Surface Of Strain Discontinuity Research Articles

Configurational phases in elastic foams under lengthscale-free punching

We carry out experiments with brick-like specimens of elastic open-cell (EOC) foams of three relative densities. Individual specimens may be “tall” (height = width = depth) or “short” (2height=width=depth). We place each specimen on a supporting plate and use a lengthscale-free (wedge-shaped or conical) punch to apply forces downward along the specimen's height. Regardless of the type of specimen, the force–penetration curves remain linear, for the wedge-shaped punch, or quadratic, for the conical punch, up to a sizable penetration commensurate with the smallest lengthscale of the specimen. After that there is an abrupt, all-but-discontinuous change in stiffness: if the specimen is tall, the stiffness drops; if the specimen is short, the stiffness shoots up. To analyze these curious experimental results, we posit that EOC foams can be found in either of two configurational phases, here termed the low-strain phase and the high-strain phase, which share a two-dimensional interface (a surface of strain discontinuity). The analysis may be outlined as follows. In the first part of an experiment, there obtains a “similarity regime” in which the penetration of the punch and the radius of the interface are the only prevailing lengthscales (because the punch is lengthscale free). In this case, it is possible to show that the force–penetration curve must be linear, or quadratic, depending on whether the punch be wedge-shaped or conical, respectively. This prediction of the analysis is consistent with the experiments. In time, the similarity regime breaks down when the interface reaches one of the specimen's boundaries distal to the tip of the punch. If the specimen is tall, the soft, stress-free lateral boundary is reached first, and the stiffness must drop; if the specimen is short, the hard boundary in contact with the supporting plate is reached first, and the stiffness must shoot up. These predictions too are consistent with the experiments. To provide direct empirical evidence of the interface, we use a digital-image correlation method. Lastly, we run computational simulations of all the experiments, using finite elements and the skeleton-and-bubble model of EOC foams. The computational results are in good accord with the experimental ones, and they allow us to carry out a detailed validation of the analysis. Our findings evince the cardinal role of configurational phases in the mechanics of EOC foams.

Interaction of a one-dimensional unloading wave with an elastoplastic boundary in an elastoviscoplastic medium

This paper presents a solution of the boundary-value problem of the theory of large elastoviscoplastic strains for the development of viscoplastic flow in a heavy layer of material located on an inclined plane and subjected to loading at the free surface with subsequent instantaneous removal of the load. This discontinuous change in the boundary conditions gives rise to a surface of strain discontinuity propagating in the medium and called an unloading wave. The reflection of the wave from the elastoviscoplastic boundary and its motion after reflection from the fixed plane and the free surface are considered.

Multidimensional stability of martensite twins under regular kinetics

This paper considers phase boundaries governed by regular kinetic relations as first proposed by Abeyaratne and Knowles [1990. On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (3), 345–360; 1991. Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114, 119–154]. It shows that static configurations of hyperelastic materials, in which two different martensitic (monoclinic) states meet along a planar interface, are dynamically stable towards fully three-dimensional perturbations. For that purpose, the reduced stability (or reduced Lopatinski) function associated to the static twin [Freistühler and Plaza, 2007. Normal modes and nonlinear stability behavior of dynamic phase boundaries in elastic materials. Arch. Ration. Mech. Anal. 186 (1), 1–24] is computed numerically. The results show that the interface is weakly stable under Maxwellian kinetics expressing conservation of energy across the boundary, whereas it is uniformly stable with respect to linearly dissipative kinetic rules of Abeyaratne and Knowles type.

Dynamic solid-solid transitions with phase characterized by an order parameter

We develop a thermodynamically consistent continuum theory for the study of solid-solid phase transitions where deformation dominates heat and mass transfer. We use an order parameter to characterize the notion of phase and identify phase interfaces with thin transition zones within which the strain and order parameter exhibit large gradients. To model the growth of one phase at the expense of another we introduce configurational forces, subject to their own balance, that work against changes in the order parameter. By studying traveling waves and the asymptotics of a transition layer, we establish connections between our theory and more standard approaches that identify phase interfaces with surfaces of strain discontinuity.

On the driving traction acting on a surface of strain discontinuity in a continuum

T he notion of the driving traction on a surface of strain discontinuity in a continuum undergoing a general thermomechanical process is defined and discussed. In addition, the associated constitutive notion of a kinetic relation, in which the normal velocity of propagation of the surface of discontinuity may be a given function of the driving traction and temperature, is introduced for the special case of a thermoelastic material.