A peridynamics model for strain localization analysis of geomaterials

Abstract

Summary Geomaterials such as sand and clay are highly heterogeneous multiphase materials. Nonlocality (or a characteristic length scale) in modeling geomaterials based on the continuum theory can be associated with several factors, for instance, the physical interactions of material points within finite distance, the homogenization or smoothing process of material heterogeneity, and the particle or problem size‐dependent mechanical behavior (eg, the thickness of shear bands) of geomaterials. In this article, we formulate a nonlocal elastoplastic constitutive model for geomaterials by adapting a local elastoplastic model for geomaterials at a constant suction through the constitutive correspondence principle of the state‐based peridynamics theory. We numerically implement this nonlocal constitutive model via the classical return‐mapping algorithm of computational plasticity. We first conduct a one‐dimensional compression test of a soil sample at a constant suction through the numerical model with three different values of the nonlocal variable (horizon) δ. We then present a strain localization analysis of a soil sample under the constant suction and plane strain conditions with different nonlocal variables. The numerical results show that the proposed nonlocal model can be used to simulate the inception and propagation of shear banding as well as to capture the thickness of shear bands in geomaterials at a constant suction.

Modeling of progressive damage in concrete using multidimensional virtual internal bond method

“…Countless experimental and numerical studies are available for analyzing fracture response of concrete under the presence of single dominant crack 2–16,22–32 . To the best of the authors knowledge, there are no studies especially numerical ones reported in literature, which deal with the fracture response of concrete containing multiple cracks.…”

“…Countless experimental and numerical studies are available for analyzing fracture response of concrete under the presence of single dominant crack. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][22][23][24][25][26][27][28][29][30][31][32] To the best of the authors knowledge, there are no studies especially numerical ones reported in literature, which deal with the fracture response of concrete containing multiple cracks. Therefore, in this section, the MVIB model is applied to the problem of growth and interaction of two notches in a plate made up of concrete while being subjected to biaxial loading.…”

“…2 Fracture being an omnipresent mode of failure in materials across length-scales, ability to simulate crack initiation and propagation is an important requirement concerning any fail-safe design employing the newer materials. 3 Towards that goal, the conventional finite element (FE) method has been supplemented by approaches like cohesive zone (CZ), [4][5][6] meshless FE method, [7][8][9][10] finite fracture mechanics, 11,12 phase-field method, 13,14 peridynamics, 15,16 and granular micromechanics (GM) [17][18][19][20] to present a robust and computationally efficient continuum level simulation capability. The relative ease of leveraging high-end computing has led to physics-based molecular dynamics simulation (MDS) of fracture wherein atomistic interactions are captured through suitable potential functions [21][22][23] albeit with severe limitation on length and time scale.…”

Molecular dynamics modeling of a partially saturated clay‐water system at finite temperature

“…However, our knowledge of the underlying fundamental mechanism governing failure or instability of multiphase porous media under the environmental loads (eg, humidity and temperature) is limited. () Computational experiments or modeling play an increasingly important role in obtaining a faithful understanding of the underlying failure mechanism as well as the complicated coupled processes of the solid deformation and fluids flow in multiphase porous media. () For example, recent mesoscale mixed finite element modeling of unsaturated soils taking into account the material heterogeneities (eg, density and the degree of saturation) for the first time has demonstrated that both the spatial variations of porosity and the degree of saturation have a first‐order triggering role in strain localization failures of unsaturated soils under the isothermal conditions.…”

Coupled Analysis of Desiccation Cracking in Unsaturated Soils through a Non-Local Mathematical Formulation

“…Peridynamics has been also applied to modeling shear band or strain localization in variably saturated geomaterials [3,21] as a discontinuity problem. Song and Khalili [58] formulated and implemented a nonlocal elastoplastic constitutive model for unsaturated soils through the principle of constitutive correspondence of in the state-based peridynamics. As demonstrated by their numerical results, the thickness of the shear band could be characterized naturally by the inherent length scale in the formulation.…”