Francesco Marotti de Sciarra

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Abstract A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano- and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward a number of difficulties. Following recent contributions within the isothermal setting, the developed model abandons the classical strain-driven methodology in favour of the modern stress-driven elasticity theory by G. Romano and R. Barretta. This effectively circumvents issues associated with strain-driven formulations. The new thermoelastic nonlocal integral model is proven to be equivalent to an adequate set of differential equations, accompanied by higher-order constitutive boundary conditions, when the special Helmholtz averaging kernel is adopted in the convolution. The example section provides several applications, thus enabling insight into performance of the formulation. Exact nonlocal solutions are established, detecting also new benchmarks for thermoelastic numerical analyses.

A Nonlocal Model of Plasticity and Damage with Different Internal Lengths

A nonlocal thermodynamically consistent model of plasticity and damage is presented using an integral approach. The theory is developed in the framework of the generalized standard material and the constitutive model is identified by the specification of a nonlocal first law of thermodynamics and of a local second one. The constitutive model is then addressed by defining a suitable expression of the free energy which yields a nonlocal plastic model in the stress space and a nonlocal damage model in the strain space. A variational formulation depending on local and nonlocal state variables is thus provided.

Modulated linear dynamics of nanobeams accounting for higher gradient effects

We present some numerical results for the linear dynamics of nanobeams modulated by an axial force, basing on a recent proposal of literature that encompasses both the standard nonlocal elasticity, according to Eringen, and second-order strain elasticity. Three different possibilities for the elastic potential energy provide different responses that highlight the contributions of nonlocality and strain gradient, plus their combination. An axial force affects the linear stationary dynamics of such nanobeams, inducing suitable variation of the natural angular frequencies for benchmark cases, until static buckling occurs when the natural angular frequency vanishes. Effects of the various elastic potentials on this modulation are investigated and thoroughly commented.