Surface interaction potentials in elasticity

On the existence of solution in the linear elasticity with surface stresses

“…We start with the set C (2) 0 of vector functions u that take values in R 3 such that each of its Cartesian components belongs to C (2) (V ) and u| Ω1 = 0. On C (2) 0 we introduce the inner product (15) and the corresponding energy norm u 2 e = u, u e that is the double strain energy of the body 2E(u). Suppose the conditions (13) are fulfilled.…”

“…The studies of the surface stresses in solids were initiated by J. W. Gibbs [7] at the end of XIXth century. The nonlinear mechanics with regard of surface stresses is developed in [8,9,[15][16][17][18]. The model proposed in [8] can be considered as a model of an elastic body with an elastic film-membrane glued to its surface.…”

Elements of Elastic Stability Theory

“…An account of this work and further references are given in Podio-Guidugli (1999). See also Podio-Guidugli and Vergara Caffarelli (1990), Sewell (1967) and Knops and Wilkes (1973).…”

A Model of Rupturing Lithospheric Faults with Reoccurring Earthquakes

“…For the tensorial variant of (3.10) used in a similar context in the mechanics of the above-mentioned nonsimple continua of the second grade, cf. [39,51].…”

“…To put it into a mathematically rigorous frame, one could adopt the concept of the so-called nonsimple materials (also called multipolar solids or complex materials), leading to the so-called hyperstresses, i.e., the gradient theory for e(u); cf. [39,51] Remark 2.2 (concepts of healing). Reversible damage (or adhesion in section 3) itself (i.e., allowing healing, or so-called rebonding) has been routinely addressed in mathematical literature; cf.…”