Engineering the undamageable material: Hyperelastic insights from biological tissues

This article introduces a comprehensive theoretical and computational framework for undamageable materials , a new class of systems that resist the initiation and accumulation of irreversible degradation under repeated loading. Drawing on multiscale design principles inspired by biological tissues, the concept integrates nanoscale crack deflection, microscale fiber reconfiguration, and macroscale adaptive chemistry to suppress damage evolution entirely. The model is implemented within the continuum mechanics framework, incorporating nonlinear elasticity, evolving internal variables, and bioinspired architecture. Two numerical examples are presented to illustrate the predictive capacity and physical insight of the formulation: (1) the dynamic response of aortic tissue under a quasi-static tensile load, and (2) the quasi-static compression behavior of swine brain tissue. Both simulations demonstrate the feasibility of achieving undamageable-like responses in soft biological materials through controlled hierarchical structuring. In the first example, the aorta is modeled as an undamageable hyperelastic composite, where collagen fiber realignment and reversible matrix reconfiguration prevent microstructural fatigue. The resulting stress–strain response exhibits full recovery over thousands of cycles, reproducing the self-preserving elasticity observed experimentally in arterial walls. In the second example, undamageable behavior is examined in swine brain tissue subjected to large deformations. The proposed constitutive model captures the tissue's remarkable resilience to permanent damage through energy dissipation and internal reorganization of microstructural networks. These results confirm that the undamageable material framework not only describes an idealized limit of damage-free performance but also provides a powerful tool for interpreting and replicating the extraordinary endurance of biological tissues.