Unconventional materials, such as elastomers, polymers, composites, and intelligent materials, have been widely used in mechanical components and structural elements in a diverse range of engineering areas such as infrastructure, civil construction, mechanical and aerospace industries, among others. In this sense, the study and characterization of their mechanical behaviours are of considerable relevance. Among these materials, it is possible to highlight those whose hyperelastic and viscoelastic behaviours should be considered for their mechanical behaviour characterization.

In the Theory of Hyperelasticity, the work done by body forces and surface tractions is stored as elastic energy, for a time-independent deformation. In the Theory of Viscoelasticity, time-dependent stress-strain relations (rheological models) are considered. Despite this fundamental difference, both theories have in common problems related to the use of conventional numerical modelling with classical constitutive relations. These problems can be found in both behaviours and are related to unstable solutions depending on spatial/transient discretization, the complex coupling between strain modes and hourglass modes (spurious strain) in the finite element analysis, leading to divergences during the iterative nonlinear solution process. Moreover, both behaviours are related to structural damping applications. It is also worth mentioning that both behaviours are essentially nonlinear, at least in the Solid Mechanics domain. Mechanical properties can vary according to a specific condition, enabling their applications to be subjected to large deformations under multiaxial loading. Thus, their mechanical behaviour should be defined based on strain energy potentials formulated according to the hyperelasticity theory. The description of viscoelastic behaviour, adopting stress-strain relations, are adequate to the response of the materials and inferred based on rheological models.

The Special Issue aims to enable discussion and exchange of ideas regarding current developments and research on hyperelasticity and viscoelasticity, focusing on computational methods and numerical modelling applied to structures. Papers published in this Special Issue should describe original works in different topics in both science and engineering, such as mechanics of solids, dynamics of structures, and nonlinear analysis. This Special Issue will be of interest to researchers and academics working with polymers, foams, composites, and auxetic materials, among other materials that present viscoelastic and/or hyperelastic behaviour.

Potential topics include but are not limited to the following:

• Rheological models
• Time-marching procedures
• Creep and relaxation
• Finite Element Analysis
• Finite Element Hybrid formulation
• Boundary Element applications
• Meshless methods applications
• Structural Engineering applications