TY - JOUR A2 - Hounkonnou, Mahouton N. AU - Clayton, J. D. PY - 2015 DA - 2015/08/31 TI - On Finsler Geometry and Applications in Mechanics: Review and New Perspectives SP - 828475 VL - 2015 AB - In Finsler geometry, each point of a base manifold can be endowed with coordinates describing its position as well as a set of one or more vectors describing directions, for example. The associated metric tensor may generally depend ondirection as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science. SN - 1687-9120 UR - https://doi.org/10.1155/2015/828475 DO - 10.1155/2015/828475 JF - Advances in Mathematical Physics PB - Hindawi Publishing Corporation KW - ER -