Timo Saksala

Rate-Dependent Embedded Discontinuity Approach Incorporating Heterogeneity for Numerical Modeling of Rock Fracture

In this paper, the embedded discontinuity approach is applied in finite element modeling of rock in compression and tension. For this end, a rate-dependent constitutive model based on (strong) embedded displacement discontinuity model is developed to describe the mode I, mode II and mixed mode fracture of rock. The constitutive model describes the bulk material as linear elastic until reaching the elastic limit. Beyond the elastic limit, the rate-dependent exponential softening law governs the evolution of the displacement jump. Rock heterogeneity is incorporated in the present approach by random description of the mineral texture of rock. Moreover, initial microcrack population always present in natural rocks is accounted for as randomly-oriented embedded discontinuities. In the numerical examples, the model properties are extensively studied in uniaxial compression. The effect of loading rate and confining pressure is also tested in the 2D (plane strain) numerical simulations. These simulations demonstrate that the model captures the salient features of rock in confined compression and uniaxial tension. The developed method has the computational efficiency of continuum plasticity models. However, it also has the advantage, over these models, of accounting for the orientation of introduced microcracks. This feature is crucial with respect to the fracture behavior of rock in compression as shown in this paper.

Modelling of Dynamic Rock Fracture Process with a Rate-Dependent Combined Continuum Damage-Embedded Discontinuity Model Incorporating Microstructure

This paper deals with numerical modelling of rock fracture under dynamic loading. For this end, a combined continuum damage-embedded discontinuity model is applied in finite element modelling of crack propagation in rock. In this model, the strong loading rate sensitivity of rock is captured by the rate-dependent continuum scalar damage model that controls the pre-peak nonlinear hardening part of rock behaviour. The post-peak exponential softening part of the rock behaviour is governed by the embedded displacement discontinuity model describing the mode I, mode II and mixed mode fracture of rock. Rock heterogeneity is incorporated in the present approach by random description of the rock mineral texture based on the Voronoi tessellation. The model performance is demonstrated in numerical examples where the uniaxial tension and compression tests on rock are simulated. Finally, the dynamic three-point bending test of a semicircular disc is simulated in order to show that the model correctly predicts the strain rate-dependent tensile strengths as well as the failure modes of rock in this test. Special emphasis is laid on modelling the loading rate sensitivity of tensile strength of Laurentian granite.

Combined Anisotropic Viscodamage-Viscoplasticity Model for Rock Under Dynamic Loading

This paper deals with numerical modelling of rock fracture under dynamic loading. For this end, an anisotropic viscodamage-viscoplasticity model for rock is developed. In the viscodamage part of the model, the Rankine criterion indicates the tensile stress states leading to rate-dependent anisotropic damaging. The anisotropy of damage is based on the compliance damage tensor given by the dyadic product of the gradient of the Rankine criterion with itself. In compression, the inelastic deformation and compressive strength degradation is governed by a Mohr-Coulomb viscoplasticity model. The model performance is first demonstrated at the material point level using a two-element model. Then, the dynamic Brazilian disc test, involving both shear and tensile fracture types along with strain rate hardening, on rock is simulated as a laboratory sample level problem.

Metallien virumismurron ja virumisväsymisen mallintaminen

This article deals with modelling of creep fracture and fatigue of metals. A short description of the physical mechanisms of creep phenomena is given. Developed thermodynamically consistent material model is described in detail. The material parameters are calibrated for the 7CrMoVTiB10-10 steel in the temperature range 500-600 oC. The model is implemented as a user subroutine in the commercial finite element code ANSYS.

On the Modelling of Creep Fracture and Fatigue

In this paper, a thermodynamically consistent formulation for the analysis of creep fracture and fatigue is presented. The model is described via two potential functions, the specific Helmholtz free energy and the complementary dissipation potential. Isotropic damage variable is used to describe the degradation of the material. In addition, the use of creep parameters, like Monkman-Grant and Larson-Miller parameters are discussed and their relation to the proposed model are derived. Developed model is implemented as a user subroutine to the commercial finite element code ANSYS and an example case of practical interest is shown.