Discontinuity-Driven Mesh Alignment for Evolving Discontinuities in Elastic Solids

A special mesh adaptation technique and a precise discontinuity tracking are presented for an accurate, efficient, and robust adaptive-mesh computational procedure for one-dimensional hyperbolic systems of conservation laws, with particular reference to problems with evolving discontinuities in solids. The main advantage of the adaptive technique is its ability to preserve the modified mesh as close to the original fixed mesh as possible. The constructed method is applied to the martensitic phase-transition front propagation in solids

Numerical Simulation of Acoustic Emission During Crack Growth in 3-point Bending Test

Numerical simulation of acoustic emission by crack propagation in 3-point bending tests is performed to investigate how the interaction of elastic waves generates a detectable signal. It is shown that the use of a kinetic relation for the crack tip velocity combined with a simple crack growth criterion provides the formation of waveforms similar to those observed in experiments

Numerical Simulation of Energy Localization in Dynamic Materials

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also space and time dependent. As a simple example of the complex behavior of dynamic materials, the one-dimensional elastic wave propagation is studied numerically in periodic structures whose properties (mass density, elasticity) can be switched suddenly in space and in time. It is shown that dynamic materials have the ability to dynamically amplify, tune, and compress initial signals. The thermodynamically consistent high-resolution finite-volume numerical method is applied to the study of the wave propagation in dynamic materials. The extended analysis of the influence of inner reflections on the energy localization in the dynamic materials is presented

Influence of Microstructure on Thermoelastic Wave Propagation

Numerical simulations of the thermoelastic response of a microstructured material on a thermal loading are performed in the one-dimensional setting to examine the influence of temperature gradient effects at the microstructure level predicted by the thermoelastic description of microstructured solids (Berezovski et al. in J. Therm. Stress. 34:413–430, 2011). The system of equations consisting of a hyperbolic equation of motion, a parabolic macroscopic heat conduction equation, and a hyperbolic evolution equation for the microtemperature is solved by a finite-volume numerical scheme. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the coupling of equations of the macromotion and evolution equations for macro- and microtemperatures

Dynamics of Discontinuities in Elastic Solids

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples

An Explicit Finite Volume Numerical Scheme for 2D Elastic Wave Propagation

The construction of the two-dimensional finite volume numerical scheme based on the representation of computational cells as thermodynamic systems is presented explicitly. The main advantage of the scheme is an accurate implementation of conditions at interfaces and boundaries. It is demonstrated that boundary conditions influence the wave motion even in the simple case of a homogeneous waveguide

Waves in Materials with Microstructure: Numerical Simulation

Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model

Waves in Microstructured Solids: A Unified Viewpoint of Modelling

The basic ideas for describing the dispersive wave motion in microstructured solids are discussed in the one-dimensional setting because then the differences between various microstructure models are clearly visible. An overview of models demonstrates a variety of approaches, but the consistent structure of the theory is best considered from the unified viewpoint of internal variables. It is shown that the unification of microstructure models can be achieved using the concept of dual internal variables

Two-Scale Microstructure Dynamics

Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlin-type model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out