An isotropic elasto-damage-plastic micromechanical framework of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931). By taking advantage of the previously proposed isotropic elastic-damage framework and considering the plastic behaviors of asphalt mastic, a class of elasto-damage-plastic model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation to predict the behaviors of the innovative materials more accurately. Specifically, the governing damage evolution is characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence; the plastic flow is introduced by means of an additive split of the stress tensor. Corresponding computational algorithms are implemented into three-dimensional finite elements numerical simulations, and the outcomes are systemically compared with suitably designed experimental results.

Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities

Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties, and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions that are related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view. In the present work, we restrict ourselves on non-relativistic models.

Simulation of admixture diffusion in a medium with traps under cascade decay of particles

By the continuum-thermodynamic approach it is proposed the mathematical model of mass transfer of admixture in a multicomponent medium with traps under cascade decay of admixture. Whithin scope of the model the admixture concentration on certain step of decay is the source of the mass of the decaying substance, that diffuses and can be sorbed, on the next step. Solutions of the initial-boundary value problems of the cascade type are constructed by the iteration procedure with using Green's functions. The formulae are obtained for finding the mass flows, as well as admixture quantity pass through the layer, at each stage of decay. Software for simulation of the diffusion processes in the body with traps under cascade decay of admixture substances is designed.