The fracture toughness (characterized by the critical energy release rate Gc) of interfaces between polystyrene (PS) and poly(2-vinylpyridine) (PVP) reinforced with poly(styrene-6-2-vinylpyridine) was measured with a double cantilever beam test geometry. The effect of the PVP block degree of polymerization (Wpvp) and the areal density of block copolymer chains at the interface (2) on the measured Gc and on the fracture mechanisms was investigated quantitatively. The PS degree of polymerization (Alps) was kept >280, while Alpvp was varied between 45 and 870. For Afpvp below 200 the interfaces showed only a small increase in Gc with increasing 2 and failed by pull-out of the short PVP chain. In this regime Gc increases linearly with 2 and scales roughly with New2, in reasonable agreement with a recently proposed model of failure by chain pull-out.1 If Npw was increased well above 200, corresponding roughly to the average molecular weight between entanglements for the PVP, two separate fracture mechanisms could be distinguished. At low values of 2, Gc increased only slowly with 2 and the interfaces failed by scission of the copolymer chains near the joint between the two blocks. At higher values of 2, the interfaces fractured by first forming a stable craze ahead of the propagating crack tip, giving rise to much higher values of the measured fracture toughness.In this regime, Gc scaled with 2,^, an areal density of chains with at least one "effective" entanglement, in very good agreement with a model recently proposed by Brown2 for failure by craze fibril breakdown.

Stamp deformation can affect the dimensional stability of the microcontact printing process. We consider limitations imposed due to reversible deformation of a single stamp. Detailed analyses of several modes of stamp deformation have been carried out. Stability criteria have been obtained for both vertical and lateral collapse of surface relief features, including buckling. The shape change of surface features imposed by surface tension has been analyzed, and the corresponding internal stresses are given in closed form. The residual stresses induced by chemical and thermal shrinkage when the elastomeric stamp is bonded to a stiff substrate are analyzed. In addition, the relation between applied load and displacement of a stamp supported by a stiff substrate is given in closed form. Contact stresses between the stamp and substrate have been analyzed both analytically and numerically by a finite element method. The role of adhesion in determining the contact area is clarified. The effect of surface roughness on the contact mechanics has been studied, and closed form solutions have been obtained for surface asperities that are periodically distributed. The contact mechanics of stamps with smooth relief features has been studied, and the dependence of contact area on the work of adhesion and the applied pressure is given in closed form. The force required to separate the stamp from the substrate has been estimated using a fracture mechanics approach. The stability and contact mechanics results are summarized by a stability and contact map.

This paper explores the contact behaviour of simple fibrillar interfaces designed to mimic natural contact surfaces in lizards and insects. A simple model of bending and buckling of fibrils shows that such a structure can enhance compliance considerably. Contact experiments on poly(dimethylsiloxane) (PDMS) fibrils confirm the model predictions. Although buckling increases compliance, it also reduces adhesion by breaking contact between fibril ends and the substrate. Also, while slender fibrils are preferred from the viewpoint of enhanced compliance, their lateral collapse under the action of surface forces limits the aspect ratio achievable. We have developed a quantitative model to understand this phenomenon, which is shown to be in good agreement with experiments.

In native states, animal cells of many types are supported by a fibrous network that forms the main structural component of the ECM. Mechanical interactions between cells and the 3D ECM critically regulate cell function, including growth and migration. However, the physical mechanism that governs the cell interaction with fibrous 3D ECM is still not known. In this article, we present single-cell traction force measurements using breast tumor cells embedded within 3D collagen matrices. We recreate the breast tumor mechanical environment by controlling the microstructure and density of type I collagen matrices. Our results reveal a positive mechanical feedback loop: cells pulling on collagen locally align and stiffen the matrix, and stiffer matrices, in return, promote greater cell force generation and a stiffer cell body. Furthermore, cell force transmission distance increases with the degree of strain-induced fiber alignment and stiffening of the collagen matrices. These findings highlight the importance of the nonlinear elasticity of fibrous matrices in regulating cell-ECM interactions within a 3D context, and the cell force regulation principle that we uncover may contribute to the rapid mechanical tissue stiffening occurring in many diseases, including cancer and fibrosis.cell traction force | 3D cell traction force microscopy | fibrous nonlinear elasticity | cell-ECM interaction | collagen A nimal cells of most cell types, including breast tumor cells, are supported structurally by a fibrous ECM within a 3D context (1, 2). Cells adhere to the fibers via the linkages between integrin receptors on the membrane surface and the adhesion molecules within the ECM. To migrate, cells pull/push along the fibers or squeeze through the pore structure of the network (3). The tensional balance between the cell and the ECM critically regulates many physiological and pathological processes, including immune response, tissue formation, and tumor progression (4-7). In the breast tumor, stiffening of the mechanical environment disrupts force balance between epithelial cells and the ECM, promoting a malignant phenotype (5, 8). Tumors stiffen as cells deposit more collagen than they digest (9-11), increasingly express cross-linking enzymes (8, 12), and exert traction forces to reorganize the ECM (13).The main structural component of the ECM is a network of cross-linked protein fibers. The fiber network aligns, stiffens, and sometimes, undergoes permanent changes when subjected to strain (14, 15). These adaptive mechanical properties of the fiber network provide cells entry points to modify their local microenvironment (16-18) and as such, perform physiologically realistic functions (1,3,(19)(20)(21)(22)(23). It has been reported that the nonlinear elasticity of fibrous matrices enables cells to transmit forces over distances of hundreds of micrometers, facilitating long-range communication between individual cells (24-26) and between tumor spheroids (27). Recent work has shown that individual cells are capable of stiffening the...

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play an central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses causes dramatic departures from classic theories for wetting (Young-Dupré), adhesion (Johnson-Kendall-Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.