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Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…

Thermodynamic formulas for investigating systems with density and/or temperature dependent particle masses are generally derived from the fundamental derivation equality of thermodynamics. Various problems in the previous treatments are…

We present a Total Lagrangian finite element framework for finite-deformation multibody dynamics. The framework combines a compact kinematic representation, a deformation-gradient-based formulation, an element-agnostic constitutive…

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an…

A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving…

A simple and effective approach to thermodynamics is suggested, which solves the major difficulties in the traditional presentation of the subject. The internal energy is introduced from the behavior of deformable bodies, whereas the…

Second gradient theories have to be used to capture how local micro heterogeneities macroscopically affect the behavior of a continuum. In this paper a configurational space for a solid matrix filled by an unknown amount of fluid is…

Repeat observations provide essential constraints on long-term changes in the ocean interior, such as warming and cooling trends. However, attributing these Eulerian signals to either reversible isopycnal heaving or irreversible diabatic…

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant…

We study the classical electrodynamics of extended bodies. Currently, there is no self-consistent dynamical theory of such bodies in the literature. Electromagnetic energy-momentum is not conserved in the presence of charge and some…

The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic…

An irreversible thermodynamical theory of solids is presented where the kinematic quantities are defined in an automatically objective way. Namely, auxiliary elements like reference frame, reference time and reference configuration are…

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can…

In this paper we present a new local Lagrangian approximation to the gravitational dynamics of cold matter. We describe the dynamics of a Lagrangian fluid element through only one quantity, the deformation tensor. We show that this tensor…

There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…

The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…

Employing the finite element and computational fluid dynamics methods, we have determined the conditions for the fragmentation of space bodies or preservation of their integrity when they penetrate into the Earth's atmosphere. The origin of…

In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes…

Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows…