Blog posts

Contact express: a new approach for contact problems

Noe Reyes Rivas
Applied Mathematics, Brown University

Time: 11:00 am - 12:00 pm (EST), Feb. 05, Thursday

Zoom Meeting ID: 824 6447 8256

Passcode: 003801

Abstract

In this paper we formulate a geometric theory of elasticity and anelasticity for bodies containing material surfaces with their own elastic energies and distributed surface eigenstrains. Bulk elasticity is written in the language of Riemannian geometry, and the framework is extended to material surfaces by using the differential geometry of hypersurfaces in Riemannian manifolds.

Two-dimensional (2D) lattice materials with well-designed microstructures exhibit extraordinary properties such as zero and negative Poisson’s effects, and play a crucial role in industrial fields. However, inevitable defects from manufacturing, storage, transportation, and service may compromise their microstructures and functionalities. Therefore, it is important but still unclear: which microstructures and associated properties are most or least sensitive to defects.

Film-substrate systems are prevalent in various industries, and manipulation of their adhesion strength is essential to guarantee their desired functionalities. Inspired by the heterogeneous characteristic of geckos’ spatulae, heterogeneous adhesion devices are proposed for enhanced directional adhesion, but experimental measurements of their adhesion strength are significantly lower than the theoretical predictions. This discrepancy is likely due to the cohesive zone, a factor that was usually overlooked in previous theoretical models.

While the surface asperities of mineral platelets are widely believed to play important roles in stiffening, strengthening, and toughening nacre, their effects have not been thoroughly investigated. Here, a computationally efficient bar-spring model is adopted to simulate, as platelets with multiple interfacial asperities slide over each other, the tensile force versus elongation behaviors as well as the effective mechanical properties such as modulus, strength, and work-to-fracture in nacre or nacre-like composites.

Fast stress wave attenuation in composites is highly desired in many industry fields. Biological composites such as those in the beak of woodpeckers provide great inspiration for us to develop their synthetic counterparts with similar mechanical functions.

Interface plays a critical role in the mechanical performance of composites. Lack of a suitable interface design has long been a bottleneck impeding the full exploitation of the mechanical strengths of many superior reinforcement phases such as the high-performance carbon fibers and carbon nanotubes.

Nacre is well known for its high strength and toughness owing to its ingenious “brick-and-mortar” microstructure. However, its impact resistance has not been studied as well as its static properties, even though protecting fragile organs from external dynamic loadings is one of its most important functions.

Osteoporosis (OP), a skeletal disease making bone mechanically deteriorate and easily fracture, is a global public health issue due to its high prevalence. It has been well recognized that besides bone loss, microarchitecture degradation plays a crucial role in the mechanical deterioration of OP bones, but the specific role of microarchitecture in OP has not been well clarified and quantified from mechanics perspective.

Based on the theory of composite mechanics, a three-pillar framework “bone mass-microarchitecture-tissue property” instead of “bone mass-bone quality”, is proposed to quantitively characterize the mechanical deterioration of osteoporotic cancellous bones related to the three aspects, and accordingly the individual and integrative influences of bone mass, microarchitecture and tissue property on the mechanical properties of cancellous bones are investigated via the μCT-based finite element method (