Mirko Maraldi

Phase field model for coupled displacive and diffusive microstructural processes under thermal loading

Abstract A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible constitutive relationships and on the coupling of the numerous physical processes that are active. Phase changes are driven by temperature-dependent free-energy functions that become non-convex below a transition temperature. Higher-order spatial gradients are present in the model to account for phase boundary energy, and these terms necessitate the introduction of non-standard terms in the energy balance equation in order to satisfy the classical entropy inequality point-wise. To solve the resulting balance equations, a Galerkin finite element scheme is elaborated. To deal rigorously with the presence of high-order spatial derivatives associated with surface energies at phase boundaries in both the momentum and mass balance equations, some novel numerical approaches are used. Numerical examples are presented that consider boundary cooling of a domain at different rates, and these results demonstrate that the model can qualitatively reproduce the evolution of microstructural features that are observed in some alloys, especially steels. The proposed model opens a number of interesting possibilities for simulating and controlling microstructure pattern development under combinations of thermal and mechanical loading.

A non-isothermal phase-field model for shape memory alloys: Numerical simulations of superelasticity and shape memory effect under stress-controlled conditions

A phase-field–based model has been employed for numerical tests on the mechanical response of a shape memory alloy. The model consists of a time-dependent Ginzburg–Landau equation for a scalar order parameter describing the local phase of the material (austenite or martensite), coupled with the balance of linear momentum and the heat equations; the mechanical effect of the martensitic phase transition is described in terms of a uniaxial deformation strain along a fixed direction, making the model suited for predictions over monodimensional specimens. A number of numerical simulations under stress-controlled conditions have been performed to investigate the mechanical behaviour of the model; the results obtained are analysed in relation to the experimental evidences available in the literature and previous investigations under strain-controlled conditions.

A Computational Study of Stress Fiber-Focal Adhesion Dynamics Governing Cell Contractility

We apply a recently developed model of cytoskeletal force generation to study a cells intrinsic contractility, as well as its response to external loading. The model is based on a nonequilibrium thermodynamic treatment of the mechanochemistry governing force in the stress fiber-focal adhesion system. Our computational study suggests that the mechanical coupling between the stress fibers and focal adhesions leads to a complex, dynamic, mechanochemical response. We collect the results in response maps whose regimes are distinguished by the initial geometry of the stress fiber-focal adhesion system, and by the external load on the cell. The results from our model connect qualitatively with recent studies on the force response of smooth muscle cells on arrays of polymeric microposts.

The mechanochemistry of cytoskeletal force generation

In this communication, we propose a model to study the non-equilibrium process by which actin stress fibers develop force in contractile cells. The emphasis here is on the non-equilibrium thermodynamics, which is necessary to address the mechanics as well as the chemistry of dynamic cell contractility. In this setting, we are able to develop a framework that relates (a) the dynamics of force generation within the cell and (b) the cell’s response to external stimuli to the chemical processes occurring within the cell, as well as to the mechanics of linkage between the stress fibers, focal adhesions and extracellular matrix.