An approach to weak balance laws in Continuum Mechanics is presented, involving densities with only divergence measure, which relies on the balance of power. An equivalence theorem between Cauchy powers and Cauchy fluxes is proved. As an application of this method, the construction of the stress tensor when the body is an orientable differential manifold is achieved under very general assumptions.

1. Preliminary concepts: Definitions and theoretical framework 2. Kinematics of deformation 2.1. The continuum setting: Mathematical description 2.2. Displacement, deformation and motion 2.3. Stretch, shear and strain 2.4. Change of reference frame and objective tensors 3. Balance laws 3.1. Mass and conservation of mass 3.2. Force, torque and theory of stress 3.3. Euler’s laws of motion 3.4. En...

Correction of the present defect in quantum education throughout the world must be performed by the new breakthrough in quantum mechanics which was re ntly achieved due to the inverse problem approach. It allows finding infinite (!) number of exactly solvable mod ls instead of only about ten previously known about 100 years. It means an incomparable more convenient bas or the quantum education ...

The recent appearance of nonlocal methods is examined in the light of traditional continuum mechanics. A comparison of nonlocal approaches in the fields of solid and fluid mechanics reveals that no consistent definition of a nonlocal theory has been used. We suggest a definition based on the violation of the principle of local action in continuum mechanics. From the consideration of the implica...

Hippo effectors YAP/TAZ act as on-off mechanosensing switches by sensing modifications in extracellular matrix (ECM) composition and mechanics. The regulation of their activity has been described by a hierarchical model in which elements of Hippo pathway are under the control of focal adhesions (FAs). Here we unveil the molecular mechanism by which cell spreading and RhoA GTPase activity contro...

We derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background. This also leads to a cluster expansion for the effective dielectric constant. It is shown that the cluster integrals of any order are absolutely convergent, so that the dielectric constant is well defined and independent of the shape of the...

Collective cell behaviors in migration and force generation were studied at the mesoscopic-level using cells grown in a 3D extracellular matrix (ECM) simulating tissues. Magnetic resonance imaging (MRI) was applied to investigate dynamic cell mechanics at this level. MDCK, NBT2, and MEF cells were embedded in 3D ECM, forming clusters that then migrated and generated forces affecting the ECM. Th...

The paper discusses the effort carried out at VNIIEF to consider the applicability of unstructured Lagrange meshes to multidimensional continuum mechanics problems with high shear strain and vortex flows. Three finite-difference numerical techniques for solving continuum mechanics problems on polyhedral unstructured Lagrange meshes are described. Examples of numerical calculations of benchmark ...

1. Basic Results in Continuum Mechanics 1.1. Kinematics 1.2. Stress Tensors and Balance of Momenta 1.3. Energy Balance Principle and Entropy Inequality 1.4. Fundamental Principles of Constitutive Models 2. Elastic and Hyperelastic Materials 2.1. Isotropic Hyperelastic Materials 2.2. Constitutive Models for Fiber-Reinforced Hyperelastic Materials 2.3. Examples of Numerical Applications 3. Elasto...

Desmosplasia is a characteristic of most solid tumors and leads to fibrosis through abnormal extracellular matrix (ECM) deposition, remodeling, and posttranslational modifications. The resulting stiff tumor stroma not only compromises vascular integrity to induce hypoxia and impede drug delivery, but also promotes aggressiveness by potentiating the activity of key growth, invasion, and survival...