An orthotropic multi-surface damage-plasticity FE-formulation for wood: Part I – Constitutive model E. Benvenuti a,⇑ , N. Orlando a , C. Gebhardt b , M. Kaliske b a Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy b Technische Universität Dresden, Fakultät Bauingenieurwesen, Institut für Statik und Dynamik der Tragwerke, 01062 Dresden, Germany article info Article history: Received 15 November 2019 Accepted 20 July 2020 Available online 18 August 2020 Keywords: Finite element method Multi-surface criteria Damage Plasticity Wood abstract Restoration of ancient wooden beams and design of smart wood-based structures are gaining an increas- ing interest in building industry. In this context, the computational challenge is to develop numerical constitutive models that account for the complex and strongly non-linear behaviour of wood. Wood is a natural composite exhibiting pronounced orthotropic behaviour, and markedly different properties along the parallel and transverse-to-the-fiber directions. It displays a strongly non-linear mechanical behavior, almost elasto-plastic at compressive loadings and elasto-damaging when subjected to tensile and shearing stresses. We devise here a novel constitutive model for wood with a multi-surface failure domain resulting from a set of plastic laws for compressive failure modes and orthotropic damage laws for tensile/shear failure modes. The advantage over existing formulations is that the coexistence of ani- sotropic damage and plasticity constitutive laws allows to correctly capture brittle failure induced by strain localization as well as the possible occurrence of ductile plastic behavior. Furthermore, the present contribution shows how to numerically treat the simultaneous presence of anisotropic damage and plas- ticity in a general algorithmic multi-surface framework. It is shown that the obtained numerical results satisfactorily fit to experimental data. Ó 2020 Elsevier Ltd. All rights reserved. 1. Introduction Wood is increasingly being used in structural engineering, for instance, for the restoration of ancient deteriorated wooden beams or to realize advanced wood-based materials for the design indus- try, one striking example being the newborn transparent wood [1]. It displays high versatility, easy workability, and worth noting aes- thetic and insulating properties. Its complex cellular-like micro- structure makes it an inhomogeneous, anisotropic and porous material with moisture-, temperature- and time-dependent beha- viour [2]. Its mechanical behavior ranges from ductile to brittle regimes, depending on the loading and stress state [3,4]. This study aims to develop a novel constitutive model that consistently cap- tures the whole structural path of wood structures until failure. Common features of state-of-the-art FE-models for wood struc- tures are the assumption of material orthotropy and the recogni- tion that both structural behavior and failure modes change depending on direction and sign of the dominant stress. In the pre- sent context, three main groups of studies can be identified: plas- ticity models, damage models and models combining plastic and damage constitutive laws. We briefly review the main contribu- tions pertaining to these three classes with a special focus on wood-dedicated FE-models. Among the contributions inherent to the first group, the earliest studies are based on orthotropic single-surface plasticity models [5–7], and combine the classical flow theory of plasticity with ani- sotropic failure criteria originally proposed for composites [8–10]. Single-surface plasticity models fail to capture the dependency of the structural response on load directionality. This motivated the development of multi-surface plasticity models [11–15], where the global yield failure surface results from multiple yield surfaces, each one associated with a specific ductile or brittle failure mode. To describe late cracking, multi-surface plasticity models are even- tually coupled to cohesive-zone-models or interface elements [14,16]. The second group of models emanate from the application of Continuum Damage Mechanics (CDM) to laminates and fiber- composites [17–23]. In this context, constitutive anisotropic dam- age tensors are often deduced with the aid of two tools: the con- cept of effective stress [24,25] and the adoption of an equivalence principle between the strain or the strain-energy char- https://doi.org/10.1016/j.compstruc.2020.106350 0045-7949/Ó 2020 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: elena.benvenuti@unife.it (E. Benvenuti), nicola.orlando@unife. it (N. Orlando), clemens.gebhardt@tu-dresden.de (C. Gebhardt), michael.kaliske@- tu-dresden.de (M. Kaliske). Computers and Structures 240 (2020) 106350 Contents lists available at ScienceDirect Computers and Structures journal homepage: www.elsevier.com/locate/compstruc