Microstructure and Fracture in Asphalt Mixtures Using a Boundary Element Approach

A fast multipole boundary element method for 2D viscoelastic problems

“…Sensale et al [11][12][13] transformed the domain integral into a boundary integral using the dual reciprocity method for the stress analysis of bodies with aging viscoelastic constitutive relations. Birgisson et al [14][15][16] applied a special boundary element-based method, called the displacement discontinuity method, and employed an explicit time-marching scheme to model the quasi-static responses of linear viscoelastic materials.…”

On finite strain micromorphic elastoplasticity

“…Much research has been done on traditional macro-continuum inelastic constitutive modeling such that a wide range of books are available to reference (Hill, 1950;Desai and Siriwardane, 1984;Lubliner, 1990;Maugin, 1992;Simo and Hughes, 1998;Simo, 1998;NematNasser, 2004). Likewise, research has been done and is ongoing on simulating directly the inelastic microstructural mechanical response-at the grain/particle/fiber scale-and reported in the literature (e.g., for polycrystalline metals (Vogler and Clayton, 2008), ceramics (Maiti et al, 2005;Molinari and Warner, 2006;Sadowski et al, 2007), concrete (Caballero et al, 2006), masonry (Formica et al, 2002), geomaterials (soils (Nezami et al, 2007) and rocks (Morris et al, 2006)), asphalt (Birgisson et al, 2004;Dai et al, 2005), bone (Chevalier et al, 2007;Lee et al, 2007)). One of the current research challenges, however, is how to bridge these length scales, from grain/particle/fiber scale (sometimes called the 'meso'-scale) to the macro-continuum scale of the engineering application, without losing salient kinematic structure and micro-stresses.…”

A time domain boundary element method for modeling the quasi-static viscoelastic behavior of asphalt pavements

“…Compared to the FEM, the boundary element method (BEM) reduces the dimension of the problem by one and provides an attractive alternative to the FEMs for elasticity and viscoelasticity problems. Birgisson et al [5,6] have recently applied a special boundary element-based method, called the displacement discontinuity (DD) method, to pavement modeling and have proven the superiority of the method over the traditional FEM for the particular problem in consideration. The DD method, originally developed by Crouch [7], solves for stresses and displacements within an elastic solid in terms of DDs (dislocations), which makes it uniquely suitable for crack problems [8][9][10].…”

“…The DD method, originally developed by Crouch [7], solves for stresses and displacements within an elastic solid in terms of DDs (dislocations), which makes it uniquely suitable for crack problems [8][9][10]. This method has been refined over years to include new features such as viscoelasticity [11], elastodynamics [12,13], and high-order elements [14] and has been successfully applied in several engineering fields such as mining and oil industry [15][16][17] as well as pavement engineering [5,6,18,19].…”