Complementary energy based FE modelling of coupled elasto-plastic and damage behavior for continuum microstructure computations

A concrete homogenisation technique at meso-scale level accounting for damaging behaviour of cement paste and aggregates

“…In the linear range this approximation must fulfil the upper and lower bounds given by Voigt and Reuss [13][14][15]. It has also been observed that in the case of concrete, especially if the softening behaviour is investigated, a method accounting for strong coupling between the meso and macro scales should be used, like those proposed in [16][17][18]. The present work, however, is limited to the analysis of the mesolevel model.…”

A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials—Application to Uniaxial Cyclic Response of Concrete

“…In the caseγ d > 0 orγ p > 0, there is damage or plasticity evolution and, according to (20), φ (σ σ σ ) as to remain null during the process so that the stresses remain admissible. We thus have the consistency conditionφ = 0 that can be rewritten as:…”

“…If trial state is not admissible, then γ n+1 > 0 and, according to equation (20), the relation φ n+1 = 0 has to be satisfied. Solving φ n+1 = 0 yields γ n+1 ν ν ν n+1 .…”

“…It results in the refinement of porosity in the ITZ cement matrix and modification of cement hydration products, represented by the reduction of both quantity and size of CH plates and the increase of more compact and strong C-S-H. Doped concrete, 20 Materials Research…”

On semi‐analytical probabilistic finite element method for homogenization of the periodic fiber‐reinforced composites

“…It is clear that instead of the polynomial fitting it is possible to use the exponential fitting or look for some harmonic representations, but general implementation with FEM programs decisively prefer polynomials similar to the shape function procedures. It also does not matter whether the finite elements will be implemented from a minimization of potential [36] or the complementary energy [41] principles. The nature of this technique allows almost automatically for sensitivity analysis since partial derivation of the sensitivity coefficients from the response function is very fast in any computer algebra system (following Direct Differentiation Method philosophy).…”