Dynamic fracture of a nano-cracked finite exponentially inhomogeneous piezoelectric solid

Dynamic response of elastic anisotropic solid with nanoinclusions

“…Atomistic models explicitly describe the individual atoms during their dynamic evolution (Robertson et al [4], Garg and Sinnott [5], Belytschko et al [6]), while the molecular dynamics (Bao et al [7]) takes into consideration the interactions occurring at the material microstructure. Continuum mechanics based models extending the range of classical continuum mechanics by bridging its basic theoretical principles with the most fundamental effects observed at the nanolevel are as follows, see Manolis et al [8]: the higher order and non-local elasticity models (Thai et al [9], Sladek et al [10,11]) and the surface elasticity ones based on the pioneering work of Gurtin and Murdoch [12,13] and Gurtin et al [14], see Parvanova et al [15][16][17][18][19], Rangelov et al [20][21][22], Dineva et al [23,24]. The Gurtin-Murdoch theory was motivated in part by empirical observations pointing to the presence of compressive surface stress in certain types of crystals.…”

“…We conclude this review by listing the following observations: (а) the most used analytical and numerical methods in the research field under consideration are as follows -the complex potential approach in conjunction with the techniques of conformal mapping (Li et al [36]), the method of potential displacements (Avazmohammadi et al [34]), the complex vari-ablesBEM (Mogilevskaya et al [28]), the finite element method (Gao et al [46], Tian and Rajapakse [27], Wang et al [47]), the finite and boundary element approach (Parvanova et al [16]), the BEM (Dineva et al [23], Dong and Pan [48], Dong and Lo [35], Parvanova et al [15,[17][18][19], Rangelov and Dineva [20], Rangelov et al [22]), the boundary elements and fractional derivatives (Rangelov et al [21]), the wave function expansion method and image method (Yang et al [45]). Although the well-known advantages of the BEM discussed in many books, among them the book by Dominguez [49], there is a lack of BEM models in the field of nanomechanics; (b) there is a lack of results for dynamic behavior of materials with nanoinclusions taking into account the following key factors: the transient character of the dynamic load, the material anisotropy, the consideration of multiple nanoinclusions with arbitrary number and geometry located in bounded anisotropic solids, the mutual play between surface elasticity and dynamic interaction of multiple nanoinclusions; (c) to the authors' best knowledge there is no solution of the problem for dynamic behavior of elastic anisotropic solids containing multiple elastic anisotropic nanoinclusions.…”

“…[20–22], Dineva et al. [23, 24]. The Gurtin‐Murdoch theory was motivated in part by empirical observations pointing to the presence of compressive surface stress in certain types of crystals.…”

“…[16]), the BEM (Dineva et al. [23], Dong and Pan [48], Dong and Lo [35], Parvanova et al. [15, 17–19], Rangelov and Dineva [20], Rangelov et al.…”

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

“…It is well established that the local elasticity theory cannot be adopted to capture mechanical responses of nano-continua, and consequently, a variety of size-dependent elasticity models are available in literature. Analysis and assessment of size-effects in nano-structures is currently a topic of major interest in the scientific community [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Torsional deformations can frequently occur in structural elements of NEMS, and therefore, various size-dependent elasticity theories have been exploited in literature [21][22][23][24][25][26][27][28][29][30][31][32], as comprehensively discussed in review contributions [33,34].…”