By Adnan Ibrahimbegovic

This quantity comprises the easiest papers offered on the 2d ECCOMAS foreign convention on Multiscale Computations for Solids and Fluids, held June 10-12, 2015.

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They are proportional to the difference of fourth power of temperatures. Multiscale Analysis as a Central Component of Urban Physics Modeling 21 Convective flow proportional to the temperature difference between the surface of the solid and a reference point of the fluid in which it merges [30]. Any other heat flow that may be estimated directly or expressed in terms of temperatures, for example, evapotranspiration [53]. In brief, the solid subjected to these heat flows and where the temperature is known at least at one point will experience modifications as a result of internal heat conduction and the ability of materials to store heat.

1) is possible to solve only by introducing an additional constraint equation g (u (t) − u (t − t) , λ (t) − λ (t − t)) = 0 (2) where is a (small) incremental change. g. [1]. The solu- 32 B. Brank et al. tion of (1) and (2) is searched for at discrete pseudo-time points 0 = t0 , t1 , . . , tn , tn+1 , . . , t f inal . Assume that configuration of solid or structure at tn is known; it is defined by the pair {u (tn ) , λ (tn )} = {un , λn }. At searching for the next configuration at tn+1 = tn + tn , we decompose un+1 and λn+1 as un+1 = un + un , λn+1 = λn + λn (3) where un and λn are the increments of the displacement vector and the load vector, respectively.

Brank et al. discontinuity. e. with a single discontinuity) and to frames with softening plastic hinges. Let the bulk of the 2-d solid or frame be modelled as elastic and let the cohesive stresses at the discontinuity be modelled by rigid-plasticity with linear softening. e. the stored energy) of the solid can be written as = (U − S) + Ss (33) where the stored energy due to elastic deformations of the bulk 1 T E DEd V = 2 U= V 1 T −1 S D Sd V 2 (34) V is diminished for S due to localized plastic deformations at the failure curve.