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Damage in soft biological tissues are a major domain of study as tissues may either undergo degradation with time or may experience in vivo failure during invasive procedures leading to a multitude of medical complications. Continuum damage models have been very successful recently to predict damage that can take place either due to fatigue loading, as a consequence of cyclic physiological loads or if the tissue is exposed to supra physiological loads especially during medical interventions. In this current work we use the mathematical framework of oblique contravariant tensors and their associated invariants to propose a damage function that takes into account the two important stages of progressive damage in collagen fibers (a) damage due to shear between matrix and fiber that can lead to debonding of the fibers and (b) total rupture of fibers. A model for the damage in the matrix has also been taken into account using the concept of equivalent stretch.The model was fitted with uniaxial experimental results from literature and showed very good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

In the present work, anr-hadaptive isogeometric analysis is proposed for plane elasticity problems. For performing ther-adaption, the control net is considered to be a network of springs with the individual spring stiffness values being proportional to the error estimated at the control points. While preserving the boundary control points, relocation of only the interior control points is made by adopting a successive relaxation approach to achieve the equilibrium of spring system. To suit the noninterpolatory nature of the isogeometric approximation, a new point-wise error estimate for theh-refinement is proposed. To evaluate the point-wise error, hierarchical B-spline functions in Sobolev spaces are considered. The proposed adaptiveh-refinement strategy is based on using De-Casteljau’s algorithm for obtaining the new control points. The subsequent control meshes are thus obtained by using a recursive subdivision of reference control mesh. Such a strategy ensures that the control points lie in the physical domain in subsequent refinements, thus making the physical mesh to exactly interpolate the control mesh and thereby allowing the exact imposition of essential boundary conditions in the classical isogeometric analysis (IGA). The combinedr-hadaptive refinement strategy results in better convergence characteristics with reduced errors thanr- orh-refinement. Several numerical examples are presented to illustrate the efficiency of the proposed approach. [ABSTRACT FROM PUBLISHER]