Computational modeling of crack-tip fields in transversely isotropic strain-limiting solids subjected to piecewise linear slope loads

TL;DR

This study models crack-tip fields in transversely isotropic strain-limiting solids under piecewise linear slope loads, using nonlinear constitutive relations and finite element methods to analyze the effects of boundary conditions and fiber orientations.

Contribution

It introduces a nonlinear strain-limiting framework combined with finite element analysis to investigate crack-tip behavior under complex boundary loads in anisotropic materials.

Findings

Piecewise slope boundary loads influence crack-tip stress fields.

Fiber orientation affects crack-tip response in the material.

The nonlinear model eliminates non-physical strain singularities.

Abstract

Crack-tip fields within a transversely isotropic strain-limiting elastic body are investigated under the influence of piecewise linear slope boundary loads. The mechanical response is characterized via a nonlinear constitutive framework relating the Cauchy stress to the linearized strain, by which non-physical strain singularities at the crack tip are eliminated. The governing system is formulated as a quasi-linear elliptic boundary value problem in terms of the displacement field and is solved utilizing a continuous Galerkin finite element method coupled with a Picard linearization scheme. Boundary conditions are prescribed such that the vertical displacement varies piecewise linearly along the top and bottom edges, exhibiting opposite slopes on each half of the boundary. Numerical results are derived for two distinct fiber orientations. It is demonstrated that piecewise slope loads provide a flexible and realistic configuration for elucidating the interplay between strain-limiting behavior and crack-tip mechanics in transversely isotropic media.