| Second Gradient Poromechanics: Constitutive Modeling and Numerical Implementation in IGA-FEM Carlos Plua1; Pierre Besuelle1; Claudio Tamagnini2; 1LABORATOIRE 3SR UNIVERSITE GRENOBLE ALPES, INP, CNRS, Grenoble, France; 2UNIVERSITY OF PERUGIA, Perugia, Italy; PAPER: 409/Geomechanics/Keynote (Oral) SCHEDULED: 12:10/Fri. 25 Oct. 2019/Athena (105/Mezz. F) ABSTRACT: In this work, a fully coupled hydromechanical formulation for unsaturated 2nd gradient elastoplastic porous media is presented and applied to the numerical modeling of some geomechanics IBVP characterized by strain localization into shear bands. The introduction of internal length scales associated to the weakly non-local character of the constitutive equations effectively regularizes the numerical solutions. The 2nd gradient elastoplastic model adopted is based on two independent plastic mechanisms. The first one is provided by a three-invariant isotropic--hardening elastoplastic model similar to the one presented by Nova et al. [1], extended to unsaturated soils. In lack of sufficient experimental evidence, the second-gradient mechanism is based on a simple elastic-perfectly plastic formulation. Foe the numerical solution of the governing system of non-linear PDEs, the Isogeometric (IGA) Finite Element Method [2] has been adopted. When applied to constrained micromorphic media such as second-gradient materials, IGA offers the advantage of providing higher-order continuity of the approximating functions across element boundaries, which allows a more efficient and straightforward implementation of the discrete equilibrium problem, as compared to existing mixed FE formulations based on conventional polynomial shape functions, see [3]. This feature is also very important in coupled hydromechanical problems. In fact, the smoothness of the approximated displacements and pore pressure fields can mitigate significantly the requirements for minimum time steps. The simulation of some relevant consolidation problems demonstrates the good performance of the IGA implementation, and shows its effectiveness in regularizing the FE solutions when localization patterns occur in the strain field. References: [1]. Nova, R., Castellanza, R., & Tamagnini, C. (2003). A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation. International Journal for Numerical and Analytical Methods in Geomechanics, 27(9), 705-732. [2]. Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39), 4135-4195. [3]. Collin, F., Chambon, R., & Charlier, R. (2006). A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models. International journal for numerical methods in engineering, 65(11), 1749-1772. |
