Presentation at the 2014 John Rudnicki Symposium at SES Meeting in celebration of his Society of Engineering Science Medal
Modeling deformation bands in thermal softening and fluid infiltrating porous solids at finite strain
WaiChing Sun, Columbia University, New York, USA
Claudio Tamagnini, Universita degli Studi di Perugia, Perugia, Italy
Onset and modes of deformation bands are often influenced by non-mechanical loading triggered by seepage of pore fluid and thermal effects. Experimental evidence has established that temperature changes can alter the shape and size of the yield surface, and cause shear band to form in geomaterials that are otherwise stable. Understanding this thermo-hydro-mechanical responses are important for many engineering applications, such as carbon dioxide storage and extraction of hydrocarbon in which hot or cool fluid are often injected into deep porous rock formations. The purpose of this research is to simulate this coupled process using a thermoporoplasticity model with extended hardening rules. A key feature of this model is that evolution of internal variables are governed by both the plastic dissipation and the change of temperature. An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo-hydro-mechanical behavior of porous media undergoing large deformation. We first formulate a finite-deformation thermo-hydro-mechanics field theory for non-isothermal porous media. The corresponding (monolithic) discrete problem is then derived adopting low-order elements with equal order of interpolation for the three coupled fields. A projection based stabilization procedure is designed to eliminate spurious pore pressure and temperature modes due to the lack of the two-fold inf-sup condition of the equal-order finite elements. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non-isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this model.
Predicting possible leakage due to dynamics strain localization in granular materials with a coupled continuum-discrete coupling model
Yang Liu, WaiChing Sun*, Zifeng Yuan, Jacob Fish
Department of Civil Engineering and Engineering Mechanics
* Email: email@example.com
A three-dimensional multiscale model has been developed and used to analyze the evolutions of microstructural attributes and hydraulic properties inside dilatant shear bands. In the proposed multiscale coupled scheme, we establish links between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures the homogenized responses of the granular assemblies. A spatial homogenization is performed to obtain the stress measure from representative elementary volume of discrete element simulations for macroscopic explicit dynamics finite element simulations. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed inside dilatant shear bands, and replicate the induced anisotropy of the elasto-plastic responses, without employing any phenomenological plasticity model at macroscopic level. To improve cost-efficiency and prevent shear locking, a one-point quadrature rule is used along with an hour-glass control algorithm. Since discrete element simulations in each representatively elementary volume (Gauss point) requires no direct communication with its neighbors, the multiscale code can be programmed as a perfectly parallel problem, which is well suited to large scale distributed platforms and does not suffer parallel slowdown.
The resultant multiscale continuum-discrete coupling method retains the simplicity and efficiency of a continuum-based finite element model while naturally introducing length-scale to cure mesh pathology. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now obtained directly from granular physics, without introducing unnecessary empirical relations and phenomenology. Microstructural information, such as force chain length, coordination numbers and pore size distribution are compared with permeability inferred from lattice Boltzmann flow simulations to explain the mechanism that leads to the formation of flow conduit during strain localization.
Keywords: multiscale; FEM-DEM model; granular materials; dynamics shear band; anisotropy
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