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Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…

The purpose of this paper is twofold. Firstly, we conduct an in-depth analysis of mathematical modeling concerning thermal-mechanical curved beams, by taking into consideration three primary forces widely accepted in the literature: axial…

A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…

The linear-$T$ resistivity is one of the hallmarks of various strange metals regardless of their microscopic details. Towards understanding this universal property, the holographic method or gauge/gravity duality has made much progress.…

A unified thermodynamic framework for characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The…

The low temperature acoustic and thermal properties of amorphous, glassy materials are remarkably similar. All these properties are described theoretically with reasonable quantitative accuracy by assuming that the amorphous solid contains…

We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…

A standard elasto-plasto-dynamic model at finite strains based on the Lie-Liu-Kr\"oner multiplicative decomposition, formulated in rates, is here enhanced to cope with spatially inhomogeneous materials by using the reference (called also…

We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…

We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter. All results are illustrated with the example of…

This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first…

The notions of uniformity and homogeneity of elastic materials are reviewed in terms of Lie groupoids and frame bundles. This framework is also extended to consider the case Functionally Graded Media, which allows us to obtain some…

Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…

Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for…

Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular,…

Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…

In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…

A law previously found for shear moduli of crystalline materials is developed and extended to all elastic moduli in solids and structures. Shear moduli were previously shown to depend only on specific volume. The bulk moduli of many…

An elasto-plastic model for concrete, based on a recently-proposed yield surface and simple hardening laws, is formulated, implemented, numerically tested and validated against available test results. The yield surface is smooth and…