Numerical study of how creep and progressive stiffening affect the growth stress formation in trees

Sigurdur Ormarsson, O. Dahlblom, M. Johansson

Research output: Contribution to journalJournal articleResearchpeer-review


It is not fully understood how much growth stresses affect the final quality of solid timber products in terms of e.g. shape stability. It is for example difficult to predict the internal growth stress field within the tree stem. Growth stresses are progressively generated during the tree growth and they are highly influenced by climate, biologic and material related factors. To increase the knowledge of the stress formation a finite element model was created to study how the growth stresses develop during the tree growth. The model is an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The material model used is based on the theory of small strains (where strains refer to the undeformed configuration which is good approximation for strains less than 4%) where so-called biological maturation strains (growth-related strains that form in the wood fibres during their maturation) are used as a driver for the stress generation. It is formulated as an incremental material model that takes into account elastic strain, maturation strain, viscoelastic strain and progressive stiffening of the wood material. The results clearly show how the growth stresses are progressively generated during the tree growth. The inner core becomes more and more compressed whereas the outer sapwood is subjected to slightly increased tension. The parametric study shows that the growth stresses are highly influenced by the creep behaviour and evolution of parameters such as modulus of elasticity, micro fibril angle and maturation strain.
Original languageEnglish
Issue number1
Pages (from-to)105-115
Publication statusPublished - 2010


  • Creep
  • Growth stresses
  • Trees
  • Wood
  • Finite element simulations
  • Distortions

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