Mechanics of Material Forces (Advances in Mechanics and Mathematics)

This book covers new theoretical and numerical developments in the mechanics of material forces. Conceptually speaking, common continuum mechanics in the sense of Newton which gives rise to the notion of spatial (mechanical) forces considers the response to variations of spatial placements of “physical particles with respect to the ambient space, whereas continuum mechanics in the sense of Eshelby  which gives rise to the notion of material (configurational) forces is concerned with the response to variations of material placements of “physical particles with respect to the ambient material.

Well-known examples of material forces are driving forces on defects like the Peach-Koehler force, the J-Integral in fracture mechanics, and energy release. The consideration of material forces goes back to the works of Eshelby, who investigated forces on defects; therefore this area of continuum mechanics is sometimes denoted Eshelbian mechanics.