Systematic remarks on objectivity and frame-indifference,liquid crystal theory as an example

In this paper objectivity and material frame-indifference are systematically discussed, because changing the observer and changing the motion of a material with respect to an observer independent standard frame of reference have to be distinguished carefully. Objectivity and observer invariance of the physical laws and of the constitutive mappings are introduced. Semi-objectivity and objectivity of different time derivative operators are investigated. As examples, changing the observer in liquid crystal theory and changing the motion in linear heat conducting materials is considered.     

On The Objective Corotational Rates of Eulerian Strain Measures

In the present paper, some new basis-free expressions for an arbitrary objective corotational rate of the general Eulerian strain measures are provided which are in compact form. Moreover, a complete discussion on the requirements for the continuity of the objective corotational rates are presented.      

Quantification in histopathology—Can magnetic particles help?

Every year, more than 270,000 people are diagnosed with cancer in the UK alone; this means that one in three people worldwide contract cancer within their lifetime. Histopathology is the principle method for confirming cancer and directing treatment. In this paper, a novel application of magnetic particles is proposed to help address the problem of subjectivity in histopathology. Preliminary results indicate that magnetic nanoparticles cannot only be used to assist diagnosis through improving quantification but also potentially increase throughput, hence offering a way of dramatically reducing costs within the routine histopathology laboratory.     

An objective rotation tensor applied to non-Newtonian fluid mechanics

To develop objective constitutive equations, local frames which translate and rotate with the fluid particle can be used. For example, the corotating frame rotates such that the curl of the velocity calculated in this frame vanishes. From the corotating frame, the Jaumann derivative can be derived. In this paper, a new local frame is developed which causes the cross product of the velocity and acceleration to vanish and is designated as the rigid-rotating frame. The corotating and rigid-rotating frames rotate identically for a rigid-body rotation of the fluid, but rotate differently in flows that contain shearing. This difference in rotation can be used to develop an objective rotation tensor that can be applied to constitutive equations for viscoelastic liquids. The rigid-rotating frame can also be used to develop a rheological time derivative which has been designated the rigid-rotating derivative. These new quantities expand the traditional set of kinematical variables and invariants available for use in constitutive equations. Use of this expanded set of kinematic variables is demonstrated in limiting constitutive equations. Received: 1 March 1999 Accepted: 5 March 1999     

Framework for non-coherent interface models at finite displacement jumps and finite strains

This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the displacement jump. This constraints the ability to model shear and, in addition, anisotropic effects are excluded. A novel, extended constitutive framework which is consistent with the above mentioned fundamental physical principles is elaborated in this paper. In addition to the classical tractions associated with a cohesive zone model, the main idea is to consider additional tractions related to membrane-like forces and out-of-plane shear forces acting within the interface. For zero displacement jump, i.e. coherent interfaces, this framework degenerates to existing formulations presented in the literature. For hyperelasticity, the Helmholtz energy of the proposed novel framework depends on the displacement jump as well as on the tangent vectors of the interface with respect to the current configuration – or equivalently – the Helmholtz energy depends on the displacement jump and the surface deformation gradient. It turns out that by defining the Helmholtz energy in terms of the invariants of these variables, all above-mentioned fundamental physical principles are automatically fulfilled. Extensions of the novel framework necessary for material degradation (damage) and plasticity are also covered.