This is a review on the emergent field of topological mechanics, where concepts from
electronic topological states of matter are applied to mechanics. We focus on the …

Articular cartilage is a remarkable material able to sustain millions of loading cycles over
decades of use outperforming any synthetic substitute. Crucially, how extracellular matrix …

This article investigates phonons and elastic response in randomly diluted lattices
constructed by combining (via the addition of next-nearest bonds) a twisted kagome lattice …

Amorphous solids may resist external deformation such as shear or compression, while they
do not present any long-range translational order or symmetry at the microscopic scale. Yet …

The discontinuous jump in the bulk modulus B at the jamming transition is a consequence of
the formation of a critical contact network of spheres that resists compression. We introduce …

Disordered spring networks can exhibit rigidity transitions, due to either the removal of
material in over-constrained networks or the application of strain in under-constrained ones …

We cast a nonzero-temperature analysis of the jamming transition into the framework of a
scaling ansatz. We show that four distinct regimes for scaling exponents of thermodynamic …

Training materials through periodic drive allows us to endow materials and structures with
complex elastic functions. As a result of the driving, the system explores the high …

The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid,
is associated with a rearrangement of the low-frequency vibrational spectrum. In this Letter …

Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling
properties. In a companion article, we have presented comprehensive new results for the …