions suggest that our proposed model can recover crack opening displacement more accurately irrespective of Biot's coefficient or the pore--pressure distribution. We then verify our model against the plane strain hydraulic fracture propagation, known as the KGD fracture, in the toughness dominated regime. Finally, we demonstrate the model's ability to handle complex hydraulic fracture interactions with a pre--existing natural fracture.

math.NA↗

arXiv2022

Orthogonal decomposition of anisotropic constitutive models for the phase field approach to fracture

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the tension-compression asymmetry. This decomposition follows a variational framework, satisfying the orthogonality condition for anisotropic materials. This implies that the present model can be applied to arbitrary anisotropic elastic behavior in a three-dimensional setting. On this basis, we generalize two existing models for tension-compression asymmetry in isotropic materials, namely the volumetric-deviatoric model and the no-tension model, towards materials with anisotropic nature. Two benchmark problems, single notched tensile shear tests, are used to study the performance of the present model. The results can retain the anisotropic constitutive behavior and the tension-compression asymmetry in the crack response, and are qualitatively in accordance with the expected behavior for orthotropic materials. Furthermore, to study the direction of maximum energy dissipation, we modify the surface integral based energy release computation, $G_θ$, to account only for the crack-driving energy. The computed energies with our proposed modifications predict the fracture propagation direction correctly compared with the standard G-theta method.

math.NA↗