There are numerous aspects in the mathematical modeling of vacuum spacetime in Cosmology. Gravitation and electromagnetism are the two actions-at-distance phenomenological fields occurring in a vacuum (without mediating matter with infinite radius).  Nowadays, since the works of Permutter et al. [1] and Riess et al. [2], one of the biggest challenges in cosmology is to understand the physics behind the acceleration of the universe expansion, assumed to be due to an unknown dark energy and also the Universe missing mass assumed to be a dark matter required for maintaining the whole Universe. The Cosmological Constant was classically introduced ad hoc to explain the dark energy. 

The main motivation of the present paper is to develop a mathematical model of Generalized Continuum for analyzing the link between spacetime continuum, gravitation and electromagnetism with the only necessary three phenomenological fields on vacuum spacetime by avoiding micro-particles physics and cosmological fluids, despite their preeminent role in cosmology. The main application is to attempt to explain the concept of dark energy and dark matter. The work rather focuses only on phenomenological fields occurring in a vacuum Universe as a continuum. 

The present paper is based some fundamental assumptions to define the geometrical background of a Generalized Continuum model and the physical events occurring within it [3] : (1) the spacetime has a structure of differentiable four-dimensional manifold endowed with a metric, and independent connection with torsion; (2) only gravitation and electromagnetism are considered as physical fields, since they are the only actions-at-distance among the four universal fundamental forces [4]. The action is composed of the Einstein-Hilbert-Palatini (for gravitation) and Yang-Mills (for electromagnetism) Lagrangians.

The general methodology consists of exploiting the geometric structure of spacetime continuum by reminding Riemann and developing Riemann-Cartan manifolds. Accounting for the torsion field in addition to macroscopic deformation (metric and strain) was inspired from the work of Rainich (1925) [5] and Misner & Wheeler (1957) [6] by adding the property of multiply-connectedness to usual Riemann manifold in the framework of continuum mechanics. These two works were themselves inspired by the works of V. Volterra on dislocations and disclinations (1901) [7]. 

The idea is to reduce the phenomena of gravitation and electromagnetism to the geometric variables  as curvature and torsion fields on the continuum. Torsion will be a matter of concern all along this work, and implicitly we show that spacetime is more and more assimilated to an infinitely small sets of microcosms, as due to brusque cooling of the Universe at the beginning. Mathematical models extending the usual framework for field equation in classical continuum mechanics are developed within the Einstein-Cartan geometric background [8]. 

For the application in Cosmology, the introduction of an ad hoc hypothetical Cosmological Constant is no more necessary as shown by our results. Models nevertheless show the presence of non homogeneous and anisotropic fields definitely replacing an hypothetical Cosmological Constant. 

In sum, only electromagnetic and gravitational fields coupled with Generalized Continuum model might be sufficient to describe dark energy and by the way dark matter by means of the torsion field of the vacuum spacetime [8]. 

It is well sound that the rigorous formulation of equations governing complex materials, where multi-scale and multi-physics phenomenon are present, still remains a big challenge in continuum mechanics e.g. [1]. Distribution of line and surface defects as dislocations and disclinations in the material implies such difficulties. Indeed, the classical divergence of a stress tensor as originally developed by Cauchy requires some subtil conditions which might sometimes underestimated. Such is the case when distribution of defects (i.e. elastoplasticity) occurs within an otherwise virgin material.

The goal of this work is to derive the generic shape of conservation laws, specially equilibrium equations of such complex material in mechanics. 

First, any mathematical equations governing physics models should be invariant under passive diffeomorphisms (i.e. change of coordinate system). We then propose a mathematical model of generalized continuum described by Lagrangian depending on metric, torsion and curvature of a Riemann-Cartan manifold [2]. 

Second, generic conservation laws of Noll first-gradient continuum (deduced rigorously by Lie derivative of metric) are extended to such generalized continuum by using active diffeomorphisms deduced by Lie derivatives of metric, torsion and curvature. The method thus uses the so-called Principle of General Covariance, based on these derivatives along a non-uniform vector field e.g.  [3].

The present work although devoted to conservation laws lies heavily on the geometric approach of generalized continuum. The main concern is then the derivation of equilibrium equations in various situations, and with some applications to defected materials or even other physics as gravitation. If time is allowed some application in coupled physics as electromagnetism will be sketched. Some hints for the use of non-smooth elastioplasticity may be presented.