TY - JOUR

T1 - Nonconvex Model of Material Growth

T2 - Mathematical Theory

AU - Ganghoffer, J. F.

AU - Plotnikov, P. I.

AU - Sokolowski, J.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

AB - The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

KW - VOLUMETRIC GROWTH

KW - STRESS

KW - TISSUE

UR - http://www.scopus.com/inward/record.url?scp=85047907761&partnerID=8YFLogxK

U2 - 10.1007/s00205-018-1259-8

DO - 10.1007/s00205-018-1259-8

M3 - Article

AN - SCOPUS:85047907761

VL - 230

SP - 839

EP - 910

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 3

ER -