arXiv subjects

L. Molari

Publications and source records attributed to L. Molari.

3 recordsLinked to original sources

arXiv2011

A macroscale, phase-field model for shape memory alloys with non-isothermal effects: influence of strain-rate and environmental conditions on the mechanical response

A Ginzburg-Landau model for the macroscopic behaviour of a shape memory alloy is proposed. The model is one-dimensional in essence, in that we consider the effect of the martensitic phase transition in terms of a uniaxial deformation along a fixed direction and we use a scalar order parameter whose equilibrium values describe the austenitic phase and the two martensitic variants. The model relies on a Ginzburg-Landau free energy defined as a function of macroscopically measurable quantities, and accounts for thermal effects; couplings between the various relevant physical aspects are established according to thermodynamic consistency. The theoretical model has been implemented within a finite-element framework and a number of numerical tests are presented which investigate the mechanical behaviour of the model under different conditions; the results obtained are analysed in relation to experimental evidences available in literature. In particular, the influence of the strain-rate and of the ambient conditions on the response of the model is highlighted.

cond-mat.mtrl-sci↗

arXiv2004

A discontinuous Galerkin method for strain gradient-dependent damage: Study of interpolations, convergence and two dimensional problems

A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of $C^0$ interpolation functions for continuum theories involving higher-order derivatives, while in a conventional framework at least $C^1$ interpolations are required. The discontinuous Galerkin formulation thereby offers significant potential for engineering computations with strain gradient-dependent models. When using basis functions with a low degree of continuity, jump conditions arise at element edges which are incorporated in the weak form. In addition to the formulation itself, a detailed study of the convergence properties of the method for various element types is presented, an error analysis is undertaken, and the method is also shown to work in two dimensions.

physics.comp-ph↗

arXiv2003

A discontinuous Galerkin formulation for a strain gradient-dependent damage model

The numerical solution of strain gradient-dependent continuum problems has been dogged by continuity demands on the basis functions. For most commonly accepted models, solutions using the finite element method demand $C^{1}$ continuity of the shape functions. Here, recent development in discontinuous Galerkin methods are explored and exploited for the solution of a prototype nonlinear strain gradient dependent continuum model. A formulation is developed that allows the rigorous solution of a strain gradient damage model using standard $C^{0}$ shape functions. The formulation is tested in one-dimension for the simplest possible finite element formulation: piecewise linear displacement and constant (on elements) internal variable. Numerical results are shown to compare excellently with a benchmark solution. The results are remarkable given the simplicity of the proposed formulation.

math.NA↗