# Three-dimensional phase field microelasticity theory and modeling of multiple cracks and voids

## Related Articles

- Reconstruction of the Dynamic Contact Stresses in an Elastic Layer from the Displacements of Its Free Surface. Vatul’yan, A. O.; Dragilev, V. M.; Dragileva, L. L. // Acoustical Physics;Nov2001, Vol. 47 Issue 6, p665
An inverse problem on the reconstruction of the wave field of contact stresses produced by an external load in an elastic layer from the displacements of its free surface is considered for the model of forced steady-state vibrations in the approximation of plane deformations. The solution is...

- An edge dislocation near a macrocrack with a microcrack. Shiue, Sham-Tsong; Zhang, Tong-Yi; Lee, Sanboh // Journal of Applied Physics;11/15/1993, Vol. 74 Issue 10, p6079
Presents a study which investigated the elastic interaction between an edge dislocation and a macrocrack with microcrack by means of the Muskhelishvili potential method. Mathematical expression of the stress and displacement field of a plane strain; Equation of the stress intensity factors.

- Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 4. Further assessment of the slip-link model for chain-entanglement effect on rubber elasticity. Urayama, Kenji; Kawamura, Takanobu; Kohjiya, Shinzo // Journal of Chemical Physics;3/22/2003, Vol. 118 Issue 12, p5658
The Edwards-Vilgis slip-link model for the chain-entanglement effect on rubber elasticity is critically assessed on the basis of quasiequilibrium biaxial stressâ€”strain data of end-linked polydimethylsiloxane (PDMS) networks with different entanglement densities. The PDMS networks with...

- Elastic strain of freely suspended single-wall carbon nanotube ropes. Walters, D. A.; Ericson, L. M. // Applied Physics Letters;6/21/1999, Vol. 74 Issue 25, p3803
Reports the induction of large elastic strains in ropes of single-wall carbon nanotubes, using an atomic force microscope in lateral force mode. Deformation of the freely suspended ropes as elastic strings with tension proportional to elongation; Maximum strain observed.

- ELASTIC DISTRIBUTION OF STRESS AROUND HOLE IN REGION SUBJECTED TO PURE SHEAR. THE CONTOUR LINES INDICATE THE CURVES OF CONSTANT MAXIMUM SHEAR. // Diagram;Jul/Aug2012, Vol. 12 Issue 4, p11
The article focuses on the elastic distribution of stress around a hole.

- On the Regularity of Stresses for a Bounded Domain in the Linear Theory of Elasticity[sup 1]. Koshelev, A. I. // Doklady Physics;Sep2002, Vol. 47 Issue 9, p690
Discusses the regularity of stresses for a bounded domain in the linear theory of elasticity. Equilibrium equations of the elasticity theory; Explicit estimation of the first derivatives of the solutions which satisfy the boundary condition; Elements of the ellipticity matrix.

- Inelasticity of solids for small strains. Kochegarov, G. G. // Technical Physics Letters;Sep99, Vol. 25 Issue 9, p688
Residual (irreversible) deformations of solids were observed under very low stresses for strains Îµ 10[sup -6], which in the literature are traditionally classed in the elastic region. Inelastic deformations appeared in this range for all types of solids (mono- and polycrystals of plastic and...

- An exact solution for tube and slit flow of a FENE-P fluid. Oliveira, P.J. // Acta Mechanica;2002, Vol. 158 Issue 3/4, p157
A fully analytical solution is derived for rectilinear flow of a nonlinear viscoelastic fluid obeying the constitutive FENE-P model, under fully developed conditions. Both the plane case (slit flow) and the axisymmetric case (tube flow) are considered. Physical interpretation of the results is...

- Stresses in an infinite medium with two similar circular cylindrical inclusions. Zou, Z.; Li, S. // Acta Mechanica;2002, Vol. 156 Issue 1/2, p93
Analyzes the stresses in an infinite medium with two similar circular cylindrical inclusions. Factors affecting the mechanical behavior of an engineering material; Accountability for complex stress potentials of Muskhelishvili; Employment of elasticity theory of complex variables and Laurent...