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Transition from meso-scale to macro-scale using non-local formulations. The physical processes occurring in the fracture process zone at the meso-scale (grain-scale) e.g. fracture and fluid infiltration leads to macroscopic crack growth. The transition between the processes occurring at meso- and macro-scales is accounted for by introducing a non-local length scale to the macroscopic behaviour (Bažant 1991; Sen and Ramos 2012)
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We present a novel approach for calculating the energy dissipated during fluid driven fracturing in saturated porous media. Analytical functions describing both of the solid and fluid energy dissipation modes are derived based on a thermodynamic formulation for Non Local Damage and Transport (NLDT) in porous media. The thermodynamically consistent...
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Citations
... In order to analyze fracture propagation in damage theory, the fracture length L F and average fracture width W F were introduced in [77,78]. L F is defined as the Fig. 28. ...
We present a unified non-local damage model for modeling hydraulic fracture processes in porous media, in which damage evolves as a function of fluid pressure. This setup allows for a non-local damage model that resembles gradient-type models without the need for additional degrees of freedom. In other words, we propose a non-local damage formulation at the same cost of a local damage approach. Nonlinear anisotropic permeability is employed to distinguish between the fluid flow velocity in the damage zone and the intact porous media. The permeability evolves as a function of an equivalent strain measure, where its anisotropic evolution behavior is controlled by the direction of principle strain. The length scale of the proposed model is analytically derived as a function of material point variables and is shown to be dependent on the pressure rate. A mixed finite element method is proposed to monolithically solve the coupled displacement–pressure system. The nonlinear system is linearized and solved using Newton’s method with analytically derived consistent Jacobian matrix and residual vector, and the evolution of the system in time is performed by a backward Euler scheme. Numerical examples of 1D and 2D hydraulic fracture problems are presented and discussed. The numerical results show that the proposed model is insensitive to the mesh size as well as the time step size and can well capture the features of hydraulic fracture in porous media.
... The energy dissipation also takes place in porous media. Mobasher and Waisman (2022) proposed a novel approach to evaluate the energy dissipation by a nonlocal damage and transport model. Energy dissipation is one typical phenomenon of material nonlinear evolution. ...
This paper proposes an algorithm to evaluate dissipation energy of an isotropic continuum damage mechanics model with an adaptive time-step control approach. The algorithm takes place at each integration point under the scope of finite element analysis. The total amount of the dissipation energy of one structure can be used to verify the conservation law of energy, where the summation of the elastic strain energy and the dissipation energy should be equal to the total work by external force. However, the paper shows that this condition may not be valid when the unstable crack propagation occurs. When the crack propagation is unstable, the development of damage can be driven by stored strain energy without external load. The strains at the beginning and ending time within one increment at the damaged elements will give inaccurate dissipation energy by the classic trapezoidal integration scheme. In addition, this paper proposes a new damage evolution shape function with C1 continuity of the strain-stress curve under the uniaxial tension test, which is used to demonstrate the numerical procedure of the adaptive algorithm.
