Abstract This paper proposes an algorithm for the synthesis/optimization of microstructures based on exact formula topological derivative macroscopic elasticity tensor and a level set domain representation. The is estimated by standard multi‐scale constitutive theory where strain stress tensors are volume averages their microscopic counterparts over representative element. simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies....

Purpose The purpose of this paper is to assess the Gurson yield criterion for porous ductile metals. Design/methodology/approach A finite element procedure used within a purely kinematical multi‐scale constitutive modelling framework determine estimates extremal overall surfaces. RVEs analysed consist an elastic‐perfectly plastic von Mises type matrix under plane strain conditions containing single centered circular hole. Macroscopic surface are obtained three different RVE assumptions:...

SUMMARY In the first part of this contribution, a brief theoretical revision mechanical and variational foundations Failure‐Oriented Multiscale Formulation devised for modeling failure in heterogeneous materials is described. The proposed model considers two well separated physical length scales, namely: (i) macro scale where nucleation evolution cohesive surface considered as medium to characterize degradation phenomenon occurring at lower scale, (ii) micro some processes that lead material...

A cohesive zone model implemented in an augmented Lagrangian functional is used for simulation of meso-scale fracture problems this paper. The method originally developed by Lorentz first presented a rigorous variational framework. equivalence between the stationary point one-field problem and saddle mixed formulation proved solving double inequality functional. An adaptation to simulate phenomena via mesh modification also as algorithm insert zero-thickness interface elements based on...

This work addresses the problem of optimal topological design three-dimensional structures composed plate arrays based on use derivatives. These structural consist planar elements linked at their edges. Their modeling is performed by coupling a membrane model and bending-plate model. The geometric material representation accomplished using level-set curves. To minimize cost function, derivative value used to guide evolution curve. A theoretical framework case studies academic industrial...

La impresión 3D por deposición fundida (FDM) es una técnica de manufactura aditiva caracteriza poder fabricar piezas con geometrías complejas, cuya principal desventaja el elevado tiempo impresión. Existe relación inversa entre y la rigidez final pieza, lo que solución para cada caso aplicación decisión técnica-económica. En base a esto, este trabajo propone estrategia determinar óptima distribución distintos patrones logren mayor pieza posible empleando menor Se considera contribución...

Purpose – The purpose of this paper is to compare between two methods volume control in the context topological derivative-based structural optimization Kirchhoff plates. Design/methodology/approach compliance topology plates subjected constraint considered. In order impose constraint, are presented. first one done by means a linear penalization method. case, penalty parameter coefficient term used amount material be removed. second approach based on Augmented Lagrangian method which has...

Piezoelectric actuators are in common use for control of distributed parameter systems. We consider the topology optimization a multiphysic model piezoelectricity into two spatial dimensions. The topological derivative tracking-type shape functional is derived its closed form purpose piezoelectric actuators. optimum design procedure applied to micromechanism which transforms electrical energy supplemented via piezoceramic part elastic an actuator. domain decomposition technique and...

This paper proposes an exact analytical formula for the topological sensitivity of macroscopic response elastic microstructures to insertion circular inclusions. The is assumed be predicted by a well-established multi-scale constitutive theory where strain and stress tensors are defined as volume averages their microscopic counterpart fields over representative element (RVE) material. proposed formula—a symmetric fourth-order tensor field RVE domain—is derivative which measures how...

Purpose The purpose of this study is to solve the inverse homogenization problem, or so-called material design using topological derivative concept. Design/methodology/approach optimal topology obtained through a relaxed formulation problem by replacing characteristic function with continuous variable, density variable. constitutive tensor then parametrized variable an analytical interpolation scheme that based on intermediate values may appear in topologies are removed penalizing perimeter...