Related papers: Equivalent Strain in Simple Shear Deformations
For homogeneous, isotropic, nonlinearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress is derived here for both compressible and incompressible materials. It is shown that…
In a 2012 article in the International Journal of Non-Linear Mechanics, Destrade et al. showed that for nonlinear elastic materials satisfying Truesdell's so-called empirical inequalities, the deformation corresponding to a Cauchy pure…
The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…
The microstructure and mechanical properties of materials saturate to steady states after severe plastic deformation (SPD). Despite the well-known effect of temperature on the steady-state microstructure, there is no general agreement on…
We test some Hooke-like isotropic hyper-/hypo-elastic material models under finite simple shear deformations (cf., Thiel et al. Int. J. Non-linear Mech. 112: 57--72, 2019) and show that (1) the components of the Cauchy stress tensor for any…
In this note we extend White's deformation theorem for G-flat chains to the setting of G-flat tensor chains. As a corollary we obtain that the groups of normal tensor chains identify with some subgroups of normal chains. Moreover the…
Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an…
Twinning is an important deformation mode of hexagonal close-packed metals. The crystallographic theory is based on the 150-years old concept of simple shear. The habit plane of the twin is the shear plane, it is invariant. Here we present…
We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear…
Electron group velocity for graphene under uniform strain is obtained analitically by using the Tight-Binding approx- imation. Such closed analytical expressions are useful in order to calculate electronic, thermal and optical properties of…
Recently, Chuanying Li, Tao Fu, Xule Li, Hao Hu, and Xianghe Peng in [Phys. Rev. B 107, 224106] investigated the mechanical behavior of cubic HfC and TaC under simple shear (SS) and pure shear (PS) using first-principles calculations.…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
This paper, originally motivated by a question raised by Wood and Hanna [Soft Matter, 15, 2411 (2019)], shows that pure measures of bending for soft plates can be defined by introducing the class of bending-neutral deformations, finite…
When amorphous solids are subjected to simple or pure strain, they exhibit elastic increase in stress, punctuated by plastic events that become denser (in strain) upon increasing the system size. It is customary to assume in theoretical…
It is well known that a state of pure shear has distinct sets of basis vectors or coordinate systems: the principal axes, in which the stress is diagonal, and pure shear bases, in which diag(stress)=0. The latter is commonly taken as the…
The influence of cyclic loading and glass stability on structural relaxation and yielding transition in amorphous alloys was investigated using molecular dynamics simulations. We considered a binary mixture cooled deep into the glass phase…
We present a detailed study of rectilinear shear deformation in the framework of orthotropic nonlinear elasticity, under Dirichlet and mixed-boundary conditions. We take a slab made of a soft matrix, reinforced with two families of…
Experiments test the dependence of shearing stress on the first two gradients of shear strain. The tests were conducted by direct numerical simulation using the Discrete Element Method (DEM) on a large two-dimensional (2D) assembly of…
The Discrete elastic rod method (Bergou et al., 2008) is a numerical method for simulating slender elastic bodies. It works by representing the center-line as a polygonal chain, attaching two perpendicular directors to each segment, and…
Strain is powerful for discovery and manipulation of new phases of matter; however, the elastic strains accessible to epitaxial films and bulk crystals are typically limited to small ($<2\%$), uniform, and often discrete values. This…