Material Instabilities in Continuum Mechanics, and Related Mathematical Problems

Continuum mechanics studies of plastic instabilities

2014 The continuum mechanics framevork for analyzing necking and shear band instabilities is discussed. The predicted onset of instability depends sensitively on the material’s constitutive characterization, not only through properties, such as strain hardening and strain rate sensitivity, that can be measured in proportional loading tests, but also through the material’s response to a change i...

SPENCER OPERATOR AND APPLICATIONS: From Continuum Mechanics to Mathematical physics

Let us revisit briefly the foundation of n-dimensional elasticity theory as it can be found today in any textbook, restricting our study to n = 2 for simplicity. If x = (x, x) is a point in the plane and ξ = (ξ(x), ξ(x)) is the displacement vector, lowering the indices by means of the Euclidean metric, we may introduce the ”small” deformation tensor ǫ = (ǫij = ǫij = (1/2)(∂iξj + ∂jξi)) with n(n...

Some Topics from Continuum Mechanics Related to Brain Neuro-mechanics

A number of topics from continuum mechanics are presented that are useful in developing mathematical models of brain neuromechanics. Part I reviews basic concepts used to describe deformation or distortion of brain tissue, strains, stresses, their connection and material stiffness. Part II presents concepts from viscoelasticity used to describe the time dependent response of brain tissue such a...

Weak or Strong On Coupled Problems in Continuum Mechanics

‌Progressive Damage Analysis of Laminated Composites using Continuum Damage Mechanics

In this paper, progressive damage and global failure of composite laminates under quasi-static, monotonic loading are investigated using 3D continuum damage mechanics. For this purpose, a finite element program has been developed using an eight-node 2D layered element including layer-wise plate theory. Damage analysis of a single orthotropic layer under various uniform in-plane and transverse l...