Abstract This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra 3D) large strain analysis nearly incompressible solids. The extends F‐bar method proposed by de Souza Neto et al . ( Int. J. Solids Struct 1996; 33 : 3277–3296) is conceptually very simple: It relies on enforcement (near‐) incompressibility over patch (rather than point‐wise conventional displacement‐based elements). Within framework method, this achieved...

In this paper, a recently proposed finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is extended to predict the nonlinear response of amorphous polymers from low high rates. The accounts for influence distinct molecular mechanisms, which become active at different deformation Therefore, equations include two relaxation phenomena describe rate sensitivity polymers. Well-established rheological elements are adopted define visco-elasticity (generalized Maxwell...

Architected materials and mechanical metamaterials are known for their unique macroscopic properties complex behaviour that often defy conventional continuum mechanics. Therefore, in this contribution, a recent multi-scale second-order computational homogenisation method (Dos Santos et al., 2023) is employed to explore these under finite strains. The approach combines second gradient theory at the macro-scale representative volume element (RVE) with classical first-order mechanics...

Abstract Computational strategies in the context of combined discrete/finite element methods for effective modelling large‐scale practical problems involving multiple fracture and discrete phenomena are reviewed present work. The issues considered include: (1) Fracture criteria propagation mechanisms within both finite elements, together with mesh adaptivity procedures discretization introduction systems; (2) Detection monitoring contact between large numbers elements; (3) Interaction laws...

The impact of non-Gaussianity on the statistical geometry isotropic random rough surfaces is analysed in this contribution. non-Gaussian height distribution modeled using Weibull probability distribution. summits distribution, expected mean curvature and density are obtained compared with analytical solutions given by Nayak's theory for Gaussian case. A significant deviation from cases observed. negatively-skewed found to decrease increase height, contradicting trend registered parameter...

Mechanical metamaterials are advanced structures with tailored microarchitectures designed to achieve unique mechanical properties for cutting-edge applications. This study explores a novel metamaterial exhibiting tension-induced undulation by combining additive manufacturing and finite element simulations. Using Fused Deposition Modelling (FDM), test specimens 3D-printed from polyethene terephthalate glycol (PETG) subjected uniaxial tensile tests analyse behaviour, including phenomena,...

This contribution is devoted to the formulation and numerical implementation of a ductile damage constitutive model enriched with thermodynamically consistent nonlocal theory integral type. In order describe deformation, takes finite strains into account. To elasticity, Hencky-like hyperelastic free energy potential coupled adopted. The thermodynamic consistency ensured by applying first second thermodynamical principles in global form dissipation inequality can be re-written local...

Abstract This paper provides an assessment of the average nodal volume methodology originally proposed by Bonet and Burton ( Commun. Numer. Meth. Engng . 1998; 14 :437–449) for analysis finitely strained nearly incompressible solids. An implicit version pressure formulation is derived re‐casting original concept in terms change ratio within framework F‐bar method de Souza Neto et al. Int. J. Solids Struct. 1996; 33 : 3277–3296). In this context, a linear triangle plane strain axisymmetric...

A multi-scale model which couples a macro-scale strain-gradient theory with classical continuum at representative volume element (RVE) level is formulated in this contribution for quasi-static problems. It enables modelling the inelastic response of heterogeneous materials finite strains incorporating their microstructural size and accounting non-uniform macroscopic deformation fields within RVE. The development based on Method Multi-Scale Virtual Power from equilibrium equations...