Abstract

There is a general interest in civil engineering to quantify the damage produced in structures by catastrophic actions. It would be convenient, from a practical point of view, to describe the state of a structure by means of a single figure that clarifies whether the structure is capable of supporting the service charges or not; if it will survive to another extraordinary load in the future; how does the present damaged state influence in its future behavior; where the most damaged points are located; what capacity of resistance remains in each point; and, in general, all kind of information that help to make design or repair decisions. The authors have proposed a solution to this problem in the specific case of earthquakes acting upon reinforced concrete building structures. A methodology has been formulated for the definition of an index of damage that can be typified for all the structures belonging to the same class and that allows classifying them according to their seismic vulnerability. In the monograph, simple beam structures are first studied in order to better describe the concepts involved and the parameters that influence the solution to the problem. The developed methodology, which models the structures using the finite element method, is directly and easily extended to shells, plates or 3D solids. The fundamental idea of ​​this work is to apply constitutive equations formulated in 3D at a material point instead of using constitutive laws formulated in generalized forces-displacements such as, for example, bending moment-curvature, shear force-angular distortion, etc. This allows modeling the behavior of composite materials directly since for each component material its own constitutive law is considered. In this way, it is sufficient to have a single 3D constitutive model and a methodology to calculate the components of the stress and strain tensors at any point of the beam section.

Abstract

A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non‐linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial configuration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non‐linear analysis combining different material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically. 

Abstract

We study three “incompressibility flavors” of linearly-elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior. We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.

Abstract

Abstract