Increasing requirements on the durability of road pavements demand the conception of innovative asphalt types. Particularly the stability under load needs improvement in order to prevent rutting. Since the load bearing capabilities of asphalt are mainly governed by the granular lattice and the binder that glues the rocks together, simulation based approaches that aim on supporting R&D in road engineering must capture the granulometry of the material. A Voronoi tesselation based description of the structure is proposed that enables the separate modelling of grains and binder as continuous materials and attempts to accurately reproduce those features. First, a neat Voronoi tesselation is created within the modelling domain. These irregular convex polyhedra representing the grains are subsequently subject to a shrinking process and further modified to accurately represent the granulometric distribution of real asphalt types. Now, the space between the grains can be used for a volumetric representation of the binder. Full-field strain measurements during the indirect tensile test of mastic asphalt, stone mastic asphalt and asphalt concrete have been performed for validation of the approach.

A fully covariant formulation for a hyperelastic solid as a four-dimensional space-time manifold is presented. It admits arbitrary coordinate transformations mixing space and time. The geometrical structure of the manifold is represented by a tetrad field. A variational formulation is given which uses the tetrad field as extra dependent variables. This formulation is able to describe a homogeneous stress state in a defect-free crystal lattice.Moving defects in solids are described by functions depending on material coordinates and time. Therefore, four-dimensional formulations of a material space-time manifold have been discussed (cf. e. g. [1][2][3][4][5]). If time-like material quantities are used, they are usually put under constraint. Epstein et al.[5] call this constraint "time consistency condition" and themselves call it into question. In this paper, the constraint is released and the now undetermined quantities are taken as new field variables. Physical space-timeThe physical space-time is the space-time of special relativity with one time-like and three space-like coordinates. The transition to general relativity is straightforward. The coordinates are denoted by x i , i = 0, 1, 2, 3. Indices belonging to physical space-time are denoted by latin minuscules in the range i, j, k, l, m. In an inertial system with cartesian space-like coordinates, we can set (c L is the velocity of light) x 0 = c L t, x 1 = x, x 2 = y, x 3 = z. The geometric structure is represented by the pseudo-Euclidian metric with components η ij = diag(−1; 1; 1; 1) in Galilean coordinates. The transformation to another inertial system does not change the structure of the metric. This represents the fact that there is no preferred timedirection in physical space-time.

The concept of material forces is well established in the continuum theory of defects. These forces are quantities in a threedimensional material manifold. The manifold can be augmented to a four-dimensional material space-time by a time-like coordinate.The inelastic phenomena caused by moving defects are highly dissipative. So a thermodynamic theory in material spacetime seems to be indispensable. Some first steps towards such a theory are developed here.

In a material space‐time manifold an expression for the entropy production is developed. It is based on a Lagrangian formulation for a hyperelastic solid. The material structure and heat transfer are represented by a tetrad field. The derivatives of the Lagrangian with respect to the time‐like vector of the tetrad yields entropy density and current. An identity for the divergence of this four‐current follows from the invariance of the Lagrangian and yields the entropy production due to heat transfer and defect movement. The latter part only depends on a kind of deviatoric stress if the conservation of mass is considered. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The well established continuum theory of lattice defects is usually formulated in a three-dimensional material space. The defects are represented by differential geometric properties of the material manifold. Moving defects lead to differential geometric quantities changing with time. This motivates to augment the three space-like coordinates in the material space by a time-like coordinate to a four-dimensional manifold. The lattice vectors of a crystalline solid represent three space-like vectors in the material manifold. They can be completed to a tetrad field by a fourth time-like vector. The additional components of the tetrad are related to temperature and heat flux. The derivatives of the Lagrangian density for a hyper-elastic solid with respect to the components of the tetrad can be arranged in a four-dimensional second-order tensor in which entropy density and current are coupled to material momentum. The representation of entropy production leads to a Cattaneo type constitutive equation for heat transfer.