A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux

A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.     

On the mechanical dissipation of solutions to the Riemann problem for impact involving a two-phase elastic material

Communicated by C. Dafermos     

Models for one-variant shape memory materials based on dissipation functions

Some simple models for the macroscopic behavior of shape memory materials whose microstructure can be described as a mixture of two phases are derived on the basis of a free energy and a dissipation function. Keeping a common expression for the free energy, each model is based on a different expression for the dissipation function. Temperature-induced as well as isothermal, adiabatic and convective stress-induced transformations are studied. Attention is paid to closed form solutions, comparison among the models and parameter identification.     

Uniaxial Modeling of Multivariant Shape-Memory Materials with Internal Sublooping using Dissipation Functions

Models for the macroscopic behavior of Shape Memory Materials can be conveniently constructed within the Ziegler–Green–Naghdi framework where all the constitutive information is encoded in two ingredients: the free energy and the dissipation function. In a previous work, we have proposed various expressions for the basic functions suitable to model pseudoelasticity with complete transformations cycles. In this work we consider additional effects due to Martensite reorientation and to transformation reversal prior to transformation completion. The new constitutive model allows for the modeling of a variety of effects including: shape memory associated with thermally induced transformation, internal pseudoelastic subloops and the determination of limit cycles associated with repetitive stress cycling.     

Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials

The kinematics of shearing deformation in fiber reinforced materials can lead to fibers that (a) first shorten, (b) then return to their original length, and (c) then elongate. In a hyperelastic constitutive treatment this can cause the shear stress to be a nonmonotone function of the amount of shear if the fibers are sufficiently more stiff than the matrix. Here, we explore how this effects the emergence and development of kink surfaces in the context of a variety of boundary value problems. Kink surfaces are surfaces across which the deformation gradient is discontinuous. For fiber reinforced materials such surfaces generate an abrupt change in the fiber orientation (a kink). We characterize the appearance of kink surfaces in terms of three general mechanisms: fade-in, pair creation, and boundary emission. Each has a counterpart for kink surface disappearance. These mechanisms are highly sensitive both to changes in the original fiber orientation field, including spatial variation in this field, and to changes in the nature of the applied boundary conditions. A variety of examples are presented.