Wyniki wyszukiwania - BazTech

1

Dynamic displacement tracking in viscoelastic solids by actuation stresses: a one-dimensional analytic example involving shock waves

Irschik Hans, Krommer Michael

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2023

|

Vol. 71, nr 3

art. no. e144616

EN

A one-dimensional (1D) analytic example for dynamic displacement tracking in linear viscoelastic solids is presented. Displacement tracking is achieved by actuation stresses that are produced by eigenstrains. Our 1D example deals with a viscoelastic half-space under the action of a suddenly applied tensile surface traction. The surface traction induces a uni-axial shock wave that travels into the half-space. Our tracking goal is to add to the applied surface traction a transient spatial distribution of actuation stresses such that the total displacement of the viscoelastic half-space coincides with the shock wave produced by the surface traction in a purely elastic half-space. We particularly consider a half-space made of a viscoelastic Maxwell-type material. Analytic solutions to this tracking problem are derived by means of the symbolic computer code MAPLE. The 1D solution presented below exemplifies a formal 3D solution derived earlier by the present authors for linear viscoelastic solids that are described by Boltzmann hereditary laws. In the latter formal solution, no reference was made to shock waves. Our present solution demonstrates its validity also in the presence of singular wave fronts. Moreover, in our example, we show that, as was also indicated in our earlier work, the actuation stress can be split into two parts, one of them producing no stresses, and the other no displacements in two properly enlarged problems.

2

On the reduction of constants in plane elasticity with eigenstrains

Jasiuk I., Boccara S. D.

Archives of Mechanics

|

2002

|

Vol. 54, nr 5-6

425-437

EN

In this paper the reduced parameter dependence in linear plane elasticity with eigenstrains (transformation strains) is studied. The focus is on simply connected inhomogeneous materials and two-phase materials with perfectly bonded interfaces. In the analysis we rely on the result of Cherkaev, Lurie and Milton (Proc. Roy. Soc. Lond. A 438, 519-529, 1992), and we show that the stress field is invariant under a shift in area bulk and shear compliances, if the eigenstrains obey certain conditions. The analysis can be extended to multiply connected inhomogeneous materials and materials with slipping interfaces.

3

3D equilibrium shapes of periodically arranged anisotropic precipitates with elastic misfit

Mueller R., Eckert S., Gross D.

Archives of Mechanics

|

2000

|

Vol. 52, nr 4-5

663-683

EN

A numerical procedure for simulating the equilibrium shapes of precipitates in two-phase materials, such as Ni-base alloys, is presented. Assuming a periodic arrangement of precipitates, a unit cell is analyzed to take particle interaction in 3D into account. Using the concept of generalized driving forces as the source of morphological evolution, a necessary condition for an equilibrium shape is derived. In the derivation of the driving force, elastic strain energy arising from the elastic misfit of the two phases and interface energy is considered. Both phases are assumed to be linear elastic but anisotropic and different from each other. The periodic cell problem is numerically solved by the Boundary Element Method. Numerical simulation for material parameters which mimic Ni-base alloys shows the influence of particle size, stiffness ratio of the two phases, volume fraction and external load on the resulting equilibrium shapes.