Exact and linearized refractive index stress-dependence in anisotropic photoelastic crystals

For the permittivity tensor of photoelastic anisotropic crystals, we obtain the exact nonlinear dependence on the Cauchy stress tensor. We obtain the same result for its square root, whose principal components, the crystal principal refractive index, are the starting point for any photoelastic analysis of transparent crystals. From these exact results we then obtain, in a totally general manner, the linearized expressions to within higher-order terms in the stress tensor for both the permittivity tensor and its square root. We finish by showing some relevant examples of both nonlinear and linearized relations for optically isotropic, uniaxial and biaxial crystals.

Static and modal analysis of a deep soil loosening machine

The article will present a static analysis of the equipment in order to calculate the vector field distribution of the relative resulting displacement in the structure, the Cauchy stress tensor and tensor fields distribution of the specific deformation in the same structure. This is done in order to improve the structure and highlight the most vulnerable points within an equipment depending on the way of working. After performing the static analysis, tensometric marks were mounted in the most vulnerable points to calculate the displacement of the material and to calculate the major forces that appeared in the structure during the field experiments. At the same time, the idea of the equipment prototype was to improve the equipment with vibrating elements on the working bodies of the body type in order to increase the degree of crushing and to reduce the advancing forces, respectively to reduce the fuel consumption. Therefore, a modal analysis was performed to calculate the vibrations that appeared in the structure in order not to resonate with the frequency of the motor mounted on the working member.

Verification of Continuum Mechanics Predictions with Experimental Mechanics

The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler–Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler–Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al–SiC composite material is carried out. Furthermore, it is proven that the Euler–Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill–Mandel sense by solving an identification problem of the constitutive model of urethane rubber.

Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth

We deal with flows of non-Newtonian fluids in three-dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by a power index [Formula: see text], we establish regularity properties of a solution with respect to time variable. Consequently, we can use this better information for showing the uniqueness of the solution provided that the initial data are good enough for all power–law indices [Formula: see text]. Such a result was available for [Formula: see text] and therefore the paper fills the gap and extends the uniqueness result to the whole range of [Formula: see text]’s for which the energy equality holds.

A Stability Estimate for Robin Boundary Coefficients in Stokes Fluid Flows

In this report, we examine the unsteady Stokes equations with non-homogeneous boundary conditions. As an application of a Carleman estimate, we first establish log type stabilities for the solution of the equations from either an interior measurement of the velocity, or a boundary observation depending on the trace of the velocity and of the Cauchy stress tensor measurements on a part of the boundary. We then consider the inverse problem of determining the time-independent Robin coefficient from a measurement of the solution and of Cauchy data on a sub-boundary.

A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations

Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress–strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.