arXiv subjects

Rodrigo Arias

Publications and source records attributed to Rodrigo Arias.

4 recordsLinked to original sources

arXiv2026

Crack-Tip Opening as a Probe for Length-Scale Separation in Geometrically Nonlinear Solids

Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale $\lambda_\mathrm{nl}$ that bounds this region and scales quadratically with the far-field stress intensity factor $K_I$. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.

cond-mat.soft↗

arXiv1997

Excitation of normal modes of a thin elastic plate by moving dislocations

We study the excitation of harmonic waves in thin elastic samples by a single dislocation in arbitrary motion. We consider both screw and edge dislocations that move perpendicularly to the surfaces of the layer. In Fourier space the displacement velocity and dynamic stress fields generated by the motion of the dislocations are factored as the product of two terms: one depends on the motion of the dislocation only, while the other is independent of it, and represents the medium's response. The latter term exhibits poles at frequencies that satisfy the dispersion relation of the harmonic modes of the plate. In the case of a screw dislocation the modes that are excited are a subfamily of the antisymmetric Rayleigh-Lamb modes. For an edge dislocation a subfamily of the symmetric Rayleigh-Lamb modes is excited, as well as the lowest lying shear mode. The expression corresponding to a uniformly moving screw is worked out in detail; it has singular behavior at velocities coincident with the phase velocities of the allowed modes.

cond-mat.mtrl-sci↗

arXiv1997

Elastic fields of stationary and moving dislocations in three dimensional finite samples

Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for the stress field, thus satisfying the expectation that stresses should depend on the location of the dislocation loop, but not on the location of surfaces bounded by such loops that are devoid of physical significance. In the stationary case the line integral representation involves a ``vector potential'' that depends on the specific geometry of the sample, through its Green's function: a specific combination of derivatives of the elastic stress produced by the Green's function appropriate for the sample is divergenceless, so it is the curl of this ``vector potential''. This ``vector potential'' is explicitely determined for an isotropic half space and for a thin plate. Earlier specific results in these geometries are recovered as special cases. In the non stationary case a line integral representation can be obtained for the time derivative of the stress field. This, combined with the static result, assures a line integral representation for the time dependent stress field.

cond-mat.mtrl-sci↗

arXiv1997

Elastic fields of stationary and moving dislocations in finite samples

Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the stress fields, a line integral representation is found, thus showing rigorously the independence of the stress fields with respect to the choice of slip planes. In the stationary case the line integral representation involves calculating a "vector potential" dependent on the specific geometry of the sample. Two examples of geometries, isotropic half space and thin plate, are shown where the "vector potential" has been explicitly determined. With this general method one recovers some earlier specific results in these geometries.

cond-mat↗