A computational model for large deformations of composites with a 2D soft matrix and 1D anticracks

Abstract

• Anticracks are rigid line inclusions in a two-dimensional deformable matrix. • For the first time, we present a meshfree method without remeshing for anticracks. • The matrix undergoes finite deformation, with anticracks moving rigidly. • The method matches available analytical solutions for stress intensity factors. • The method can handle nonlinear constitutive models and multiple anticracks. Anticracks (also known as rigid line inclusions) occur frequently in a variety of natural and engineered composites as very stiff and extremely sharp (almost zero-thickness) fibers or lamellae embedded in a softer matrix. In the linear elastic regime, similarly to cracks, anticracks generate a singularity in the stress distribution around the tip. Because of this similarity, existing analytical techniques and solutions (for simple cases) can be easily translated to anticracks. However, despite their importance in many biological and engineering composites, there has been surprisingly little development of numerical methods that would account simultaneously for the presence of multiple fibers or lamellae, arbitrary loadings and nonlinear behavior of the matrix. This paper presents the first numerical approach for rigid line inclusions, based on a meshfree scheme recently developed for multiple crack growth in elastic media. The inclusion of zero thickness is created as a crack, and a rigid motion (rotation and translation) is enforced at the anticrack faces. The equations of motion are solved according to a Total Lagrangian framework, and the matrix supposed hyperelastic. Contrarily to available analytical solutions, the degrees of freedom of the rigid motion are determined a posteriori as a consequence of the (discretized) elastic equilibrium, expressed in a variational approach. Results show that the proposed approach match well the analytical solutions and provides accurate stress intensity factors (SIFs) for relatively little computational cost. Moreover, the method can reproduce some peculiar features of the anticracks: unlike cracks, singularities also appear under compressive and parallel loads; moreover, for a certain combination of biaxial load, stress concentrations disappear. Finally, the paper presents examples drawn from biological and engineering composites: the reorientation of one or more fibers under large strains, resulting in a smart stiffening and strengthening mechanism. Reorienting towards the direction of applied load has structural importance since reinforcements can have the most effectiveness in withstanding loads. If the matrix is compliant, the reorientation is eased.