Silk features exceptional mechanical properties such as high tensile strength and great extensibility, making it one of the toughest materials known. The exceptional strength of silkworm and spider silks, exceeding that of steel, arises from beta-sheet nanocrystals that universally consist of highly conserved poly-(Gly-Ala) and poly-Ala domains. This is counterintuitive because the key molecular interactions in beta-sheet nanocrystals are hydrogen bonds, one of the weakest chemical bonds known. Here we report a series of large-scale molecular dynamics simulations, revealing that beta-sheet nanocrystals confined to a few nanometres achieve higher stiffness, strength and mechanical toughness than larger nanocrystals. We illustrate that through nanoconfinement, a combination of uniform shear deformation that makes most efficient use of hydrogen bonds and the emergence of dissipative molecular stick-slip deformation leads to significantly enhanced mechanical properties. Our findings explain how size effects can be exploited to create bioinspired materials with superior mechanical properties in spite of relying on mechanically inferior, weak hydrogen bonds.

Nanoconfinement controls stiffness, strength and mechanical toughness of β-sheet crystals in silk

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Perspective: Coarse-grained models for biomolecular systems.

A gspeneral Expression for the yield surface of polycrystalline materials is developed. The proposed yield surface can describe both isotropic and anisotropic materials. The isotropic surface can be reduced to either the Tresca or von Mises surface if appropriate, or can be used to capture the yield behavior of materials (e.g. aluminum) which do not fall into either category. Anisotropy can be described by introducing a set of irreducible tensorial state variables. The introduced linear transformation is capable of describing different anisotropic states, including the most general anisotropy (triclinic) as opposed to existing criteria which describe only orthotropic materials. Also, it can successfully describe the variation of the plastic strain ratio (R-ratio), where polycrystalline plasticity models usually fail. A method for obtaining the material constants using only uniaxial test data is described and utilized for the special case of orthotropic anisotropy. Finally, the use of tensorial state variables together with the introduced mathematical formulation make the proposed yield function a very convenient tool for numerical implementation in finite element analysis.

A general anisotropic yield criterion using bounds and a transformation weighting tensor

https://repository.upenn.edu/cgi/viewcontent.cgi?article=1001&context=meam_papers

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

Fast multipole accelerated boundary integral equation methods

Hierarchical modeling of heterogeneous solids

An algorithmic closed-form solution is derived for Eshelby's problem for polygonal and polyhedral inclusions. Illustrative calculations are presented for two- and three-dimensional problems. Also it is proven that polyhedra with constant Eshelby's tensor do not exist.

Eshelby's inclusion problem for polygons and polyhedra

A boundary element method for solving three-dimensional linear elasticity problems that involve a large number of particles embedded in a binder is introduced. The proposed method relies on an iterative solution strategy in which matrix—vector multiplication is performed with the fast multipole method. As a result the method is capable of solving problems with N unknowns using only O(N) memory and O(N) operations. Results are given for problems with hundreds of particles in which N"O(105). ( 1998 John Wiley & Sons, Ltd.

A fast solution method for three‐dimensional many‐particle problems of linear elasticity

On the problem of linear elasticity for an infinite region containing a finite number of non-intersecting spherical inhomogeneities

We derive asymptotic expansions for the Green functions associated with coercive difference equations on general lattices. These expansions lead to rigorous methods for approximating the lattice Green functions by polyharmonic rational functions.

Gregory J. Rodin

Papers

Hierarchical modeling of heterogeneous solids

Eshelby's inclusion problem for polygons and polyhedra

A fast solution method for three‐dimensional many‐particle problems of linear elasticity

On the problem of linear elasticity for an infinite region containing a finite number of non-intersecting spherical inhomogeneities

Asymptotic expansions of lattice Green's functions